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个神经元的激活值",[1111,1714,1715,1803],{},[1126,1716,1717],{},[1129,1718,1720,1741],{"className":1719},[1132],[1129,1721,1723],{"className":1722},[1136],[1138,1724,1725],{"xmlns":1140},[1142,1726,1727,1738],{},[1145,1728,1729],{},[1148,1730,1731,1734,1736],{},[1151,1732,1733],{},"z",[1151,1735,1158],{},[1151,1737,1164],{},[1166,1739,1740],{"encoding":1168},"z^l_j",[1129,1742,1744],{"className":1743,"ariaHidden":1174},[1173],[1129,1745,1747,1750],{"className":1746},[1178],[1129,1748],{"className":1749,"style":1453},[1182],[1129,1751,1753,1757],{"className":1752},[1187],[1129,1754,1733],{"className":1755,"style":1756},[1187,1191],"margin-right:0.044em;",[1129,1758,1760],{"className":1759},[1196],[1129,1761,1763,1795],{"className":1762},[1200,1201],[1129,1764,1766,1792],{"className":1765},[1205],[1129,1767,1769,1781],{"className":1768,"style":1210},[1209],[1129,1770,1772,1775],{"style":1771},"top:-2.4413em;margin-left:-0.044em;margin-right:0.05em;",[1129,1773],{"className":1774,"style":1218},[1217],[1129,1776,1778],{"className":1777},[1222,1223,1224,1225],[1129,1779,1158],{"className":1780,"style":1232},[1187,1191,1225],[1129,1782,1783,1786],{"style":1239},[1129,1784],{"className":1785,"style":1218},[1217],[1129,1787,1789],{"className":1788},[1222,1223,1224,1225],[1129,1790,1164],{"className":1791,"style":1249},[1187,1191,1225],[1129,1793,1254],{"className":1794},[1253],[1129,1796,1798],{"className":1797},[1205],[1129,1799,1801],{"className":1800,"style":1504},[1209],[1129,1802],{},[1126,1804,1266,1805,1296,1833,1861,1862],{},[1129,1806,1808,1821],{"className":1807},[1132],[1129,1809,1811],{"className":1810},[1136],[1138,1812,1813],{"xmlns":1140},[1142,1814,1815,1819],{},[1145,1816,1817],{},[1151,1818,1164],{},[1166,1820,1164],{"encoding":1168},[1129,1822,1824],{"className":1823,"ariaHidden":1174},[1173],[1129,1825,1827,1830],{"className":1826},[1178],[1129,1828],{"className":1829,"style":1292},[1182],[1129,1831,1164],{"className":1832,"style":1249},[1187,1191],[1129,1834,1836,1849],{"className":1835},[1132],[1129,1837,1839],{"className":1838},[1136],[1138,1840,1841],{"xmlns":1140},[1142,1842,1843,1847],{},[1145,1844,1845],{},[1151,1846,1158],{},[1166,1848,1158],{"encoding":1168},[1129,1850,1852],{"className":1851,"ariaHidden":1174},[1173],[1129,1853,1855,1858],{"className":1854},[1178],[1129,1856],{"className":1857,"style":1322},[1182],[1129,1859,1158],{"className":1860,"style":1232},[1187,1191]," 个神经元的加权输入：",[1129,1863,1865,1933],{"className":1864},[1132],[1129,1866,1868],{"className":1867},[1136],[1138,1869,1870],{"xmlns":1140},[1142,1871,1872,1930],{},[1145,1873,1874,1882,1885,1893,1905,1919,1922],{},[1148,1875,1876,1878,1880],{},[1151,1877,1733],{},[1151,1879,1158],{},[1151,1881,1164],{},[1342,1883,1884],{},"=",[1886,1887,1888,1891],"msub",{},[1342,1889,1890],{},"∑",[1151,1892,1161],{},[1148,1894,1895,1897,1903],{},[1151,1896,1153],{},[1145,1898,1899,1901],{},[1151,1900,1158],{},[1151,1902,1161],{},[1151,1904,1164],{},[1148,1906,1907,1909,1911],{},[1151,1908,1586],{},[1151,1910,1161],{},[1145,1912,1913,1915,1917],{},[1151,1914,1164],{},[1342,1916,1344],{},[1346,1918,1348],{},[1342,1920,1921],{},"+",[1148,1923,1924,1926,1928],{},[1151,1925,1436],{},[1151,1927,1158],{},[1151,1929,1164],{},[1166,1931,1932],{"encoding":1168},"z^l_j = \\sum_k w^l_{jk} a^{l-1}_k + 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个神经元的误差",[1096,2399,2401],{"id":2400},"_12-反向传播四个基本方程","1.2 反向传播四个基本方程",[1101,2403,2404],{},[2405,2406,2407],"strong",{},"BP 四个核心方程（必记）",[2409,2410,2411,2668,3000,3267],"ul",{},[2412,2413,2414,2417,2418],"li",{},[2405,2415,2416],{},"BP1（输出层误差）","：",[1129,2419,2421,2479],{"className":2420},[1132],[1129,2422,2424],{"className":2423},[1136],[1138,2425,2426],{"xmlns":1140},[1142,2427,2428,2476],{},[1145,2429,2430,2438,2440,2448,2451,2454,2463,2467,2473],{},[2431,2432,2433,2435],"msup",{},[1151,2434,2269],{},[1151,2436,2437],{},"L",[1342,2439,1884],{},[1886,2441,2442,2446],{},[1151,2443,2445],{"mathvariant":2444},"normal","∇",[1151,2447,1586],{},[1151,2449,2450],{},"C",[1342,2452,2453],{},"⊙",[2431,2455,2456,2459],{},[1151,2457,2458],{},"σ",[1342,2460,2462],{"mathvariant":2444,"lspace":2461,"rspace":2461},"0em","′",[1342,2464,2466],{"stretchy":2465},"false","(",[2431,2468,2469,2471],{},[1151,2470,1733],{},[1151,2472,2437],{},[1342,2474,2475],{"stretchy":2465},")",[1166,2477,2478],{"encoding":1168},"\\delta^L = \\nabla_a C \\odot 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= ((w^{l+1})^T \\delta^{l+1}) \\odot 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C}{\\partial b^l_j} = 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反向传播算法步骤（随机梯度下降）",[3608,3609,3610,3700,4148,4380,4846],"ol",{},[2412,3611,3612,3615,3616],{},[2405,3613,3614],{},"输入","：设置输入层激活值 ",[1129,3617,3619,3642],{"className":3618},[1132],[1129,3620,3622],{"className":3621},[1136],[1138,3623,3624],{"xmlns":1140},[1142,3625,3626,3639],{},[1145,3627,3628,3634,3636],{},[2431,3629,3630,3632],{},[1151,3631,1586],{},[1346,3633,1348],{},[1342,3635,1884],{},[1151,3637,3638],{},"x",[1166,3640,3641],{"encoding":1168},"a^1 = x",[1129,3643,3645,3690],{"className":3644,"ariaHidden":1174},[1173],[1129,3646,3648,3652,3681,3684,3687],{"className":3647},[1178],[1129,3649],{"className":3650,"style":3651},[1182],"height:0.8141em;",[1129,3653,3655,3658],{"className":3654},[1187],[1129,3656,1586],{"className":3657},[1187,1191],[1129,3659,3661],{"className":3660},[1196],[1129,3662,3664],{"className":3663},[1200],[1129,3665,3667],{"className":3666},[1205],[1129,3668,3670],{"className":3669,"style":3651},[1209],[1129,3671,3672,3675],{"style":1239},[1129,3673],{"className":3674,"style":1218},[1217],[1129,3676,3678],{"className":3677},[1222,1223,1224,1225],[1129,3679,1348],{"className":3680},[1187,1225],[1129,3682],{"className":3683,"style":1996},[1368],[1129,3685,1884],{"className":3686},[2000],[1129,3688],{"className":3689,"style":1996},[1368],[1129,3691,3693,3697],{"className":3692},[1178],[1129,3694],{"className":3695,"style":3696},[1182],"height:0.4306em;",[1129,3698,3638],{"className":3699},[1187,1191],[2412,3701,3702,3705,3706,3806,3807,4021,4022],{},[2405,3703,3704],{},"前馈","：对每一层 ",[1129,3707,3709,3743],{"className":3708},[1132],[1129,3710,3712],{"className":3711},[1136],[1138,3713,3714],{"xmlns":1140},[1142,3715,3716,3740],{},[1145,3717,3718,3720,3722,3725,3728,3731,3733,3736,3738],{},[1151,3719,1164],{},[1342,3721,1884],{},[1346,3723,3724],{},"2",[1342,3726,3727],{"separator":1174},",",[1346,3729,3730],{},"3",[1342,3732,3727],{"separator":1174},[1342,3734,3735],{},"…",[1342,3737,3727],{"separator":1174},[1151,3739,2437],{},[1166,3741,3742],{"encoding":1168},"l = 2, 3, \\ldots, L",[1129,3744,3746,3764],{"className":3745,"ariaHidden":1174},[1173],[1129,3747,3749,3752,3755,3758,3761],{"className":3748},[1178],[1129,3750],{"className":3751,"style":1292},[1182],[1129,3753,1164],{"className":3754,"style":1249},[1187,1191],[1129,3756],{"className":3757,"style":1996},[1368],[1129,3759,1884],{"className":3760},[2000],[1129,3762],{"className":3763,"style":1996},[1368],[1129,3765,3767,3771,3774,3778,3781,3784,3787,3790,3794,3797,3800,3803],{"className":3766},[1178],[1129,3768],{"className":3769,"style":3770},[1182],"height:0.8778em;vertical-align:-0.1944em;",[1129,3772,3724],{"className":3773},[1187],[1129,3775,3727],{"className":3776},[3777],"mpunct",[1129,3779],{"className":3780,"style":2061},[1368],[1129,3782,3730],{"className":3783},[1187],[1129,3785,3727],{"className":3786},[3777],[1129,3788],{"className":3789,"style":2061},[1368],[1129,3791,3735],{"className":3792},[3793],"minner",[1129,3795],{"className":3796,"style":2061},[1368],[1129,3798,3727],{"className":3799},[3777],[1129,3801],{"className":3802,"style":2061},[1368],[1129,3804,2437],{"className":3805},[1187,1191],"，计算 ",[1129,3808,3810,3856],{"className":3809},[1132],[1129,3811,3813],{"className":3812},[1136],[1138,3814,3815],{"xmlns":1140},[1142,3816,3817,3853],{},[1145,3818,3819,3825,3827,3833,3845,3847],{},[2431,3820,3821,3823],{},[1151,3822,1733],{},[1151,3824,1164],{},[1342,3826,1884],{},[2431,3828,3829,3831],{},[1151,3830,1153],{},[1151,3832,1164],{},[2431,3834,3835,3837],{},[1151,3836,1586],{},[1145,3838,3839,3841,3843],{},[1151,3840,1164],{},[1342,3842,1344],{},[1346,3844,1348],{},[1342,3846,1921],{},[2431,3848,3849,3851],{},[1151,3850,1436],{},[1151,3852,1164],{},[1166,3854,3855],{"encoding":1168},"z^l = w^l a^{l-1} + b^l",[1129,3857,3859,3903,3986],{"className":3858,"ariaHidden":1174},[1173],[1129,3860,3862,3865,3894,3897,3900],{"className":3861},[1178],[1129,3863],{"className":3864,"style":1210},[1182],[1129,3866,3868,3871],{"className":3867},[1187],[1129,3869,1733],{"className":3870,"style":1756},[1187,1191],[1129,3872,3874],{"className":3873},[1196],[1129,3875,3877],{"className":3876},[1200],[1129,3878,3880],{"className":3879},[1205],[1129,3881,3883],{"className":3882,"style":1210},[1209],[1129,3884,3885,3888],{"style":1239},[1129,3886],{"className":3887,"style":1218},[1217],[1129,3889,3891],{"className":3890},[1222,1223,1224,1225],[1129,3892,1164],{"className":3893,"style":1249},[1187,1191,1225],[1129,3895],{"className":3896,"style":1996},[1368],[1129,3898,1884],{"className":3899},[2000],[1129,3901],{"className":3902,"style":1996},[1368],[1129,3904,3906,3910,3939,3977,3980,3983],{"className":3905},[1178],[1129,3907],{"className":3908,"style":3909},[1182],"height:0.9324em;vertical-align:-0.0833em;",[1129,3911,3913,3916],{"className":3912},[1187],[1129,3914,1153],{"className":3915,"style":1192},[1187,1191],[1129,3917,3919],{"className":3918},[1196],[1129,3920,3922],{"className":3921},[1200],[1129,3923,3925],{"className":3924},[1205],[1129,3926,3928],{"className":3927,"style":1210},[1209],[1129,3929,3930,3933],{"style":1239},[1129,3931],{"className":3932,"style":1218},[1217],[1129,3934,3936],{"className":3935},[1222,1223,1224,1225],[1129,3937,1164],{"className":3938,"style":1249},[1187,1191,1225],[1129,3940,3942,3945],{"className":3941},[1187],[1129,3943,1586],{"className":3944},[1187,1191],[1129,3946,3948],{"className":3947},[1196],[1129,3949,3951],{"className":3950},[1200],[1129,3952,3954],{"className":3953},[1205],[1129,3955,3957],{"className":3956,"style":1210},[1209],[1129,3958,3959,3962],{"style":1239},[1129,3960],{"className":3961,"style":1218},[1217],[1129,3963,3965],{"className":3964},[1222,1223,1224,1225],[1129,3966,3968,3971,3974],{"className":3967},[1187,1225],[1129,3969,1164],{"className":3970,"style":1249},[1187,1191,1225],[1129,3972,1344],{"className":3973},[1373,1225],[1129,3975,1348],{"className":3976},[1187,1225],[1129,3978],{"className":3979,"style":1369},[1368],[1129,3981,1921],{"className":3982},[1373],[1129,3984],{"className":3985,"style":1369},[1368],[1129,3987,3989,3992],{"className":3988},[1178],[1129,3990],{"className":3991,"style":1210},[1182],[1129,3993,3995,3998],{"className":3994},[1187],[1129,3996,1436],{"className":3997},[1187,1191],[1129,3999,4001],{"className":4000},[1196],[1129,4002,4004],{"className":4003},[1200],[1129,4005,4007],{"className":4006},[1205],[1129,4008,4010],{"className":4009,"style":1210},[1209],[1129,4011,4012,4015],{"style":1239},[1129,4013],{"className":4014,"style":1218},[1217],[1129,4016,4018],{"className":4017},[1222,1223,1224,1225],[1129,4019,1164],{"className":4020,"style":1249},[1187,1191,1225]," 和 ",[1129,4023,4025,4057],{"className":4024},[1132],[1129,4026,4028],{"className":4027},[1136],[1138,4029,4030],{"xmlns":1140},[1142,4031,4032,4054],{},[1145,4033,4034,4040,4042,4044,4046,4052],{},[2431,4035,4036,4038],{},[1151,4037,1586],{},[1151,4039,1164],{},[1342,4041,1884],{},[1151,4043,2458],{},[1342,4045,2466],{"stretchy":2465},[2431,4047,4048,4050],{},[1151,4049,1733],{},[1151,4051,1164],{},[1342,4053,2475],{"stretchy":2465},[1166,4055,4056],{"encoding":1168},"a^l = \\sigma(z^l)",[1129,4058,4060,4104],{"className":4059,"ariaHidden":1174},[1173],[1129,4061,4063,4066,4095,4098,4101],{"className":4062},[1178],[1129,4064],{"className":4065,"style":1210},[1182],[1129,4067,4069,4072],{"className":4068},[1187],[1129,4070,1586],{"className":4071},[1187,1191],[1129,4073,4075],{"className":4074},[1196],[1129,4076,4078],{"className":4077},[1200],[1129,4079,4081],{"className":4080},[1205],[1129,4082,4084],{"className":4083,"style":1210},[1209],[1129,4085,4086,4089],{"style":1239},[1129,4087],{"className":4088,"style":1218},[1217],[1129,4090,4092],{"className":4091},[1222,1223,1224,1225],[1129,4093,1164],{"className":4094,"style":1249},[1187,1191,1225],[1129,4096],{"className":4097,"style":1996},[1368],[1129,4099,1884],{"className":4100},[2000],[1129,4102],{"className":4103,"style":1996},[1368],[1129,4105,4107,4110,4113,4116,4145],{"className":4106},[1178],[1129,4108],{"className":4109,"style":2804},[1182],[1129,4111,2458],{"className":4112,"style":2603},[1187,1191],[1129,4114,2466],{"className":4115},[2634],[1129,4117,4119,4122],{"className":4118},[1187],[1129,4120,1733],{"className":4121,"style":1756},[1187,1191],[1129,4123,4125],{"className":4124},[1196],[1129,4126,4128],{"className":4127},[1200],[1129,4129,4131],{"className":4130},[1205],[1129,4132,4134],{"className":4133,"style":1210},[1209],[1129,4135,4136,4139],{"style":1239},[1129,4137],{"className":4138,"style":1218},[1217],[1129,4140,4142],{"className":4141},[1222,1223,1224,1225],[1129,4143,1164],{"className":4144,"style":1249},[1187,1191,1225],[1129,4146,2475],{"className":4147},[2667],[2412,4149,4150,4153,4154],{},[2405,4151,4152],{},"输出层误差","：计算 ",[1129,4155,4157,4202],{"className":4156},[1132],[1129,4158,4160],{"className":4159},[1136],[1138,4161,4162],{"xmlns":1140},[1142,4163,4164,4200],{},[1145,4165,4166,4172,4174,4180,4182,4184,4190,4192,4198],{},[2431,4167,4168,4170],{},[1151,4169,2269],{},[1151,4171,2437],{},[1342,4173,1884],{},[1886,4175,4176,4178],{},[1151,4177,2445],{"mathvariant":2444},[1151,4179,1586],{},[1151,4181,2450],{},[1342,4183,2453],{},[2431,4185,4186,4188],{},[1151,4187,2458],{},[1342,4189,2462],{"mathvariant":2444,"lspace":2461,"rspace":2461},[1342,4191,2466],{"stretchy":2465},[2431,4193,4194,4196],{},[1151,4195,1733],{},[1151,4197,2437],{},[1342,4199,2475],{"stretchy":2465},[1166,4201,2478],{"encoding":1168},[1129,4203,4205,4249,4307],{"className":4204,"ariaHidden":1174},[1173],[1129,4206,4208,4211,4240,4243,4246],{"className":4207},[1178],[1129,4209],{"className":4210,"style":2488},[1182],[1129,4212,4214,4217],{"className":4213},[1187],[1129,4215,2269],{"className":4216,"style":2292},[1187,1191],[1129,4218,4220],{"className":4219},[1196],[1129,4221,4223],{"className":4222},[1200],[1129,4224,4226],{"className":4225},[1205],[1129,4227,4229],{"className":4228,"style":2488},[1209],[1129,4230,4231,4234],{"style":1239},[1129,4232],{"className":4233,"style":1218},[1217],[1129,4235,4237],{"className":4236},[1222,1223,1224,1225],[1129,4238,2437],{"className":4239},[1187,1191,1225],[1129,4241],{"className":4242,"style":1996},[1368],[1129,4244,1884],{"className":4245},[2000],[1129,4247],{"className":4248,"style":1996},[1368],[1129,4250,4252,4255,4295,4298,4301,4304],{"className":4251},[1178],[1129,4253],{"className":4254,"style":2533},[1182],[1129,4256,4258,4261],{"className":4257},[1187],[1129,4259,2445],{"className":4260},[1187],[1129,4262,4264],{"className":4263},[1196],[1129,4265,4267,4287],{"className":4266},[1200,1201],[1129,4268,4270,4284],{"className":4269},[1205],[1129,4271,4273],{"className":4272,"style":2552},[1209],[1129,4274,4275,4278],{"style":2555},[1129,4276],{"className":4277,"style":1218},[1217],[1129,4279,4281],{"className":4280},[1222,1223,1224,1225],[1129,4282,1586],{"className":4283},[1187,1191,1225],[1129,4285,1254],{"className":4286},[1253],[1129,4288,4290],{"className":4289},[1205],[1129,4291,4293],{"className":4292,"style":2574},[1209],[1129,4294],{},[1129,4296,2450],{"className":4297,"style":2580},[1187,1191],[1129,4299],{"className":4300,"style":1369},[1368],[1129,4302,2453],{"className":4303},[1373],[1129,4305],{"className":4306,"style":1369},[1368],[1129,4308,4310,4313,4345,4348,4377],{"className":4309},[1178],[1129,4311],{"className":4312,"style":2596},[1182],[1129,4314,4316,4319],{"className":4315},[1187],[1129,4317,2458],{"className":4318,"style":2603},[1187,1191],[1129,4320,4322],{"className":4321},[1196],[1129,4323,4325],{"className":4324},[1200],[1129,4326,4328],{"className":4327},[1205],[1129,4329,4331],{"className":4330,"style":2616},[1209],[1129,4332,4333,4336],{"style":1239},[1129,4334],{"className":4335,"style":1218},[1217],[1129,4337,4339],{"className":4338},[1222,1223,1224,1225],[1129,4340,4342],{"className":4341},[1187,1225],[1129,4343,2462],{"className":4344},[1187,1225],[1129,4346,2466],{"className":4347},[2634],[1129,4349,4351,4354],{"className":4350},[1187],[1129,4352,1733],{"className":4353,"style":1756},[1187,1191],[1129,4355,4357],{"className":4356},[1196],[1129,4358,4360],{"className":4359},[1200],[1129,4361,4363],{"className":4362},[1205],[1129,4364,4366],{"className":4365,"style":2488},[1209],[1129,4367,4368,4371],{"style":1239},[1129,4369],{"className":4370,"style":1218},[1217],[1129,4372,4374],{"className":4373},[1222,1223,1224,1225],[1129,4375,2437],{"className":4376},[1187,1191,1225],[1129,4378,2475],{"className":4379},[2667],[2412,4381,4382,3705,4385,3806,4524],{},[2405,4383,4384],{},"反向传播误差",[1129,4386,4388,4426],{"className":4387},[1132],[1129,4389,4391],{"className":4390},[1136],[1138,4392,4393],{"xmlns":1140},[1142,4394,4395,4423],{},[1145,4396,4397,4399,4401,4403,4405,4407,4409,4411,4413,4415,4417,4419,4421],{},[1151,4398,1164],{},[1342,4400,1884],{},[1151,4402,2437],{},[1342,4404,1344],{},[1346,4406,1348],{},[1342,4408,3727],{"separator":1174},[1151,4410,2437],{},[1342,4412,1344],{},[1346,4414,3724],{},[1342,4416,3727],{"separator":1174},[1342,4418,3735],{},[1342,4420,3727],{"separator":1174},[1346,4422,3724],{},[1166,4424,4425],{"encoding":1168},"l = L-1, L-2, \\ldots, 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从权重 ",[1129,5784,5786,5809],{"className":5785},[1132],[1129,5787,5789],{"className":5788},[1136],[1138,5790,5791],{"xmlns":1140},[1142,5792,5793,5807],{},[1145,5794,5795],{},[1148,5796,5797,5799,5805],{},[1151,5798,1153],{},[1145,5800,5801,5803],{},[1151,5802,1158],{},[1151,5804,1161],{},[1151,5806,1164],{},[1166,5808,1169],{"encoding":1168},[1129,5810,5812],{"className":5811,"ariaHidden":1174},[1173],[1129,5813,5815,5818],{"className":5814},[1178],[1129,5816],{"className":5817,"style":1183},[1182],[1129,5819,5821,5824],{"className":5820},[1187],[1129,5822,1153],{"className":5823,"style":1192},[1187,1191],[1129,5825,5827],{"className":5826},[1196],[1129,5828,5830,5867],{"className":5829},[1200,1201],[1129,5831,5833,5864],{"className":5832},[1205],[1129,5834,5836,5853],{"className":5835,"style":1210},[1209],[1129,5837,5838,5841],{"style":1213},[1129,5839],{"className":5840,"style":1218},[1217],[1129,5842,5844],{"className":5843},[1222,1223,1224,1225],[1129,5845,5847,5850],{"className":5846},[1187,1225],[1129,5848,1158],{"className":5849,"style":1232},[1187,1191,1225],[1129,5851,1161],{"className":5852,"style":1236},[1187,1191,1225],[1129,5854,5855,5858],{"style":1239},[1129,5856],{"className":5857,"style":1218},[1217],[1129,5859,5861],{"className":5860},[1222,1223,1224,1225],[1129,5862,1164],{"className":5863,"style":1249},[1187,1191,1225],[1129,5865,1254],{"className":5866},[1253],[1129,5868,5870],{"className":5869},[1205],[1129,5871,5873],{"className":5872,"style":1261},[1209],[1129,5874],{}," 到代价 ",[1129,5877,5879,5892],{"className":5878},[1132],[1129,5880,5882],{"className":5881},[1136],[1138,5883,5884],{"xmlns":1140},[1142,5885,5886,5890],{},[1145,5887,5888],{},[1151,5889,2450],{},[1166,5891,2450],{"encoding":1168},[1129,5893,5895],{"className":5894,"ariaHidden":1174},[1173],[1129,5896,5898,5902],{"className":5897},[1178],[1129,5899],{"className":5900,"style":5901},[1182],"height:0.6833em;",[1129,5903,2450],{"className":5904,"style":2580},[1187,1191]," 的路径，其贡献为路径上所有偏导数的乘积。反向传播算法本质上是高效地计算这些路径求和。",[5907,5908],"hr",{},[1091,5910,5912],{"id":5911},"二交叉熵代价函数","二、交叉熵代价函数",[1096,5914,5916],{"id":5915},"_21-mse-的学习缓慢问题","2.1 MSE 的学习缓慢问题",[1101,5918,5919],{},"使用均方误差（MSE）作为代价函数时，当神经元输出严重错误且饱和时，学习速度非常缓慢。",[1101,5921,5922],{},[2405,5923,5924],{},"问题示例",[1101,5926,5927],{},"单个神经元，期望输出 0，使用 MSE 代价函数：",[2409,5929,5930,6177],{},[2412,5931,5932,5933,6022,6023,6176],{},"当 ",[1129,5934,5936,5964],{"className":5935},[1132],[1129,5937,5939],{"className":5938},[1136],[1138,5940,5941],{"xmlns":1140},[1142,5942,5943,5961],{},[1145,5944,5945,5947,5949,5952,5954,5956,5958],{},[1151,5946,1153],{},[1342,5948,1884],{},[1346,5950,5951],{},"0.6",[1342,5953,3727],{"separator":1174},[1151,5955,1436],{},[1342,5957,1884],{},[1346,5959,5960],{},"0.9",[1166,5962,5963],{"encoding":1168},"w=0.6, b=0.9",[1129,5965,5967,5985,6013],{"className":5966,"ariaHidden":1174},[1173],[1129,5968,5970,5973,5976,5979,5982],{"className":5969},[1178],[1129,5971],{"className":5972,"style":3696},[1182],[1129,5974,1153],{"className":5975,"style":1192},[1187,1191],[1129,5977],{"className":5978,"style":1996},[1368],[1129,5980,1884],{"className":5981},[2000],[1129,5983],{"className":5984,"style":1996},[1368],[1129,5986,5988,5992,5995,5998,6001,6004,6007,6010],{"className":5987},[1178],[1129,5989],{"className":5990,"style":5991},[1182],"height:0.8889em;vertical-align:-0.1944em;",[1129,5993,5951],{"className":5994},[1187],[1129,5996,3727],{"className":5997},[3777],[1129,5999],{"className":6000,"style":2061},[1368],[1129,6002,1436],{"className":6003},[1187,1191],[1129,6005],{"className":6006,"style":1996},[1368],[1129,6008,1884],{"className":6009},[2000],[1129,6011],{"className":6012,"style":1996},[1368],[1129,6014,6016,6019],{"className":6015},[1178],[1129,6017],{"className":6018,"style":1383},[1182],[1129,6020,5960],{"className":6021},[1187]," 时：初始输出 ",[1129,6024,6026,6072],{"className":6025},[1132],[1129,6027,6029],{"className":6028},[1136],[1138,6030,6031],{"xmlns":1140},[1142,6032,6033,6069],{},[1145,6034,6035,6037,6039,6041,6044,6046,6048,6050,6052,6054,6056,6058,6061,6063,6066],{},[1151,6036,2458],{},[1342,6038,2466],{"stretchy":2465},[1346,6040,5951],{},[1342,6042,6043],{},"×",[1346,6045,1348],{},[1342,6047,1921],{},[1346,6049,5960],{},[1342,6051,2475],{"stretchy":2465},[1342,6053,1884],{},[1151,6055,2458],{},[1342,6057,2466],{"stretchy":2465},[1346,6059,6060],{},"1.5",[1342,6062,2475],{"stretchy":2465},[1342,6064,6065],{},"≈",[1346,6067,6068],{},"0.82",[1166,6070,6071],{"encoding":1168},"\\sigma(0.6 \\times 1 + 0.9) = \\sigma(1.5) \\approx 0.82",[1129,6073,6075,6100,6119,6140,6167],{"className":6074,"ariaHidden":1174},[1173],[1129,6076,6078,6082,6085,6088,6091,6094,6097],{"className":6077},[1178],[1129,6079],{"className":6080,"style":6081},[1182],"height:1em;vertical-align:-0.25em;",[1129,6083,2458],{"className":6084,"style":2603},[1187,1191],[1129,6086,2466],{"className":6087},[2634],[1129,6089,5951],{"className":6090},[1187],[1129,6092],{"className":6093,"style":1369},[1368],[1129,6095,6043],{"className":6096},[1373],[1129,6098],{"className":6099,"style":1369},[1368],[1129,6101,6103,6107,6110,6113,6116],{"className":6102},[1178],[1129,6104],{"className":6105,"style":6106},[1182],"height:0.7278em;vertical-align:-0.0833em;",[1129,6108,1348],{"className":6109},[1187],[1129,6111],{"className":6112,"style":1369},[1368],[1129,6114,1921],{"className":6115},[1373],[1129,6117],{"className":6118,"style":1369},[1368],[1129,6120,6122,6125,6128,6131,6134,6137],{"className":6121},[1178],[1129,6123],{"className":6124,"style":6081},[1182],[1129,6126,5960],{"className":6127},[1187],[1129,6129,2475],{"className":6130},[2667],[1129,6132],{"className":6133,"style":1996},[1368],[1129,6135,1884],{"className":6136},[2000],[1129,6138],{"className":6139,"style":1996},[1368],[1129,6141,6143,6146,6149,6152,6155,6158,6161,6164],{"className":6142},[1178],[1129,6144],{"className":6145,"style":6081},[1182],[1129,6147,2458],{"className":6148,"style":2603},[1187,1191],[1129,6150,2466],{"className":6151},[2634],[1129,6153,6060],{"className":6154},[1187],[1129,6156,2475],{"className":6157},[2667],[1129,6159],{"className":6160,"style":1996},[1368],[1129,6162,6065],{"className":6163},[2000],[1129,6165],{"className":6166,"style":1996},[1368],[1129,6168,6170,6173],{"className":6169},[1178],[1129,6171],{"className":6172,"style":1383},[1182],[1129,6174,6068],{"className":6175},[1187],"，学习缓慢",[2412,6178,5932,6179,6022,6266,6415],{},[1129,6180,6182,6209],{"className":6181},[1132],[1129,6183,6185],{"className":6184},[1136],[1138,6186,6187],{"xmlns":1140},[1142,6188,6189,6206],{},[1145,6190,6191,6193,6195,6198,6200,6202,6204],{},[1151,6192,1153],{},[1342,6194,1884],{},[1346,6196,6197],{},"2.0",[1342,6199,3727],{"separator":1174},[1151,6201,1436],{},[1342,6203,1884],{},[1346,6205,6197],{},[1166,6207,6208],{"encoding":1168},"w=2.0, b=2.0",[1129,6210,6212,6230,6257],{"className":6211,"ariaHidden":1174},[1173],[1129,6213,6215,6218,6221,6224,6227],{"className":6214},[1178],[1129,6216],{"className":6217,"style":3696},[1182],[1129,6219,1153],{"className":6220,"style":1192},[1187,1191],[1129,6222],{"className":6223,"style":1996},[1368],[1129,6225,1884],{"className":6226},[2000],[1129,6228],{"className":6229,"style":1996},[1368],[1129,6231,6233,6236,6239,6242,6245,6248,6251,6254],{"className":6232},[1178],[1129,6234],{"className":6235,"style":5991},[1182],[1129,6237,6197],{"className":6238},[1187],[1129,6240,3727],{"className":6241},[3777],[1129,6243],{"className":6244,"style":2061},[1368],[1129,6246,1436],{"className":6247},[1187,1191],[1129,6249],{"className":6250,"style":1996},[1368],[1129,6252,1884],{"className":6253},[2000],[1129,6255],{"className":6256,"style":1996},[1368],[1129,6258,6260,6263],{"className":6259},[1178],[1129,6261],{"className":6262,"style":1383},[1182],[1129,6264,6197],{"className":6265},[1187],[1129,6267,6269,6313],{"className":6268},[1132],[1129,6270,6272],{"className":6271},[1136],[1138,6273,6274],{"xmlns":1140},[1142,6275,6276,6310],{},[1145,6277,6278,6280,6282,6284,6286,6288,6290,6292,6294,6296,6298,6300,6303,6305,6307],{},[1151,6279,2458],{},[1342,6281,2466],{"stretchy":2465},[1346,6283,6197],{},[1342,6285,6043],{},[1346,6287,1348],{},[1342,6289,1921],{},[1346,6291,6197],{},[1342,6293,2475],{"stretchy":2465},[1342,6295,1884],{},[1151,6297,2458],{},[1342,6299,2466],{"stretchy":2465},[1346,6301,6302],{},"4.0",[1342,6304,2475],{"stretchy":2465},[1342,6306,6065],{},[1346,6308,6309],{},"0.98",[1166,6311,6312],{"encoding":1168},"\\sigma(2.0 \\times 1 + 2.0) = \\sigma(4.0) \\approx 0.98",[1129,6314,6316,6340,6358,6379,6406],{"className":6315,"ariaHidden":1174},[1173],[1129,6317,6319,6322,6325,6328,6331,6334,6337],{"className":6318},[1178],[1129,6320],{"className":6321,"style":6081},[1182],[1129,6323,2458],{"className":6324,"style":2603},[1187,1191],[1129,6326,2466],{"className":6327},[2634],[1129,6329,6197],{"className":6330},[1187],[1129,6332],{"className":6333,"style":1369},[1368],[1129,6335,6043],{"className":6336},[1373],[1129,6338],{"className":6339,"style":1369},[1368],[1129,6341,6343,6346,6349,6352,6355],{"className":6342},[1178],[1129,6344],{"className":6345,"style":6106},[1182],[1129,6347,1348],{"className":6348},[1187],[1129,6350],{"className":6351,"style":1369},[1368],[1129,6353,1921],{"className":6354},[1373],[1129,6356],{"className":6357,"style":1369},[1368],[1129,6359,6361,6364,6367,6370,6373,6376],{"className":6360},[1178],[1129,6362],{"className":6363,"style":6081},[1182],[1129,6365,6197],{"className":6366},[1187],[1129,6368,2475],{"className":6369},[2667],[1129,6371],{"className":6372,"style":1996},[1368],[1129,6374,1884],{"className":6375},[2000],[1129,6377],{"className":6378,"style":1996},[1368],[1129,6380,6382,6385,6388,6391,6394,6397,6400,6403],{"className":6381},[1178],[1129,6383],{"className":6384,"style":6081},[1182],[1129,6386,2458],{"className":6387,"style":2603},[1187,1191],[1129,6389,2466],{"className":6390},[2634],[1129,6392,6302],{"className":6393},[1187],[1129,6395,2475],{"className":6396},[2667],[1129,6398],{"className":6399,"style":1996},[1368],[1129,6401,6065],{"className":6402},[2000],[1129,6404],{"className":6405,"style":1996},[1368],[1129,6407,6409,6412],{"className":6408},[1178],[1129,6410],{"className":6411,"style":1383},[1182],[1129,6413,6309],{"className":6414},[1187],"，学习更加缓慢！",[1101,6417,6418,6419,6497,6498,6598],{},"原因：MSE 梯度中含有 ",[1129,6420,6422,6446],{"className":6421},[1132],[1129,6423,6425],{"className":6424},[1136],[1138,6426,6427],{"xmlns":1140},[1142,6428,6429,6443],{},[1145,6430,6431,6437,6439,6441],{},[2431,6432,6433,6435],{},[1151,6434,2458],{},[1342,6436,2462],{"mathvariant":2444,"lspace":2461,"rspace":2461},[1342,6438,2466],{"stretchy":2465},[1151,6440,1733],{},[1342,6442,2475],{"stretchy":2465},[1166,6444,6445],{"encoding":1168},"\\sigma'(z)",[1129,6447,6449],{"className":6448,"ariaHidden":1174},[1173],[1129,6450,6452,6456,6488,6491,6494],{"className":6451},[1178],[1129,6453],{"className":6454,"style":6455},[1182],"height:1.0019em;vertical-align:-0.25em;",[1129,6457,6459,6462],{"className":6458},[1187],[1129,6460,2458],{"className":6461,"style":2603},[1187,1191],[1129,6463,6465],{"className":6464},[1196],[1129,6466,6468],{"className":6467},[1200],[1129,6469,6471],{"className":6470},[1205],[1129,6472,6474],{"className":6473,"style":2616},[1209],[1129,6475,6476,6479],{"style":1239},[1129,6477],{"className":6478,"style":1218},[1217],[1129,6480,6482],{"className":6481},[1222,1223,1224,1225],[1129,6483,6485],{"className":6484},[1187,1225],[1129,6486,2462],{"className":6487},[1187,1225],[1129,6489,2466],{"className":6490},[2634],[1129,6492,1733],{"className":6493,"style":1756},[1187,1191],[1129,6495,2475],{"className":6496},[2667]," 项，当神经元饱和时 ",[1129,6499,6501,6530],{"className":6500},[1132],[1129,6502,6504],{"className":6503},[1136],[1138,6505,6506],{"xmlns":1140},[1142,6507,6508,6527],{},[1145,6509,6510,6516,6518,6520,6522,6524],{},[2431,6511,6512,6514],{},[1151,6513,2458],{},[1342,6515,2462],{"mathvariant":2444,"lspace":2461,"rspace":2461},[1342,6517,2466],{"stretchy":2465},[1151,6519,1733],{},[1342,6521,2475],{"stretchy":2465},[1342,6523,6065],{},[1346,6525,6526],{},"0",[1166,6528,6529],{"encoding":1168},"\\sigma'(z) \\approx 0",[1129,6531,6533,6589],{"className":6532,"ariaHidden":1174},[1173],[1129,6534,6536,6539,6571,6574,6577,6580,6583,6586],{"className":6535},[1178],[1129,6537],{"className":6538,"style":6455},[1182],[1129,6540,6542,6545],{"className":6541},[1187],[1129,6543,2458],{"className":6544,"style":2603},[1187,1191],[1129,6546,6548],{"className":6547},[1196],[1129,6549,6551],{"className":6550},[1200],[1129,6552,6554],{"className":6553},[1205],[1129,6555,6557],{"className":6556,"style":2616},[1209],[1129,6558,6559,6562],{"style":1239},[1129,6560],{"className":6561,"style":1218},[1217],[1129,6563,6565],{"className":6564},[1222,1223,1224,1225],[1129,6566,6568],{"className":6567},[1187,1225],[1129,6569,2462],{"className":6570},[1187,1225],[1129,6572,2466],{"className":6573},[2634],[1129,6575,1733],{"className":6576,"style":1756},[1187,1191],[1129,6578,2475],{"className":6579},[2667],[1129,6581],{"className":6582,"style":1996},[1368],[1129,6584,6065],{"className":6585},[2000],[1129,6587],{"className":6588,"style":1996},[1368],[1129,6590,6592,6595],{"className":6591},[1178],[1129,6593],{"className":6594,"style":1383},[1182],[1129,6596,6526],{"className":6597},[1187],"，梯度趋近于零。",[1096,6600,6602],{"id":6601},"_22-交叉熵定义","2.2 交叉熵定义",[1101,6604,6605],{},"为解决学习缓慢问题，引入交叉熵代价函数：",[1101,6607,6608],{},[1129,6609,6611,6687],{"className":6610},[1132],[1129,6612,6614],{"className":6613},[1136],[1138,6615,6616],{"xmlns":1140},[1142,6617,6618,6684],{},[1145,6619,6620,6622,6624,6626,6633,6639],{},[1151,6621,2450],{},[1342,6623,1884],{},[1342,6625,1344],{},[3018,6627,6628,6630],{},[1346,6629,1348],{},[1151,6631,6632],{},"n",[1886,6634,6635,6637],{},[1342,6636,1890],{},[1151,6638,3638],{},[1145,6640,6641,6644,6647,6650,6653,6655,6657,6659,6661,6663,6665,6667,6669,6671,6673,6675,6677,6679,6681],{},[1342,6642,6643],{"fence":1174},"[",[1151,6645,6646],{},"y",[1151,6648,6649],{},"ln",[1342,6651,6652],{},"⁡",[1151,6654,1586],{},[1342,6656,1921],{},[1342,6658,2466],{"stretchy":2465},[1346,6660,1348],{},[1342,6662,1344],{},[1151,6664,6646],{},[1342,6666,2475],{"stretchy":2465},[1151,6668,6649],{},[1342,6670,6652],{},[1342,6672,2466],{"stretchy":2465},[1346,6674,1348],{},[1342,6676,1344],{},[1151,6678,1586],{},[1342,6680,2475],{"stretchy":2465},[1342,6682,6683],{"fence":1174},"]",[1166,6685,6686],{"encoding":1168},"C = -\\frac{1}{n} \\sum_x \\left[ y \\ln a + (1-y) \\ln(1-a) \\right]",[1129,6688,6690,6708],{"className":6689,"ariaHidden":1174},[1173],[1129,6691,6693,6696,6699,6702,6705],{"className":6692},[1178],[1129,6694],{"className":6695,"style":5901},[1182],[1129,6697,2450],{"className":6698,"style":2580},[1187,1191],[1129,6700],{"className":6701,"style":1996},[1368],[1129,6703,1884],{"className":6704},[2000],[1129,6706],{"className":6707,"style":1996},[1368],[1129,6709,6711,6715,6718,6789,6792,6833,6836],{"className":6710},[1178],[1129,6712],{"className":6713,"style":6714},[1182],"height:1.1901em;vertical-align:-0.345em;",[1129,6716,1344],{"className":6717},[1187],[1129,6719,6721,6724,6786],{"className":6720},[1187],[1129,6722],{"className":6723},[2634,3068],[1129,6725,6727],{"className":6726},[3018],[1129,6728,6730,6777],{"className":6729},[1200,1201],[1129,6731,6733,6774],{"className":6732},[1205],[1129,6734,6737,6752,6760],{"className":6735,"style":6736},[1209],"height:0.8451em;",[1129,6738,6740,6743],{"style":6739},"top:-2.655em;",[1129,6741],{"className":6742,"style":3088},[1217],[1129,6744,6746],{"className":6745},[1222,1223,1224,1225],[1129,6747,6749],{"className":6748},[1187,1225],[1129,6750,6632],{"className":6751},[1187,1191,1225],[1129,6753,6754,6757],{"style":3159},[1129,6755],{"className":6756,"style":3088},[1217],[1129,6758],{"className":6759,"style":3167},[3166],[1129,6761,6762,6765],{"style":3170},[1129,6763],{"className":6764,"style":3088},[1217],[1129,6766,6768],{"className":6767},[1222,1223,1224,1225],[1129,6769,6771],{"className":6770},[1187,1225],[1129,6772,1348],{"className":6773},[1187,1225],[1129,6775,1254],{"className":6776},[1253],[1129,6778,6780],{"className":6779},[1205],[1129,6781,6784],{"className":6782,"style":6783},[1209],"height:0.345em;",[1129,6785],{},[1129,6787],{"className":6788},[2667,3068],[1129,6790],{"className":6791,"style":2061},[1368],[1129,6793,6795,6798],{"className":6794},[2014],[1129,6796,1890],{"className":6797,"style":2020},[2014,2018,2019],[1129,6799,6801],{"className":6800},[1196],[1129,6802,6804,6825],{"className":6803},[1200,1201],[1129,6805,6807,6822],{"className":6806},[1205],[1129,6808,6811],{"className":6809,"style":6810},[1209],"height:0.0017em;",[1129,6812,6813,6816],{"style":2036},[1129,6814],{"className":6815,"style":1218},[1217],[1129,6817,6819],{"className":6818},[1222,1223,1224,1225],[1129,6820,3638],{"className":6821},[1187,1191,1225],[1129,6823,1254],{"className":6824},[1253],[1129,6826,6828],{"className":6827},[1205],[1129,6829,6831],{"className":6830,"style":2055},[1209],[1129,6832],{},[1129,6834],{"className":6835,"style":2061},[1368],[1129,6837,6839,6844,6847,6850,6853,6856,6859,6862,6865,6868,6871,6874,6877,6880,6883,6886,6889,6892,6895,6898,6901,6904,6907,6910,6913,6916],{"className":6838},[3793],[1129,6840,6643],{"className":6841,"style":6843},[2634,6842],"delimcenter","top:0em;",[1129,6845,6646],{"className":6846,"style":2603},[1187,1191],[1129,6848],{"className":6849,"style":2061},[1368],[1129,6851,6649],{"className":6852},[2014],[1129,6854],{"className":6855,"style":2061},[1368],[1129,6857,1586],{"className":6858},[1187,1191],[1129,6860],{"className":6861,"style":1369},[1368],[1129,6863,1921],{"className":6864},[1373],[1129,6866],{"className":6867,"style":1369},[1368],[1129,6869,2466],{"className":6870},[2634],[1129,6872,1348],{"className":6873},[1187],[1129,6875],{"className":6876,"style":1369},[1368],[1129,6878,1344],{"className":6879},[1373],[1129,6881],{"className":6882,"style":1369},[1368],[1129,6884,6646],{"className":6885,"style":2603},[1187,1191],[1129,6887,2475],{"className":6888},[2667],[1129,6890],{"className":6891,"style":2061},[1368],[1129,6893,6649],{"className":6894},[2014],[1129,6896,2466],{"className":6897},[2634],[1129,6899,1348],{"className":6900},[1187],[1129,6902],{"className":6903,"style":1369},[1368],[1129,6905,1344],{"className":6906},[1373],[1129,6908],{"className":6909,"style":1369},[1368],[1129,6911,1586],{"className":6912},[1187,1191],[1129,6914,2475],{"className":6915},[2667],[1129,6917,6683],{"className":6918,"style":6843},[2667,6842],[1101,6920,6921,6922,6950,6951,6979,6980,7009],{},"其中 ",[1129,6923,6925,6938],{"className":6924},[1132],[1129,6926,6928],{"className":6927},[1136],[1138,6929,6930],{"xmlns":1140},[1142,6931,6932,6936],{},[1145,6933,6934],{},[1151,6935,6632],{},[1166,6937,6632],{"encoding":1168},[1129,6939,6941],{"className":6940,"ariaHidden":1174},[1173],[1129,6942,6944,6947],{"className":6943},[1178],[1129,6945],{"className":6946,"style":3696},[1182],[1129,6948,6632],{"className":6949},[1187,1191]," 为训练样本总数，",[1129,6952,6954,6967],{"className":6953},[1132],[1129,6955,6957],{"className":6956},[1136],[1138,6958,6959],{"xmlns":1140},[1142,6960,6961,6965],{},[1145,6962,6963],{},[1151,6964,1586],{},[1166,6966,1586],{"encoding":1168},[1129,6968,6970],{"className":6969,"ariaHidden":1174},[1173],[1129,6971,6973,6976],{"className":6972},[1178],[1129,6974],{"className":6975,"style":3696},[1182],[1129,6977,1586],{"className":6978},[1187,1191]," 为神经元输出，",[1129,6981,6983,6996],{"className":6982},[1132],[1129,6984,6986],{"className":6985},[1136],[1138,6987,6988],{"xmlns":1140},[1142,6989,6990,6994],{},[1145,6991,6992],{},[1151,6993,6646],{},[1166,6995,6646],{"encoding":1168},[1129,6997,6999],{"className":6998,"ariaHidden":1174},[1173],[1129,7000,7002,7006],{"className":7001},[1178],[1129,7003],{"className":7004,"style":7005},[1182],"height:0.625em;vertical-align:-0.1944em;",[1129,7007,6646],{"className":7008,"style":2603},[1187,1191]," 为期望输出。",[1096,7011,7013],{"id":7012},"_23-交叉熵的关键性质","2.3 交叉熵的关键性质",[1101,7015,7016,7019,7020],{},[2405,7017,7018],{},"优势：梯度中不含"," ",[1129,7021,7023,7046],{"className":7022},[1132],[1129,7024,7026],{"className":7025},[1136],[1138,7027,7028],{"xmlns":1140},[1142,7029,7030,7044],{},[1145,7031,7032,7038,7040,7042],{},[2431,7033,7034,7036],{},[1151,7035,2458],{},[1342,7037,2462],{"mathvariant":2444,"lspace":2461,"rspace":2461},[1342,7039,2466],{"stretchy":2465},[1151,7041,1733],{},[1342,7043,2475],{"stretchy":2465},[1166,7045,6445],{"encoding":1168},[1129,7047,7049],{"className":7048,"ariaHidden":1174},[1173],[1129,7050,7052,7055,7087,7090,7093],{"className":7051},[1178],[1129,7053],{"className":7054,"style":6455},[1182],[1129,7056,7058,7061],{"className":7057},[1187],[1129,7059,2458],{"className":7060,"style":2603},[1187,1191],[1129,7062,7064],{"className":7063},[1196],[1129,7065,7067],{"className":7066},[1200],[1129,7068,7070],{"className":7069},[1205],[1129,7071,7073],{"className":7072,"style":2616},[1209],[1129,7074,7075,7078],{"style":1239},[1129,7076],{"className":7077,"style":1218},[1217],[1129,7079,7081],{"className":7080},[1222,1223,1224,1225],[1129,7082,7084],{"className":7083},[1187,1225],[1129,7085,2462],{"className":7086},[1187,1225],[1129,7088,2466],{"className":7089},[2634],[1129,7091,1733],{"className":7092,"style":1756},[1187,1191],[1129,7094,2475],{"className":7095},[2667],[1101,7097,7098],{},"计算交叉熵对权重的偏导数：",[1101,7100,7101],{},[1129,7102,7104,7170],{"className":7103},[1132],[1129,7105,7107],{"className":7106},[1136],[1138,7108,7109],{"xmlns":1140},[1142,7110,7111,7167],{},[1145,7112,7113,7131,7133,7139,7145,7151,7153,7155,7157,7159,7161,7163,7165],{},[3018,7114,7115,7121],{},[1145,7116,7117,7119],{},[1151,7118,3024],{"mathvariant":2444},[1151,7120,2450],{},[1145,7122,7123,7125],{},[1151,7124,3024],{"mathvariant":2444},[1886,7126,7127,7129],{},[1151,7128,1153],{},[1151,7130,1158],{},[1342,7132,1884],{},[3018,7134,7135,7137],{},[1346,7136,1348],{},[1151,7138,6632],{},[1886,7140,7141,7143],{},[1342,7142,1890],{},[1151,7144,3638],{},[1886,7146,7147,7149],{},[1151,7148,3638],{},[1151,7150,1158],{},[1342,7152,2466],{"stretchy":2465},[1151,7154,2458],{},[1342,7156,2466],{"stretchy":2465},[1151,7158,1733],{},[1342,7160,2475],{"stretchy":2465},[1342,7162,1344],{},[1151,7164,6646],{},[1342,7166,2475],{"stretchy":2465},[1166,7168,7169],{"encoding":1168},"\\frac{\\partial C}{\\partial w_j} = \\frac{1}{n} \\sum_x x_j (\\sigma(z) - y)",[1129,7171,7173,7304,7490],{"className":7172,"ariaHidden":1174},[1173],[1129,7174,7176,7180,7295,7298,7301],{"className":7175},[1178],[1129,7177],{"className":7178,"style":7179},[1182],"height:1.4224em;vertical-align:-0.5423em;",[1129,7181,7183,7186,7292],{"className":7182},[1187],[1129,7184],{"className":7185},[2634,3068],[1129,7187,7189],{"className":7188},[3018],[1129,7190,7192,7283],{"className":7191},[1200,1201],[1129,7193,7195,7280],{"className":7194},[1205],[1129,7196,7198,7255,7263],{"className":7197,"style":3081},[1209],[1129,7199,7200,7203],{"style":6739},[1129,7201],{"className":7202,"style":3088},[1217],[1129,7204,7206],{"className":7205},[1222,1223,1224,1225],[1129,7207,7209,7212],{"className":7208},[1187,1225],[1129,7210,3024],{"className":7211,"style":3098},[1187,1225],[1129,7213,7215,7218],{"className":7214},[1187,1225],[1129,7216,1153],{"className":7217,"style":1192},[1187,1191,1225],[1129,7219,7221],{"className":7220},[1196],[1129,7222,7224,7246],{"className":7223},[1200,1201],[1129,7225,7227,7243],{"className":7226},[1205],[1129,7228,7231],{"className":7229,"style":7230},[1209],"height:0.3281em;",[1129,7232,7234,7237],{"style":7233},"top:-2.357em;margin-left:-0.0269em;margin-right:0.0714em;",[1129,7235],{"className":7236,"style":3124},[1217],[1129,7238,7240],{"className":7239},[1222,3128,3129,1225],[1129,7241,1158],{"className":7242,"style":1232},[1187,1191,1225],[1129,7244,1254],{"className":7245},[1253],[1129,7247,7249],{"className":7248},[1205],[1129,7250,7253],{"className":7251,"style":7252},[1209],"height:0.2819em;",[1129,7254],{},[1129,7256,7257,7260],{"style":3159},[1129,7258],{"className":7259,"style":3088},[1217],[1129,7261],{"className":7262,"style":3167},[3166],[1129,7264,7265,7268],{"style":3170},[1129,7266],{"className":7267,"style":3088},[1217],[1129,7269,7271],{"className":7270},[1222,1223,1224,1225],[1129,7272,7274,7277],{"className":7273},[1187,1225],[1129,7275,3024],{"className":7276,"style":3098},[1187,1225],[1129,7278,2450],{"className":7279,"style":2580},[1187,1191,1225],[1129,7281,1254],{"className":7282},[1253],[1129,7284,7286],{"className":7285},[1205],[1129,7287,7290],{"className":7288,"style":7289},[1209],"height:0.5423em;",[1129,7291],{},[1129,7293],{"className":7294},[2667,3068],[1129,7296],{"className":7297,"style":1996},[1368],[1129,7299,1884],{"className":7300},[2000],[1129,7302],{"className":7303,"style":1996},[1368],[1129,7305,7307,7310,7378,7381,7421,7424,7466,7469,7472,7475,7478,7481,7484,7487],{"className":7306},[1178],[1129,7308],{"className":7309,"style":6714},[1182],[1129,7311,7313,7316,7375],{"className":7312},[1187],[1129,7314],{"className":7315},[2634,3068],[1129,7317,7319],{"className":7318},[3018],[1129,7320,7322,7367],{"className":7321},[1200,1201],[1129,7323,7325,7364],{"className":7324},[1205],[1129,7326,7328,7342,7350],{"className":7327,"style":6736},[1209],[1129,7329,7330,7333],{"style":6739},[1129,7331],{"className":7332,"style":3088},[1217],[1129,7334,7336],{"className":7335},[1222,1223,1224,1225],[1129,7337,7339],{"className":7338},[1187,1225],[1129,7340,6632],{"className":7341},[1187,1191,1225],[1129,7343,7344,7347],{"style":3159},[1129,7345],{"className":7346,"style":3088},[1217],[1129,7348],{"className":7349,"style":3167},[3166],[1129,7351,7352,7355],{"style":3170},[1129,7353],{"className":7354,"style":3088},[1217],[1129,7356,7358],{"className":7357},[1222,1223,1224,1225],[1129,7359,7361],{"className":7360},[1187,1225],[1129,7362,1348],{"className":7363},[1187,1225],[1129,7365,1254],{"className":7366},[1253],[1129,7368,7370],{"className":7369},[1205],[1129,7371,7373],{"className":7372,"style":6783},[1209],[1129,7374],{},[1129,7376],{"className":7377},[2667,3068],[1129,7379],{"className":7380,"style":2061},[1368],[1129,7382,7384,7387],{"className":7383},[2014],[1129,7385,1890],{"className":7386,"style":2020},[2014,2018,2019],[1129,7388,7390],{"className":7389},[1196],[1129,7391,7393,7413],{"className":7392},[1200,1201],[1129,7394,7396,7410],{"className":7395},[1205],[1129,7397,7399],{"className":7398,"style":6810},[1209],[1129,7400,7401,7404],{"style":2036},[1129,7402],{"className":7403,"style":1218},[1217],[1129,7405,7407],{"className":7406},[1222,1223,1224,1225],[1129,7408,3638],{"className":7409},[1187,1191,1225],[1129,7411,1254],{"className":7412},[1253],[1129,7414,7416],{"className":7415},[1205],[1129,7417,7419],{"className":7418,"style":2055},[1209],[1129,7420],{},[1129,7422],{"className":7423,"style":2061},[1368],[1129,7425,7427,7430],{"className":7426},[1187],[1129,7428,3638],{"className":7429},[1187,1191],[1129,7431,7433],{"className":7432},[1196],[1129,7434,7436,7457],{"className":7435},[1200,1201],[1129,7437,7439,7454],{"className":7438},[1205],[1129,7440,7443],{"className":7441,"style":7442},[1209],"height:0.3117em;",[1129,7444,7445,7448],{"style":2555},[1129,7446],{"className":7447,"style":1218},[1217],[1129,7449,7451],{"className":7450},[1222,1223,1224,1225],[1129,7452,1158],{"className":7453,"style":1232},[1187,1191,1225],[1129,7455,1254],{"className":7456},[1253],[1129,7458,7460],{"className":7459},[1205],[1129,7461,7464],{"className":7462,"style":7463},[1209],"height:0.2861em;",[1129,7465],{},[1129,7467,2466],{"className":7468},[2634],[1129,7470,2458],{"className":7471,"style":2603},[1187,1191],[1129,7473,2466],{"className":7474},[2634],[1129,7476,1733],{"className":7477,"style":1756},[1187,1191],[1129,7479,2475],{"className":7480},[2667],[1129,7482],{"className":7483,"style":1369},[1368],[1129,7485,1344],{"className":7486},[1373],[1129,7488],{"className":7489,"style":1369},[1368],[1129,7491,7493,7496,7499],{"className":7492},[1178],[1129,7494],{"className":7495,"style":6081},[1182],[1129,7497,6646],{"className":7498,"style":2603},[1187,1191],[1129,7500,2475],{"className":7501},[2667],[1101,7503,7504,7505,7581],{},"梯度仅取决于输出误差 ",[1129,7506,7508,7536],{"className":7507},[1132],[1129,7509,7511],{"className":7510},[1136],[1138,7512,7513],{"xmlns":1140},[1142,7514,7515,7533],{},[1145,7516,7517,7519,7521,7523,7525,7527,7529,7531],{},[1342,7518,2466],{"stretchy":2465},[1151,7520,2458],{},[1342,7522,2466],{"stretchy":2465},[1151,7524,1733],{},[1342,7526,2475],{"stretchy":2465},[1342,7528,1344],{},[1151,7530,6646],{},[1342,7532,2475],{"stretchy":2465},[1166,7534,7535],{"encoding":1168},"(\\sigma(z) - y)",[1129,7537,7539,7569],{"className":7538,"ariaHidden":1174},[1173],[1129,7540,7542,7545,7548,7551,7554,7557,7560,7563,7566],{"className":7541},[1178],[1129,7543],{"className":7544,"style":6081},[1182],[1129,7546,2466],{"className":7547},[2634],[1129,7549,2458],{"className":7550,"style":2603},[1187,1191],[1129,7552,2466],{"className":7553},[2634],[1129,7555,1733],{"className":7556,"style":1756},[1187,1191],[1129,7558,2475],{"className":7559},[2667],[1129,7561],{"className":7562,"style":1369},[1368],[1129,7564,1344],{"className":7565},[1373],[1129,7567],{"className":7568,"style":1369},[1368],[1129,7570,7572,7575,7578],{"className":7571},[1178],[1129,7573],{"className":7574,"style":6081},[1182],[1129,7576,6646],{"className":7577,"style":2603},[1187,1191],[1129,7579,2475],{"className":7580},[2667],"，误差越大学习越快",[1096,7583,7585],{"id":7584},"_24-详细推导","2.4 详细推导",[1101,7587,7588],{},"对单个训练样本，代价函数为：",[1101,7590,7591],{},[1129,7592,7594,7652],{"className":7593},[1132],[1129,7595,7597],{"className":7596},[1136],[1138,7598,7599],{"xmlns":1140},[1142,7600,7601,7649],{},[1145,7602,7603,7605,7607,7609],{},[1151,7604,2450],{},[1342,7606,1884],{},[1342,7608,1344],{},[1145,7610,7611,7613,7615,7617,7619,7621,7623,7625,7627,7629,7631,7633,7635,7637,7639,7641,7643,7645,7647],{},[1342,7612,6643],{"fence":1174},[1151,7614,6646],{},[1151,7616,6649],{},[1342,7618,6652],{},[1151,7620,1586],{},[1342,7622,1921],{},[1342,7624,2466],{"stretchy":2465},[1346,7626,1348],{},[1342,7628,1344],{},[1151,7630,6646],{},[1342,7632,2475],{"stretchy":2465},[1151,7634,6649],{},[1342,7636,6652],{},[1342,7638,2466],{"stretchy":2465},[1346,7640,1348],{},[1342,7642,1344],{},[1151,7644,1586],{},[1342,7646,2475],{"stretchy":2465},[1342,7648,6683],{"fence":1174},[1166,7650,7651],{"encoding":1168},"C = -\\left[ y \\ln a + (1-y) \\ln(1-a) \\right]",[1129,7653,7655,7673],{"className":7654,"ariaHidden":1174},[1173],[1129,7656,7658,7661,7664,7667,7670],{"className":7657},[1178],[1129,7659],{"className":7660,"style":5901},[1182],[1129,7662,2450],{"className":7663,"style":2580},[1187,1191],[1129,7665],{"className":7666,"style":1996},[1368],[1129,7668,1884],{"className":7669},[2000],[1129,7671],{"className":7672,"style":1996},[1368],[1129,7674,7676,7679,7682,7685],{"className":7675},[1178],[1129,7677],{"className":7678,"style":6081},[1182],[1129,7680,1344],{"className":7681},[1187],[1129,7683],{"className":7684,"style":2061},[1368],[1129,7686,7688,7691,7694,7697,7700,7703,7706,7709,7712,7715,7718,7721,7724,7727,7730,7733,7736,7739,7742,7745,7748,7751,7754,7757,7760,7763],{"className":7687},[3793],[1129,7689,6643],{"className":7690,"style":6843},[2634,6842],[1129,7692,6646],{"className":7693,"style":2603},[1187,1191],[1129,7695],{"className":7696,"style":2061},[1368],[1129,7698,6649],{"className":7699},[2014],[1129,7701],{"className":7702,"style":2061},[1368],[1129,7704,1586],{"className":7705},[1187,1191],[1129,7707],{"className":7708,"style":1369},[1368],[1129,7710,1921],{"className":7711},[1373],[1129,7713],{"className":7714,"style":1369},[1368],[1129,7716,2466],{"className":7717},[2634],[1129,7719,1348],{"className":7720},[1187],[1129,7722],{"className":7723,"style":1369},[1368],[1129,7725,1344],{"className":7726},[1373],[1129,7728],{"className":7729,"style":1369},[1368],[1129,7731,6646],{"className":7732,"style":2603},[1187,1191],[1129,7734,2475],{"className":7735},[2667],[1129,7737],{"className":7738,"style":2061},[1368],[1129,7740,6649],{"className":7741},[2014],[1129,7743,2466],{"className":7744},[2634],[1129,7746,1348],{"className":7747},[1187],[1129,7749],{"className":7750,"style":1369},[1368],[1129,7752,1344],{"className":7753},[1373],[1129,7755],{"className":7756,"style":1369},[1368],[1129,7758,1586],{"className":7759},[1187,1191],[1129,7761,2475],{"className":7762},[2667],[1129,7764,6683],{"className":7765,"style":6843},[2667,6842],[1101,7767,6921,7768,7898],{},[1129,7769,7771,7811],{"className":7770},[1132],[1129,7772,7774],{"className":7773},[1136],[1138,7775,7776],{"xmlns":1140},[1142,7777,7778,7808],{},[1145,7779,7780,7782,7784,7786,7788,7790,7792,7794,7796,7798,7800,7802,7804,7806],{},[1151,7781,1586],{},[1342,7783,1884],{},[1151,7785,2458],{},[1342,7787,2466],{"stretchy":2465},[1151,7789,1733],{},[1342,7791,2475],{"stretchy":2465},[1342,7793,1884],{},[1151,7795,2458],{},[1342,7797,2466],{"stretchy":2465},[1151,7799,1153],{},[1151,7801,3638],{},[1342,7803,1921],{},[1151,7805,1436],{},[1342,7807,2475],{"stretchy":2465},[1166,7809,7810],{"encoding":1168},"a = \\sigma(z) = \\sigma(wx + b)",[1129,7812,7814,7832,7859,7886],{"className":7813,"ariaHidden":1174},[1173],[1129,7815,7817,7820,7823,7826,7829],{"className":7816},[1178],[1129,7818],{"className":7819,"style":3696},[1182],[1129,7821,1586],{"className":7822},[1187,1191],[1129,7824],{"className":7825,"style":1996},[1368],[1129,7827,1884],{"className":7828},[2000],[1129,7830],{"className":7831,"style":1996},[1368],[1129,7833,7835,7838,7841,7844,7847,7850,7853,7856],{"className":7834},[1178],[1129,7836],{"className":7837,"style":6081},[1182],[1129,7839,2458],{"className":7840,"style":2603},[1187,1191],[1129,7842,2466],{"className":7843},[2634],[1129,7845,1733],{"className":7846,"style":1756},[1187,1191],[1129,7848,2475],{"className":7849},[2667],[1129,7851],{"className":7852,"style":1996},[1368],[1129,7854,1884],{"className":7855},[2000],[1129,7857],{"className":7858,"style":1996},[1368],[1129,7860,7862,7865,7868,7871,7874,7877,7880,7883],{"className":7861},[1178],[1129,7863],{"className":7864,"style":6081},[1182],[1129,7866,2458],{"className":7867,"style":2603},[1187,1191],[1129,7869,2466],{"className":7870},[2634],[1129,7872,1153],{"className":7873,"style":1192},[1187,1191],[1129,7875,3638],{"className":7876},[1187,1191],[1129,7878],{"className":7879,"style":1369},[1368],[1129,7881,1921],{"className":7882},[1373],[1129,7884],{"className":7885,"style":1369},[1368],[1129,7887,7889,7892,7895],{"className":7888},[1178],[1129,7890],{"className":7891,"style":6081},[1182],[1129,7893,1436],{"className":7894},[1187,1191],[1129,7896,2475],{"className":7897},[2667],"。计算偏导数：",[1101,7900,7901],{},[1129,7902,7904,8007],{"className":7903},[1132],[1129,7905,7907],{"className":7906},[1136],[1138,7908,7909],{"xmlns":1140},[1142,7910,7911,8004],{},[1145,7912,7913,7931,7933,7935,7981,7984,7990,7992,7994,7996,7998],{},[3018,7914,7915,7921],{},[1145,7916,7917,7919],{},[1151,7918,3024],{"mathvariant":2444},[1151,7920,2450],{},[1145,7922,7923,7925],{},[1151,7924,3024],{"mathvariant":2444},[1886,7926,7927,7929],{},[1151,7928,1153],{},[1151,7930,1158],{},[1342,7932,1884],{},[1342,7934,1344],{},[1145,7936,7937,7939,7953,7955,7979],{},[1342,7938,6643],{"fence":1174},[3018,7940,7941,7943],{},[1151,7942,6646],{},[1145,7944,7945,7947,7949,7951],{},[1151,7946,2458],{},[1342,7948,2466],{"stretchy":2465},[1151,7950,1733],{},[1342,7952,2475],{"stretchy":2465},[1342,7954,1344],{},[3018,7956,7957,7965],{},[1145,7958,7959,7961,7963],{},[1346,7960,1348],{},[1342,7962,1344],{},[1151,7964,6646],{},[1145,7966,7967,7969,7971,7973,7975,7977],{},[1346,7968,1348],{},[1342,7970,1344],{},[1151,7972,2458],{},[1342,7974,2466],{"stretchy":2465},[1151,7976,1733],{},[1342,7978,2475],{"stretchy":2465},[1342,7980,6683],{"fence":1174},[1342,7982,7983],{},"⋅",[2431,7985,7986,7988],{},[1151,7987,2458],{},[1342,7989,2462],{"mathvariant":2444,"lspace":2461,"rspace":2461},[1342,7991,2466],{"stretchy":2465},[1151,7993,1733],{},[1342,7995,2475],{"stretchy":2465},[1342,7997,7983],{},[1886,7999,8000,8002],{},[1151,8001,3638],{},[1151,8003,1158],{},[1166,8005,8006],{"encoding":1168},"\\frac{\\partial C}{\\partial w_j} = -\\left[ \\frac{y}{\\sigma(z)} - \\frac{1-y}{1-\\sigma(z)} \\right] \\cdot \\sigma'(z) \\cdot x_j",[1129,8008,8010,8136,8354,8410],{"className":8009,"ariaHidden":1174},[1173],[1129,8011,8013,8016,8127,8130,8133],{"className":8012},[1178],[1129,8014],{"className":8015,"style":7179},[1182],[1129,8017,8019,8022,8124],{"className":8018},[1187],[1129,8020],{"className":8021},[2634,3068],[1129,8023,8025],{"className":8024},[3018],[1129,8026,8028,8116],{"className":8027},[1200,1201],[1129,8029,8031,8113],{"className":8030},[1205],[1129,8032,8034,8088,8096],{"className":8033,"style":3081},[1209],[1129,8035,8036,8039],{"style":6739},[1129,8037],{"className":8038,"style":3088},[1217],[1129,8040,8042],{"className":8041},[1222,1223,1224,1225],[1129,8043,8045,8048],{"className":8044},[1187,1225],[1129,8046,3024],{"className":8047,"style":3098},[1187,1225],[1129,8049,8051,8054],{"className":8050},[1187,1225],[1129,8052,1153],{"className":8053,"style":1192},[1187,1191,1225],[1129,8055,8057],{"className":8056},[1196],[1129,8058,8060,8080],{"className":8059},[1200,1201],[1129,8061,8063,8077],{"className":8062},[1205],[1129,8064,8066],{"className":8065,"style":7230},[1209],[1129,8067,8068,8071],{"style":7233},[1129,8069],{"className":8070,"style":3124},[1217],[1129,8072,8074],{"className":8073},[1222,3128,3129,1225],[1129,8075,1158],{"className":8076,"style":1232},[1187,1191,1225],[1129,8078,1254],{"className":8079},[1253],[1129,8081,8083],{"className":8082},[1205],[1129,8084,8086],{"className":8085,"style":7252},[1209],[1129,8087],{},[1129,8089,8090,8093],{"style":3159},[1129,8091],{"className":8092,"style":3088},[1217],[1129,8094],{"className":8095,"style":3167},[3166],[1129,8097,8098,8101],{"style":3170},[1129,8099],{"className":8100,"style":3088},[1217],[1129,8102,8104],{"className":8103},[1222,1223,1224,1225],[1129,8105,8107,8110],{"className":8106},[1187,1225],[1129,8108,3024],{"className":8109,"style":3098},[1187,1225],[1129,8111,2450],{"className":8112,"style":2580},[1187,1191,1225],[1129,8114,1254],{"className":8115},[1253],[1129,8117,8119],{"className":8118},[1205],[1129,8120,8122],{"className":8121,"style":7289},[1209],[1129,8123],{},[1129,8125],{"className":8126},[2667,3068],[1129,8128],{"className":8129,"style":1996},[1368],[1129,8131,1884],{"className":8132},[2000],[1129,8134],{"className":8135,"style":1996},[1368],[1129,8137,8139,8143,8146,8149,8345,8348,8351],{"className":8138},[1178],[1129,8140],{"className":8141,"style":8142},[1182],"height:1.8em;vertical-align:-0.65em;",[1129,8144,1344],{"className":8145},[1187],[1129,8147],{"className":8148,"style":2061},[1368],[1129,8150,8152,8160,8240,8243,8246,8249,8339],{"className":8151},[3793],[1129,8153,8155],{"className":8154,"style":6843},[2634,6842],[1129,8156,6643],{"className":8157},[8158,8159],"delimsizing","size2",[1129,8161,8163,8166,8237],{"className":8162},[1187],[1129,8164],{"className":8165},[2634,3068],[1129,8167,8169],{"className":8168},[3018],[1129,8170,8172,8228],{"className":8171},[1200,1201],[1129,8173,8175,8225],{"className":8174},[1205],[1129,8176,8179,8202,8210],{"className":8177,"style":8178},[1209],"height:0.7475em;",[1129,8180,8181,8184],{"style":6739},[1129,8182],{"className":8183,"style":3088},[1217],[1129,8185,8187],{"className":8186},[1222,1223,1224,1225],[1129,8188,8190,8193,8196,8199],{"className":8189},[1187,1225],[1129,8191,2458],{"className":8192,"style":2603},[1187,1191,1225],[1129,8194,2466],{"className":8195},[2634,1225],[1129,8197,1733],{"className":8198,"style":1756},[1187,1191,1225],[1129,8200,2475],{"className":8201},[2667,1225],[1129,8203,8204,8207],{"style":3159},[1129,8205],{"className":8206,"style":3088},[1217],[1129,8208],{"className":8209,"style":3167},[3166],[1129,8211,8213,8216],{"style":8212},"top:-3.4461em;",[1129,8214],{"className":8215,"style":3088},[1217],[1129,8217,8219],{"className":8218},[1222,1223,1224,1225],[1129,8220,8222],{"className":8221},[1187,1225],[1129,8223,6646],{"className":8224,"style":2603},[1187,1191,1225],[1129,8226,1254],{"className":8227},[1253],[1129,8229,8231],{"className":8230},[1205],[1129,8232,8235],{"className":8233,"style":8234},[1209],"height:0.52em;",[1129,8236],{},[1129,8238],{"className":8239},[2667,3068],[1129,8241],{"className":8242,"style":1369},[1368],[1129,8244,1344],{"className":8245},[1373],[1129,8247],{"className":8248,"style":1369},[1368],[1129,8250,8252,8255,8336],{"className":8251},[1187],[1129,8253],{"className":8254},[2634,3068],[1129,8256,8258],{"className":8257},[3018],[1129,8259,8261,8328],{"className":8260},[1200,1201],[1129,8262,8264,8325],{"className":8263},[1205],[1129,8265,8268,8297,8305],{"className":8266,"style":8267},[1209],"height:0.8972em;",[1129,8269,8270,8273],{"style":6739},[1129,8271],{"className":8272,"style":3088},[1217],[1129,8274,8276],{"className":8275},[1222,1223,1224,1225],[1129,8277,8279,8282,8285,8288,8291,8294],{"className":8278},[1187,1225],[1129,8280,1348],{"className":8281},[1187,1225],[1129,8283,1344],{"className":8284},[1373,1225],[1129,8286,2458],{"className":8287,"style":2603},[1187,1191,1225],[1129,8289,2466],{"className":8290},[2634,1225],[1129,8292,1733],{"className":8293,"style":1756},[1187,1191,1225],[1129,8295,2475],{"className":8296},[2667,1225],[1129,8298,8299,8302],{"style":3159},[1129,8300],{"className":8301,"style":3088},[1217],[1129,8303],{"className":8304,"style":3167},[3166],[1129,8306,8307,8310],{"style":8212},[1129,8308],{"className":8309,"style":3088},[1217],[1129,8311,8313],{"className":8312},[1222,1223,1224,1225],[1129,8314,8316,8319,8322],{"className":8315},[1187,1225],[1129,8317,1348],{"className":8318},[1187,1225],[1129,8320,1344],{"className":8321},[1373,1225],[1129,8323,6646],{"className":8324,"style":2603},[1187,1191,1225],[1129,8326,1254],{"className":8327},[1253],[1129,8329,8331],{"className":8330},[1205],[1129,8332,8334],{"className":8333,"style":8234},[1209],[1129,8335],{},[1129,8337],{"className":8338},[2667,3068],[1129,8340,8342],{"className":8341,"style":6843},[2667,6842],[1129,8343,6683],{"className":8344},[8158,8159],[1129,8346],{"className":8347,"style":1369},[1368],[1129,8349,7983],{"className":8350},[1373],[1129,8352],{"className":8353,"style":1369},[1368],[1129,8355,8357,8360,8392,8395,8398,8401,8404,8407],{"className":8356},[1178],[1129,8358],{"className":8359,"style":6455},[1182],[1129,8361,8363,8366],{"className":8362},[1187],[1129,8364,2458],{"className":8365,"style":2603},[1187,1191],[1129,8367,8369],{"className":8368},[1196],[1129,8370,8372],{"className":8371},[1200],[1129,8373,8375],{"className":8374},[1205],[1129,8376,8378],{"className":8377,"style":2616},[1209],[1129,8379,8380,8383],{"style":1239},[1129,8381],{"className":8382,"style":1218},[1217],[1129,8384,8386],{"className":8385},[1222,1223,1224,1225],[1129,8387,8389],{"className":8388},[1187,1225],[1129,8390,2462],{"className":8391},[1187,1225],[1129,8393,2466],{"className":8394},[2634],[1129,8396,1733],{"className":8397,"style":1756},[1187,1191],[1129,8399,2475],{"className":8400},[2667],[1129,8402],{"className":8403,"style":1369},[1368],[1129,8405,7983],{"className":8406},[1373],[1129,8408],{"className":8409,"style":1369},[1368],[1129,8411,8413,8417],{"className":8412},[1178],[1129,8414],{"className":8415,"style":8416},[1182],"height:0.7167em;vertical-align:-0.2861em;",[1129,8418,8420,8423],{"className":8419},[1187],[1129,8421,3638],{"className":8422},[1187,1191],[1129,8424,8426],{"className":8425},[1196],[1129,8427,8429,8449],{"className":8428},[1200,1201],[1129,8430,8432,8446],{"className":8431},[1205],[1129,8433,8435],{"className":8434,"style":7442},[1209],[1129,8436,8437,8440],{"style":2555},[1129,8438],{"className":8439,"style":1218},[1217],[1129,8441,8443],{"className":8442},[1222,1223,1224,1225],[1129,8444,1158],{"className":8445,"style":1232},[1187,1191,1225],[1129,8447,1254],{"className":8448},[1253],[1129,8450,8452],{"className":8451},[1205],[1129,8453,8455],{"className":8454,"style":7463},[1209],[1129,8456],{},[1101,8458,8459,8460,2417],{},"利用 ",[1129,8461,8463,8513],{"className":8462},[1132],[1129,8464,8466],{"className":8465},[1136],[1138,8467,8468],{"xmlns":1140},[1142,8469,8470,8510],{},[1145,8471,8472,8478,8480,8482,8484,8486,8488,8490,8492,8494,8496,8498,8500,8502,8504,8506,8508],{},[2431,8473,8474,8476],{},[1151,8475,2458],{},[1342,8477,2462],{"mathvariant":2444,"lspace":2461,"rspace":2461},[1342,8479,2466],{"stretchy":2465},[1151,8481,1733],{},[1342,8483,2475],{"stretchy":2465},[1342,8485,1884],{},[1151,8487,2458],{},[1342,8489,2466],{"stretchy":2465},[1151,8491,1733],{},[1342,8493,2475],{"stretchy":2465},[1342,8495,2466],{"stretchy":2465},[1346,8497,1348],{},[1342,8499,1344],{},[1151,8501,2458],{},[1342,8503,2466],{"stretchy":2465},[1151,8505,1733],{},[1342,8507,2475],{"stretchy":2465},[1342,8509,2475],{"stretchy":2465},[1166,8511,8512],{"encoding":1168},"\\sigma'(z) = 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x_j",[1129,8744,8746,8872,9083,9116,9143],{"className":8745,"ariaHidden":1174},[1173],[1129,8747,8749,8752,8863,8866,8869],{"className":8748},[1178],[1129,8750],{"className":8751,"style":7179},[1182],[1129,8753,8755,8758,8860],{"className":8754},[1187],[1129,8756],{"className":8757},[2634,3068],[1129,8759,8761],{"className":8760},[3018],[1129,8762,8764,8852],{"className":8763},[1200,1201],[1129,8765,8767,8849],{"className":8766},[1205],[1129,8768,8770,8824,8832],{"className":8769,"style":3081},[1209],[1129,8771,8772,8775],{"style":6739},[1129,8773],{"className":8774,"style":3088},[1217],[1129,8776,8778],{"className":8777},[1222,1223,1224,1225],[1129,8779,8781,8784],{"className":8780},[1187,1225],[1129,8782,3024],{"className":8783,"style":3098},[1187,1225],[1129,8785,8787,8790],{"className":8786},[1187,1225],[1129,8788,1153],{"className":8789,"style":1192},[1187,1191,1225],[1129,8791,8793],{"className":8792},[1196],[1129,8794,8796,8816],{"className":8795},[1200,1201],[1129,8797,8799,8813],{"className":8798},[1205],[1129,8800,8802],{"className":8801,"style":7230},[1209],[1129,8803,8804,8807],{"style":7233},[1129,8805],{"className":8806,"style":3124},[1217],[1129,8808,8810],{"className":8809},[1222,3128,3129,1225],[1129,8811,1158],{"className":8812,"style":1232},[1187,1191,1225],[1129,8814,1254],{"className":8815},[1253],[1129,8817,8819],{"className":8818},[1205],[1129,8820,8822],{"className":8821,"style":7252},[1209],[1129,8823],{},[1129,8825,8826,8829],{"style":3159},[1129,8827],{"className":8828,"style":3088},[1217],[1129,8830],{"className":8831,"style":3167},[3166],[1129,8833,8834,8837],{"style":3170},[1129,8835],{"className":8836,"style":3088},[1217],[1129,8838,8840],{"className":8839},[1222,1223,1224,1225],[1129,8841,8843,8846],{"className":8842},[1187,1225],[1129,8844,3024],{"className":8845,"style":3098},[1187,1225],[1129,8847,2450],{"className":8848,"style":2580},[1187,1191,1225],[1129,8850,1254],{"className":8851},[1253],[1129,8853,8855],{"className":8854},[1205],[1129,8856,8858],{"className":8857,"style":7289},[1209],[1129,8859],{},[1129,8861],{"className":8862},[2667,3068],[1129,8864],{"className":8865,"style":1996},[1368],[1129,8867,1884],{"className":8868},[2000],[1129,8870],{"className":8871,"style":1996},[1368],[1129,8873,8875,8878,8881,8884,9074,9077,9080],{"className":8874},[1178],[1129,8876],{"className":8877,"style":8142},[1182],[1129,8879,1344],{"className":8880},[1187],[1129,8882],{"className":8883,"style":2061},[1368],[1129,8885,8887,8893,8970,8973,8976,8979,9068],{"className":8886},[3793],[1129,8888,8890],{"className":8889,"style":6843},[2634,6842],[1129,8891,6643],{"className":8892},[8158,8159],[1129,8894,8896,8899,8967],{"className":8895},[1187],[1129,8897],{"className":8898},[2634,3068],[1129,8900,8902],{"className":8901},[3018],[1129,8903,8905,8959],{"className":8904},[1200,1201],[1129,8906,8908,8956],{"className":8907},[1205],[1129,8909,8911,8934,8942],{"className":8910,"style":8178},[1209],[1129,8912,8913,8916],{"style":6739},[1129,8914],{"className":8915,"style":3088},[1217],[1129,8917,8919],{"className":8918},[1222,1223,1224,1225],[1129,8920,8922,8925,8928,8931],{"className":8921},[1187,1225],[1129,8923,2458],{"className":8924,"style":2603},[1187,1191,1225],[1129,8926,2466],{"className":8927},[2634,1225],[1129,8929,1733],{"className":8930,"style":1756},[1187,1191,1225],[1129,8932,2475],{"className":8933},[2667,1225],[1129,8935,8936,8939],{"style":3159},[1129,8937],{"className":8938,"style":3088},[1217],[1129,8940],{"className":8941,"style":3167},[3166],[1129,8943,8944,8947],{"style":8212},[1129,8945],{"className":8946,"style":3088},[1217],[1129,8948,8950],{"className":8949},[1222,1223,1224,1225],[1129,8951,8953],{"className":8952},[1187,1225],[1129,8954,6646],{"className":8955,"style":2603},[1187,1191,1225],[1129,8957,1254],{"className":8958},[1253],[1129,8960,8962],{"className":8961},[1205],[1129,8963,8965],{"className":8964,"style":8234},[1209],[1129,8966],{},[1129,8968],{"className":8969},[2667,3068],[1129,8971],{"className":8972,"style":1369},[1368],[1129,8974,1344],{"className":8975},[1373],[1129,8977],{"className":8978,"style":1369},[1368],[1129,8980,8982,8985,9065],{"className":8981},[1187],[1129,8983],{"className":8984},[2634,3068],[1129,8986,8988],{"className":8987},[3018],[1129,8989,8991,9057],{"className":8990},[1200,1201],[1129,8992,8994,9054],{"className":8993},[1205],[1129,8995,8997,9026,9034],{"className":8996,"style":8267},[1209],[1129,8998,8999,9002],{"style":6739},[1129,9000],{"className":9001,"style":3088},[1217],[1129,9003,9005],{"className":9004},[1222,1223,1224,1225],[1129,9006,9008,9011,9014,9017,9020,9023],{"className":9007},[1187,1225],[1129,9009,1348],{"className":9010},[1187,1225],[1129,9012,1344],{"className":9013},[1373,1225],[1129,9015,2458],{"className":9016,"style":2603},[1187,1191,1225],[1129,9018,2466],{"className":9019},[2634,1225],[1129,9021,1733],{"className":9022,"style":1756},[1187,1191,1225],[1129,9024,2475],{"className":9025},[2667,1225],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x_j",[1129,9263,9265,9278,9380],{"className":9264,"ariaHidden":1174},[1173],[1129,9266,9268,9272,9275],{"className":9267},[1178],[1129,9269],{"className":9270,"style":9271},[1182],"height:0.3669em;",[1129,9273,1884],{"className":9274},[2000],[1129,9276],{"className":9277,"style":1996},[1368],[1129,9279,9281,9284,9287,9290,9371,9374,9377],{"className":9280},[1178],[1129,9282],{"className":9283,"style":6081},[1182],[1129,9285,1344],{"className":9286},[1187],[1129,9288],{"className":9289,"style":2061},[1368],[1129,9291,9293,9296,9299,9302,9305,9308,9311,9314,9317,9320,9323,9326,9329,9332,9335,9338,9341,9344,9347,9350,9353,9356,9359,9362,9365,9368],{"className":9292},[3793],[1129,9294,6643],{"className":9295,"style":6843},[2634,6842],[1129,9297,6646],{"className":9298,"style":2603},[1187,1191],[1129,9300,2466],{"className":9301},[2634],[1129,9303,1348],{"className":9304},[1187],[1129,9306],{"className":9307,"style":1369},[1368],[1129,9309,1344],{"className":9310},[1373],[1129,9312],{"className":9313,"style":1369},[1368],[1129,9315,2458],{"className":9316,"style":2603},[1187,1191],[1129,9318,2466],{"className":9319},[2634],[1129,9321,1733],{"className":9322,"style":1756},[1187,1191],[1129,9324,8623],{"className":9325},[2667],[1129,9327],{"className":9328,"style":1369},[1368],[1129,9330,1344],{"className":9331},[1373],[1129,9333],{"className":9334,"style":1369},[1368],[1129,9336,2466],{"className":9337},[2634],[1129,9339,1348],{"className":9340},[1187],[1129,9342],{"className":9343,"style":1369},[1368],[1129,9345,1344],{"className":9346},[1373],[1129,9348],{"className":9349,"style":1369},[1368],[1129,9351,6646],{"className":9352,"style":2603},[1187,1191],[1129,9354,2475],{"className":9355},[2667],[1129,9357,2458],{"className":9358,"style":2603},[1187,1191],[1129,9360,2466],{"className":9361},[2634],[1129,9363,1733],{"className":9364,"style":1756},[1187,1191],[1129,9366,2475],{"className":9367},[2667],[1129,9369,6683],{"className":9370,"style":6843},[2667,6842],[1129,9372],{"className":9373,"style":1369},[1368],[1129,9375,7983],{"className":9376},[1373],[1129,9378],{"className":9379,"style":1369},[1368],[1129,9381,9383,9386],{"className":9382},[1178],[1129,9384],{"className":9385,"style":8416},[1182],[1129,9387,9389,9392],{"className":9388},[1187],[1129,9390,3638],{"className":9391},[1187,1191],[1129,9393,9395],{"className":9394},[1196],[1129,9396,9398,9418],{"className":9397},[1200,1201],[1129,9399,9401,9415],{"className":9400},[1205],[1129,9402,9404],{"className":9403,"style":7442},[1209],[1129,9405,9406,9409],{"style":2555},[1129,9407],{"className":9408,"style":1218},[1217],[1129,9410,9412],{"className":9411},[1222,1223,1224,1225],[1129,9413,1158],{"className":9414,"style":1232},[1187,1191,1225],[1129,9416,1254],{"className":9417},[1253],[1129,9419,9421],{"className":9420},[1205],[1129,9422,9424],{"className":9423,"style":7463},[1209],[1129,9425],{},[1101,9427,9428],{},[1129,9429,9431,9497],{"className":9430},[1132],[1129,9432,9434],{"className":9433},[1136],[1138,9435,9436],{"xmlns":1140},[1142,9437,9438,9494],{},[1145,9439,9440,9442,9444,9486,9488],{},[1342,9441,1884],{},[1342,9443,1344],{},[1145,9445,9446,9448,9450,9452,9454,9456,9458,9460,9462,9464,9466,9468,9470,9472,9474,9476,9478,9480,9482,9484],{},[1342,9447,6643],{"fence":1174},[1151,9449,6646],{},[1342,9451,1344],{},[1151,9453,6646],{},[1151,9455,2458],{},[1342,9457,2466],{"stretchy":2465},[1151,9459,1733],{},[1342,9461,2475],{"stretchy":2465},[1342,9463,1344],{},[1151,9465,2458],{},[1342,9467,2466],{"stretchy":2465},[1151,9469,1733],{},[1342,9471,2475],{"stretchy":2465},[1342,9473,1921],{},[1151,9475,6646],{},[1151,9477,2458],{},[1342,9479,2466],{"stretchy":2465},[1151,9481,1733],{},[1342,9483,2475],{"stretchy":2465},[1342,9485,6683],{"fence":1174},[1342,9487,7983],{},[1886,9489,9490,9492],{},[1151,9491,3638],{},[1151,9493,1158],{},[1166,9495,9496],{"encoding":1168},"= 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x_j",[1129,9498,9500,9512,9614],{"className":9499,"ariaHidden":1174},[1173],[1129,9501,9503,9506,9509],{"className":9502},[1178],[1129,9504],{"className":9505,"style":9271},[1182],[1129,9507,1884],{"className":9508},[2000],[1129,9510],{"className":9511,"style":1996},[1368],[1129,9513,9515,9518,9521,9524,9605,9608,9611],{"className":9514},[1178],[1129,9516],{"className":9517,"style":6081},[1182],[1129,9519,1344],{"className":9520},[1187],[1129,9522],{"className":9523,"style":2061},[1368],[1129,9525,9527,9530,9533,9536,9539,9542,9545,9548,9551,9554,9557,9560,9563,9566,9569,9572,9575,9578,9581,9584,9587,9590,9593,9596,9599,9602],{"className":9526},[3793],[1129,9528,6643],{"className":9529,"style":6843},[2634,6842],[1129,9531,6646],{"className":9532,"style":2603},[1187,1191],[1129,9534],{"className":9535,"style":1369},[1368],[1129,9537,1344],{"className":9538},[1373],[1129,9540],{"className":9541,"style":1369},[1368],[1129,9543,6646],{"className":9544,"style":2603},[1187,1191],[1129,9546,2458],{"className":9547,"style":2603},[1187,1191],[1129,9549,2466],{"className":9550},[2634],[1129,9552,1733],{"className":9553,"style":1756},[1187,1191],[1129,9555,2475],{"className":9556},[2667],[1129,9558],{"className":9559,"style":1369},[1368],[1129,9561,1344],{"className":9562},[1373],[1129,9564],{"className":9565,"style":1369},[1368],[1129,9567,2458],{"className":9568,"style":2603},[1187,1191],[1129,9570,2466],{"className":9571},[2634],[1129,9573,1733],{"className":9574,"style":1756},[1187,1191],[1129,9576,2475],{"className":9577},[2667],[1129,9579],{"className":9580,"style":1369},[1368],[1129,9582,1921],{"className":9583},[1373],[1129,9585],{"className":9586,"style":1369},[1368],[1129,9588,6646],{"className":9589,"style":2603},[1187,1191],[1129,9591,2458],{"className":9592,"style":2603},[1187,1191],[1129,9594,2466],{"className":9595},[2634],[1129,9597,1733],{"className":9598,"style":1756},[1187,1191],[1129,9600,2475],{"className":9601},[2667],[1129,9603,6683],{"className":9604,"style":6843},[2667,6842],[1129,9606],{"className":9607,"style":1369},[1368],[1129,9609,7983],{"className":9610},[1373],[1129,9612],{"className":9613,"style":1369},[1368],[1129,9615,9617,9620],{"className":9616},[1178],[1129,9618],{"className":9619,"style":8416},[1182],[1129,9621,9623,9626],{"className":9622},[1187],[1129,9624,3638],{"className":9625},[1187,1191],[1129,9627,9629],{"className":9628},[1196],[1129,9630,9632,9652],{"className":9631},[1200,1201],[1129,9633,9635,9649],{"className":9634},[1205],[1129,9636,9638],{"className":9637,"style":7442},[1209],[1129,9639,9640,9643],{"style":2555},[1129,9641],{"className":9642,"style":1218},[1217],[1129,9644,9646],{"className":9645},[1222,1223,1224,1225],[1129,9647,1158],{"className":9648,"style":1232},[1187,1191,1225],[1129,9650,1254],{"className":9651},[1253],[1129,9653,9655],{"className":9654},[1205],[1129,9656,9658],{"className":9657,"style":7463},[1209],[1129,9659],{},[1101,9661,9662],{},[1129,9663,9665,9703],{"className":9664},[1132],[1129,9666,9668],{"className":9667},[1136],[1138,9669,9670],{"xmlns":1140},[1142,9671,9672,9700],{},[1145,9673,9674,9676,9678,9680,9682,9684,9686,9688,9690,9692,9694],{},[1342,9675,1884],{},[1342,9677,2466],{"stretchy":2465},[1151,9679,2458],{},[1342,9681,2466],{"stretchy":2465},[1151,9683,1733],{},[1342,9685,2475],{"stretchy":2465},[1342,9687,1344],{},[1151,9689,6646],{},[1342,9691,2475],{"stretchy":2465},[1342,9693,7983],{},[1886,9695,9696,9698],{},[1151,9697,3638],{},[1151,9699,1158],{},[1166,9701,9702],{"encoding":1168},"= (\\sigma(z) - y) \\cdot x_j",[1129,9704,9706,9718,9748,9769],{"className":9705,"ariaHidden":1174},[1173],[1129,9707,9709,9712,9715],{"className":9708},[1178],[1129,9710],{"className":9711,"style":9271},[1182],[1129,9713,1884],{"className":9714},[2000],[1129,9716],{"className":9717,"style":1996},[1368],[1129,9719,9721,9724,9727,9730,9733,9736,9739,9742,9745],{"className":9720},[1178],[1129,9722],{"className":9723,"style":6081},[1182],[1129,9725,2466],{"className":9726},[2634],[1129,9728,2458],{"className":9729,"style":2603},[1187,1191],[1129,9731,2466],{"className":9732},[2634],[1129,9734,1733],{"className":9735,"style":1756},[1187,1191],[1129,9737,2475],{"className":9738},[2667],[1129,9740],{"className":9741,"style":1369},[1368],[1129,9743,1344],{"className":9744},[1373],[1129,9746],{"className":9747,"style":1369},[1368],[1129,9749,9751,9754,9757,9760,9763,9766],{"className":9750},[1178],[1129,9752],{"className":9753,"style":6081},[1182],[1129,9755,6646],{"className":9756,"style":2603},[1187,1191],[1129,9758,2475],{"className":9759},[2667],[1129,9761],{"className":9762,"style":1369},[1368],[1129,9764,7983],{"className":9765},[1373],[1129,9767],{"className":9768,"style":1369},[1368],[1129,9770,9772,9775],{"className":9771},[1178],[1129,9773],{"className":9774,"style":8416},[1182],[1129,9776,9778,9781],{"className":9777},[1187],[1129,9779,3638],{"className":9780},[1187,1191],[1129,9782,9784],{"className":9783},[1196],[1129,9785,9787,9807],{"className":9786},[1200,1201],[1129,9788,9790,9804],{"className":9789},[1205],[1129,9791,9793],{"className":9792,"style":7442},[1209],[1129,9794,9795,9798],{"style":2555},[1129,9796],{"className":9797,"style":1218},[1217],[1129,9799,9801],{"className":9800},[1222,1223,1224,1225],[1129,9802,1158],{"className":9803,"style":1232},[1187,1191,1225],[1129,9805,1254],{"className":9806},[1253],[1129,9808,9810],{"className":9809},[1205],[1129,9811,9813],{"className":9812,"style":7463},[1209],[1129,9814],{},[1101,9816,9817],{},"类似地，对偏置的偏导数为：",[1101,9819,9820],{},[1129,9821,9823,9879],{"className":9822},[1132],[1129,9824,9826],{"className":9825},[1136],[1138,9827,9828],{"xmlns":1140},[1142,9829,9830,9876],{},[1145,9831,9832,9846,9848,9854,9860,9862,9864,9866,9868,9870,9872,9874],{},[3018,9833,9834,9840],{},[1145,9835,9836,9838],{},[1151,9837,3024],{"mathvariant":2444},[1151,9839,2450],{},[1145,9841,9842,9844],{},[1151,9843,3024],{"mathvariant":2444},[1151,9845,1436],{},[1342,9847,1884],{},[3018,9849,9850,9852],{},[1346,9851,1348],{},[1151,9853,6632],{},[1886,9855,9856,9858],{},[1342,9857,1890],{},[1151,9859,3638],{},[1342,9861,2466],{"stretchy":2465},[1151,9863,2458],{},[1342,9865,2466],{"stretchy":2465},[1151,9867,1733],{},[1342,9869,2475],{"stretchy":2465},[1342,9871,1344],{},[1151,9873,6646],{},[1342,9875,2475],{"stretchy":2465},[1166,9877,9878],{"encoding":1168},"\\frac{\\partial C}{\\partial b} = \\frac{1}{n} \\sum_x (\\sigma(z) - y)",[1129,9880,9882,9972,10113],{"className":9881,"ariaHidden":1174},[1173],[1129,9883,9885,9889,9963,9966,9969],{"className":9884},[1178],[1129,9886],{"className":9887,"style":9888},[1182],"height:1.2251em;vertical-align:-0.345em;",[1129,9890,9892,9895,9960],{"className":9891},[1187],[1129,9893],{"className":9894},[2634,3068],[1129,9896,9898],{"className":9897},[3018],[1129,9899,9901,9952],{"className":9900},[1200,1201],[1129,9902,9904,9949],{"className":9903},[1205],[1129,9905,9907,9924,9932],{"className":9906,"style":3081},[1209],[1129,9908,9909,9912],{"style":6739},[1129,9910],{"className":9911,"style":3088},[1217],[1129,9913,9915],{"className":9914},[1222,1223,1224,1225],[1129,9916,9918,9921],{"className":9917},[1187,1225],[1129,9919,3024],{"className":9920,"style":3098},[1187,1225],[1129,9922,1436],{"className":9923},[1187,1191,1225],[1129,9925,9926,9929],{"style":3159},[1129,9927],{"className":9928,"style":3088},[1217],[1129,9930],{"className":9931,"style":3167},[3166],[1129,9933,9934,9937],{"style":3170},[1129,9935],{"className":9936,"style":3088},[1217],[1129,9938,9940],{"className":9939},[1222,1223,1224,1225],[1129,9941,9943,9946],{"className":9942},[1187,1225],[1129,9944,3024],{"className":9945,"style":3098},[1187,1225],[1129,9947,2450],{"className":9948,"style":2580},[1187,1191,1225],[1129,9950,1254],{"className":9951},[1253],[1129,9953,9955],{"className":9954},[1205],[1129,9956,9958],{"className":9957,"style":6783},[1209],[1129,9959],{},[1129,9961],{"className":9962},[2667,3068],[1129,9964],{"className":9965,"style":1996},[1368],[1129,9967,1884],{"className":9968},[2000],[1129,9970],{"className":9971,"style":1996},[1368],[1129,9973,9975,9978,10046,10049,10089,10092,10095,10098,10101,10104,10107,10110],{"className":9974},[1178],[1129,9976],{"className":9977,"style":6714},[1182],[1129,9979,9981,9984,10043],{"className":9980},[1187],[1129,9982],{"className":9983},[2634,3068],[1129,9985,9987],{"className":9986},[3018],[1129,9988,9990,10035],{"className":9989},[1200,1201],[1129,9991,9993,10032],{"className":9992},[1205],[1129,9994,9996,10010,10018],{"className":9995,"style":6736},[1209],[1129,9997,9998,10001],{"style":6739},[1129,9999],{"className":10000,"style":3088},[1217],[1129,10002,10004],{"className":10003},[1222,1223,1224,1225],[1129,10005,10007],{"className":10006},[1187,1225],[1129,10008,6632],{"className":10009},[1187,1191,1225],[1129,10011,10012,10015],{"style":3159},[1129,10013],{"className":10014,"style":3088},[1217],[1129,10016],{"className":10017,"style":3167},[3166],[1129,10019,10020,10023],{"style":3170},[1129,10021],{"className":10022,"style":3088},[1217],[1129,10024,10026],{"className":10025},[1222,1223,1224,1225],[1129,10027,10029],{"className":10028},[1187,1225],[1129,10030,1348],{"className":10031},[1187,1225],[1129,10033,1254],{"className":10034},[1253],[1129,10036,10038],{"className":10037},[1205],[1129,10039,10041],{"className":10040,"style":6783},[1209],[1129,10042],{},[1129,10044],{"className":10045},[2667,3068],[1129,10047],{"className":10048,"style":2061},[1368],[1129,10050,10052,10055],{"className":10051},[2014],[1129,10053,1890],{"className":10054,"style":2020},[2014,2018,2019],[1129,10056,10058],{"className":10057},[1196],[1129,10059,10061,10081],{"className":10060},[1200,1201],[1129,10062,10064,10078],{"className":10063},[1205],[1129,10065,10067],{"className":10066,"style":6810},[1209],[1129,10068,10069,10072],{"style":2036},[1129,10070],{"className":10071,"style":1218},[1217],[1129,10073,10075],{"className":10074},[1222,1223,1224,1225],[1129,10076,3638],{"className":10077},[1187,1191,1225],[1129,10079,1254],{"className":10080},[1253],[1129,10082,10084],{"className":10083},[1205],[1129,10085,10087],{"className":10086,"style":2055},[1209],[1129,10088],{},[1129,10090,2466],{"className":10091},[2634],[1129,10093,2458],{"className":10094,"style":2603},[1187,1191],[1129,10096,2466],{"className":10097},[2634],[1129,10099,1733],{"className":10100,"style":1756},[1187,1191],[1129,10102,2475],{"className":10103},[2667],[1129,10105],{"className":10106,"style":1369},[1368],[1129,10108,1344],{"className":10109},[1373],[1129,10111],{"className":10112,"style":1369},[1368],[1129,10114,10116,10119,10122],{"className":10115},[1178],[1129,10117],{"className":10118,"style":6081},[1182],[1129,10120,6646],{"className":10121,"style":2603},[1187,1191],[1129,10123,2475],{"className":10124},[2667],[1096,10126,10128],{"id":10127},"_25-从期望性质反推交叉熵","2.5 从期望性质反推交叉熵",[1101,10130,10131],{},"如果我们希望代价函数满足以下性质：",[1101,10133,10134],{},[1129,10135,10137,10177],{"className":10136},[1132],[1129,10138,10140],{"className":10139},[1136],[1138,10141,10142],{"xmlns":1140},[1142,10143,10144,10174],{},[1145,10145,10146,10160,10162,10164,10166,10168,10170,10172],{},[3018,10147,10148,10154],{},[1145,10149,10150,10152],{},[1151,10151,3024],{"mathvariant":2444},[1151,10153,2450],{},[1145,10155,10156,10158],{},[1151,10157,3024],{"mathvariant":2444},[1151,10159,1153],{},[1342,10161,1884],{},[1151,10163,3638],{},[1342,10165,2466],{"stretchy":2465},[1151,10167,1586],{},[1342,10169,1344],{},[1151,10171,6646],{},[1342,10173,2475],{"stretchy":2465},[1166,10175,10176],{"encoding":1168},"\\frac{\\partial C}{\\partial w} = x(a - y)",[1129,10178,10180,10269,10293],{"className":10179,"ariaHidden":1174},[1173],[1129,10181,10183,10186,10260,10263,10266],{"className":10182},[1178],[1129,10184],{"className":10185,"style":9888},[1182],[1129,10187,10189,10192,10257],{"className":10188},[1187],[1129,10190],{"className":10191},[2634,3068],[1129,10193,10195],{"className":10194},[3018],[1129,10196,10198,10249],{"className":10197},[1200,1201],[1129,10199,10201,10246],{"className":10200},[1205],[1129,10202,10204,10221,10229],{"className":10203,"style":3081},[1209],[1129,10205,10206,10209],{"style":6739},[1129,10207],{"className":10208,"style":3088},[1217],[1129,10210,10212],{"className":10211},[1222,1223,1224,1225],[1129,10213,10215,10218],{"className":10214},[1187,1225],[1129,10216,3024],{"className":10217,"style":3098},[1187,1225],[1129,10219,1153],{"className":10220,"style":1192},[1187,1191,1225],[1129,10222,10223,10226],{"style":3159},[1129,10224],{"className":10225,"style":3088},[1217],[1129,10227],{"className":10228,"style":3167},[3166],[1129,10230,10231,10234],{"style":3170},[1129,10232],{"className":10233,"style":3088},[1217],[1129,10235,10237],{"className":10236},[1222,1223,1224,1225],[1129,10238,10240,10243],{"className":10239},[1187,1225],[1129,10241,3024],{"className":10242,"style":3098},[1187,1225],[1129,10244,2450],{"className":10245,"style":2580},[1187,1191,1225],[1129,10247,1254],{"className":10248},[1253],[1129,10250,10252],{"className":10251},[1205],[1129,10253,10255],{"className":10254,"style":6783},[1209],[1129,10256],{},[1129,10258],{"className":10259},[2667,3068],[1129,10261],{"className":10262,"style":1996},[1368],[1129,10264,1884],{"className":10265},[2000],[1129,10267],{"className":10268,"style":1996},[1368],[1129,10270,10272,10275,10278,10281,10284,10287,10290],{"className":10271},[1178],[1129,10273],{"className":10274,"style":6081},[1182],[1129,10276,3638],{"className":10277},[1187,1191],[1129,10279,2466],{"className":10280},[2634],[1129,10282,1586],{"className":10283},[1187,1191],[1129,10285],{"className":10286,"style":1369},[1368],[1129,10288,1344],{"className":10289},[1373],[1129,10291],{"className":10292,"style":1369},[1368],[1129,10294,10296,10299,10302],{"className":10295},[1178],[1129,10297],{"className":10298,"style":6081},[1182],[1129,10300,6646],{"className":10301,"style":2603},[1187,1191],[1129,10303,2475],{"className":10304},[2667],[1101,10306,10307,10308,10552,10553,10581],{},"从这个期望出发，通过积分可以推导出交叉熵的形式。由 ",[1129,10309,10311,10363],{"className":10310},[1132],[1129,10312,10314],{"className":10313},[1136],[1138,10315,10316],{"xmlns":1140},[1142,10317,10318,10360],{},[1145,10319,10320,10334,10336],{},[3018,10321,10322,10328],{},[1145,10323,10324,10326],{},[1151,10325,3024],{"mathvariant":2444},[1151,10327,2450],{},[1145,10329,10330,10332],{},[1151,10331,3024],{"mathvariant":2444},[1151,10333,1586],{},[1342,10335,1884],{},[3018,10337,10338,10346],{},[1145,10339,10340,10342,10344],{},[1151,10341,1586],{},[1342,10343,1344],{},[1151,10345,6646],{},[1145,10347,10348,10350,10352,10354,10356,10358],{},[1151,10349,1586],{},[1342,10351,2466],{"stretchy":2465},[1346,10353,1348],{},[1342,10355,1344],{},[1151,10357,1586],{},[1342,10359,2475],{"stretchy":2465},[1166,10361,10362],{"encoding":1168},"\\frac{\\partial C}{\\partial a} = \\frac{a-y}{a(1-a)}",[1129,10364,10366,10455],{"className":10365,"ariaHidden":1174},[1173],[1129,10367,10369,10372,10446,10449,10452],{"className":10368},[1178],[1129,10370],{"className":10371,"style":9888},[1182],[1129,10373,10375,10378,10443],{"className":10374},[1187],[1129,10376],{"className":10377},[2634,3068],[1129,10379,10381],{"className":10380},[3018],[1129,10382,10384,10435],{"className":10383},[1200,1201],[1129,10385,10387,10432],{"className":10386},[1205],[1129,10388,10390,10407,10415],{"className":10389,"style":3081},[1209],[1129,10391,10392,10395],{"style":6739},[1129,10393],{"className":10394,"style":3088},[1217],[1129,10396,10398],{"className":10397},[1222,1223,1224,1225],[1129,10399,10401,10404],{"className":10400},[1187,1225],[1129,10402,3024],{"className":10403,"style":3098},[1187,1225],[1129,10405,1586],{"className":10406},[1187,1191,1225],[1129,10408,10409,10412],{"style":3159},[1129,10410],{"className":10411,"style":3088},[1217],[1129,10413],{"className":10414,"style":3167},[3166],[1129,10416,10417,10420],{"style":3170},[1129,10418],{"className":10419,"style":3088},[1217],[1129,10421,10423],{"className":10422},[1222,1223,1224,1225],[1129,10424,10426,10429],{"className":10425},[1187,1225],[1129,10427,3024],{"className":10428,"style":3098},[1187,1225],[1129,10430,2450],{"className":10431,"style":2580},[1187,1191,1225],[1129,10433,1254],{"className":10434},[1253],[1129,10436,10438],{"className":10437},[1205],[1129,10439,10441],{"className":10440,"style":6783},[1209],[1129,10442],{},[1129,10444],{"className":10445},[2667,3068],[1129,10447],{"className":10448,"style":1996},[1368],[1129,10450,1884],{"className":10451},[2000],[1129,10453],{"className":10454,"style":1996},[1368],[1129,10456,10458,10462],{"className":10457},[1178],[1129,10459],{"className":10460,"style":10461},[1182],"height:1.3744em;vertical-align:-0.52em;",[1129,10463,10465,10468,10549],{"className":10464},[1187],[1129,10466],{"className":10467},[2634,3068],[1129,10469,10471],{"className":10470},[3018],[1129,10472,10474,10541],{"className":10473},[1200,1201],[1129,10475,10477,10538],{"className":10476},[1205],[1129,10478,10481,10510,10518],{"className":10479,"style":10480},[1209],"height:0.8544em;",[1129,10482,10483,10486],{"style":6739},[1129,10484],{"className":10485,"style":3088},[1217],[1129,10487,10489],{"className":10488},[1222,1223,1224,1225],[1129,10490,10492,10495,10498,10501,10504,10507],{"className":10491},[1187,1225],[1129,10493,1586],{"className":10494},[1187,1191,1225],[1129,10496,2466],{"className":10497},[2634,1225],[1129,10499,1348],{"className":10500},[1187,1225],[1129,10502,1344],{"className":10503},[1373,1225],[1129,10505,1586],{"className":10506},[1187,1191,1225],[1129,10508,2475],{"className":10509},[2667,1225],[1129,10511,10512,10515],{"style":3159},[1129,10513],{"className":10514,"style":3088},[1217],[1129,10516],{"className":10517,"style":3167},[3166],[1129,10519,10520,10523],{"style":8212},[1129,10521],{"className":10522,"style":3088},[1217],[1129,10524,10526],{"className":10525},[1222,1223,1224,1225],[1129,10527,10529,10532,10535],{"className":10528},[1187,1225],[1129,10530,1586],{"className":10531},[1187,1191,1225],[1129,10533,1344],{"className":10534},[1373,1225],[1129,10536,6646],{"className":10537,"style":2603},[1187,1191,1225],[1129,10539,1254],{"className":10540},[1253],[1129,10542,10544],{"className":10543},[1205],[1129,10545,10547],{"className":10546,"style":8234},[1209],[1129,10548],{},[1129,10550],{"className":10551},[2667,3068],"，对 ",[1129,10554,10556,10569],{"className":10555},[1132],[1129,10557,10559],{"className":10558},[1136],[1138,10560,10561],{"xmlns":1140},[1142,10562,10563,10567],{},[1145,10564,10565],{},[1151,10566,1586],{},[1166,10568,1586],{"encoding":1168},[1129,10570,10572],{"className":10571,"ariaHidden":1174},[1173],[1129,10573,10575,10578],{"className":10574},[1178],[1129,10576],{"className":10577,"style":3696},[1182],[1129,10579,1586],{"className":10580},[1187,1191]," 积分得：",[1101,10583,10584],{},[1129,10585,10587,10650],{"className":10586},[1132],[1129,10588,10590],{"className":10589},[1136],[1138,10591,10592],{"xmlns":1140},[1142,10593,10594,10647],{},[1145,10595,10596,10598,10600,10602,10642,10644],{},[1151,10597,2450],{},[1342,10599,1884],{},[1342,10601,1344],{},[1145,10603,10604,10606,10608,10610,10612,10614,10616,10618,10620,10622,10624,10626,10628,10630,10632,10634,10636,10638,10640],{},[1342,10605,6643],{"fence":1174},[1151,10607,6646],{},[1151,10609,6649],{},[1342,10611,6652],{},[1151,10613,1586],{},[1342,10615,1921],{},[1342,10617,2466],{"stretchy":2465},[1346,10619,1348],{},[1342,10621,1344],{},[1151,10623,6646],{},[1342,10625,2475],{"stretchy":2465},[1151,10627,6649],{},[1342,10629,6652],{},[1342,10631,2466],{"stretchy":2465},[1346,10633,1348],{},[1342,10635,1344],{},[1151,10637,1586],{},[1342,10639,2475],{"stretchy":2465},[1342,10641,6683],{"fence":1174},[1342,10643,1921],{},[5470,10645,10646],{},"const",[1166,10648,10649],{"encoding":1168},"C = -\\left[ y \\ln a + (1-y) \\ln(1-a) \\right] + \\text{const}",[1129,10651,10653,10671,10773],{"className":10652,"ariaHidden":1174},[1173],[1129,10654,10656,10659,10662,10665,10668],{"className":10655},[1178],[1129,10657],{"className":10658,"style":5901},[1182],[1129,10660,2450],{"className":10661,"style":2580},[1187,1191],[1129,10663],{"className":10664,"style":1996},[1368],[1129,10666,1884],{"className":10667},[2000],[1129,10669],{"className":10670,"style":1996},[1368],[1129,10672,10674,10677,10680,10683,10764,10767,10770],{"className":10673},[1178],[1129,10675],{"className":10676,"style":6081},[1182],[1129,10678,1344],{"className":10679},[1187],[1129,10681],{"className":10682,"style":2061},[1368],[1129,10684,10686,10689,10692,10695,10698,10701,10704,10707,10710,10713,10716,10719,10722,10725,10728,10731,10734,10737,10740,10743,10746,10749,10752,10755,10758,10761],{"className":10685},[3793],[1129,10687,6643],{"className":10688,"style":6843},[2634,6842],[1129,10690,6646],{"className":10691,"style":2603},[1187,1191],[1129,10693],{"className":10694,"style":2061},[1368],[1129,10696,6649],{"className":10697},[2014],[1129,10699],{"className":10700,"style":2061},[1368],[1129,10702,1586],{"className":10703},[1187,1191],[1129,10705],{"className":10706,"style":1369},[1368],[1129,10708,1921],{"className":10709},[1373],[1129,10711],{"className":10712,"style":1369},[1368],[1129,10714,2466],{"className":10715},[2634],[1129,10717,1348],{"className":10718},[1187],[1129,10720],{"className":10721,"style":1369},[1368],[1129,10723,1344],{"className":10724},[1373],[1129,10726],{"className":10727,"style":1369},[1368],[1129,10729,6646],{"className":10730,"style":2603},[1187,1191],[1129,10732,2475],{"className":10733},[2667],[1129,10735],{"className":10736,"style":2061},[1368],[1129,10738,6649],{"className":10739},[2014],[1129,10741,2466],{"className":10742},[2634],[1129,10744,1348],{"className":10745},[1187],[1129,10747],{"className":10748,"style":1369},[1368],[1129,10750,1344],{"className":10751},[1373],[1129,10753],{"className":10754,"style":1369},[1368],[1129,10756,1586],{"className":10757},[1187,1191],[1129,10759,2475],{"className":10760},[2667],[1129,10762,6683],{"className":10763,"style":6843},[2667,6842],[1129,10765],{"className":10766,"style":1369},[1368],[1129,10768,1921],{"className":10769},[1373],[1129,10771],{"className":10772,"style":1369},[1368],[1129,10774,10776,10780],{"className":10775},[1178],[1129,10777],{"className":10778,"style":10779},[1182],"height:0.6151em;",[1129,10781,10783],{"className":10782},[1187,5683],[1129,10784,10646],{"className":10785},[1187],[1096,10787,10789],{"id":10788},"_26-多神经元推广","2.6 多神经元推广",[1101,10791,10792],{},"对于输出层有多个神经元的网络，交叉熵推广为：",[1101,10794,10795],{},[1129,10796,10798,10894],{"className":10797},[1132],[1129,10799,10801],{"className":10800},[1136],[1138,10802,10803],{"xmlns":1140},[1142,10804,10805,10891],{},[1145,10806,10807,10809,10811,10813,10819,10825,10831],{},[1151,10808,2450],{},[1342,10810,1884],{},[1342,10812,1344],{},[3018,10814,10815,10817],{},[1346,10816,1348],{},[1151,10818,6632],{},[1886,10820,10821,10823],{},[1342,10822,1890],{},[1151,10824,3638],{},[1886,10826,10827,10829],{},[1342,10828,1890],{},[1151,10830,1158],{},[1145,10832,10833,10835,10841,10843,10845,10853,10855,10857,10859,10861,10867,10869,10871,10873,10875,10877,10879,10887,10889],{},[1342,10834,6643],{"fence":1174},[1886,10836,10837,10839],{},[1151,10838,6646],{},[1151,10840,1158],{},[1151,10842,6649],{},[1342,10844,6652],{},[1148,10846,10847,10849,10851],{},[1151,10848,1586],{},[1151,10850,1158],{},[1151,10852,2437],{},[1342,10854,1921],{},[1342,10856,2466],{"stretchy":2465},[1346,10858,1348],{},[1342,10860,1344],{},[1886,10862,10863,10865],{},[1151,10864,6646],{},[1151,10866,1158],{},[1342,10868,2475],{"stretchy":2465},[1151,10870,6649],{},[1342,10872,6652],{},[1342,10874,2466],{"stretchy":2465},[1346,10876,1348],{},[1342,10878,1344],{},[1148,10880,10881,10883,10885],{},[1151,10882,1586],{},[1151,10884,1158],{},[1151,10886,2437],{},[1342,10888,2475],{"stretchy":2465},[1342,10890,6683],{"fence":1174},[1166,10892,10893],{"encoding":1168},"C = -\\frac{1}{n} \\sum_x \\sum_j \\left[ y_j \\ln a^L_j + (1-y_j) \\ln(1-a^L_j) \\right]",[1129,10895,10897,10915],{"className":10896,"ariaHidden":1174},[1173],[1129,10898,10900,10903,10906,10909,10912],{"className":10899},[1178],[1129,10901],{"className":10902,"style":5901},[1182],[1129,10904,2450],{"className":10905,"style":2580},[1187,1191],[1129,10907],{"className":10908,"style":1996},[1368],[1129,10910,1884],{"className":10911},[2000],[1129,10913],{"className":10914,"style":1996},[1368],[1129,10916,10918,10922,10925,10993,10996,11036,11039,11080,11083],{"className":10917},[1178],[1129,10919],{"className":10920,"style":10921},[1182],"height:1.2858em;vertical-align:-0.4358em;",[1129,10923,1344],{"className":10924},[1187],[1129,10926,10928,10931,10990],{"className":10927},[1187],[1129,10929],{"className":10930},[2634,3068],[1129,10932,10934],{"className":10933},[3018],[1129,10935,10937,10982],{"className":10936},[1200,1201],[1129,10938,10940,10979],{"className":10939},[1205],[1129,10941,10943,10957,10965],{"className":10942,"style":6736},[1209],[1129,10944,10945,10948],{"style":6739},[1129,10946],{"className":10947,"style":3088},[1217],[1129,10949,10951],{"className":10950},[1222,1223,1224,1225],[1129,10952,10954],{"className":10953},[1187,1225],[1129,10955,6632],{"className":10956},[1187,1191,1225],[1129,10958,10959,10962],{"style":3159},[1129,10960],{"className":10961,"style":3088},[1217],[1129,10963],{"className":10964,"style":3167},[3166],[1129,10966,10967,10970],{"style":3170},[1129,10968],{"className":10969,"style":3088},[1217],[1129,10971,10973],{"className":10972},[1222,1223,1224,1225],[1129,10974,10976],{"className":10975},[1187,1225],[1129,10977,1348],{"className":10978},[1187,1225],[1129,10980,1254],{"className":10981},[1253],[1129,10983,10985],{"className":10984},[1205],[1129,10986,10988],{"className":10987,"style":6783},[1209],[1129,10989],{},[1129,10991],{"className":10992},[2667,3068],[1129,10994],{"className":10995,"style":2061},[1368],[1129,10997,10999,11002],{"className":10998},[2014],[1129,11000,1890],{"className":11001,"style":2020},[2014,2018,2019],[1129,11003,11005],{"className":11004},[1196],[1129,11006,11008,11028],{"className":11007},[1200,1201],[1129,11009,11011,11025],{"className":11010},[1205],[1129,11012,11014],{"className":11013,"style":6810},[1209],[1129,11015,11016,11019],{"style":2036},[1129,11017],{"className":11018,"style":1218},[1217],[1129,11020,11022],{"className":11021},[1222,1223,1224,1225],[1129,11023,3638],{"className":11024},[1187,1191,1225],[1129,11026,1254],{"className":11027},[1253],[1129,11029,11031],{"className":11030},[1205],[1129,11032,11034],{"className":11033,"style":2055},[1209],[1129,11035],{},[1129,11037],{"className":11038,"style":2061},[1368],[1129,11040,11042,11045],{"className":11041},[2014],[1129,11043,1890],{"className":11044,"style":2020},[2014,2018,2019],[1129,11046,11048],{"className":11047},[1196],[1129,11049,11051,11072],{"className":11050},[1200,1201],[1129,11052,11054,11069],{"className":11053},[1205],[1129,11055,11058],{"className":11056,"style":11057},[1209],"height:0.162em;",[1129,11059,11060,11063],{"style":2036},[1129,11061],{"className":11062,"style":1218},[1217],[1129,11064,11066],{"className":11065},[1222,1223,1224,1225],[1129,11067,1158],{"className":11068,"style":1232},[1187,1191,1225],[1129,11070,1254],{"className":11071},[1253],[1129,11073,11075],{"className":11074},[1205],[1129,11076,11078],{"className":11077,"style":5696},[1209],[1129,11079],{},[1129,11081],{"className":11082,"style":2061},[1368],[1129,11084,11086,11092,11133,11136,11139,11142,11193,11196,11199,11202,11205,11208,11211,11214,11217,11257,11260,11263,11266,11269,11272,11275,11278,11281,11332,11335],{"className":11085},[3793],[1129,11087,11089],{"className":11088,"style":6843},[2634,6842],[1129,11090,6643],{"className":11091},[8158,3129],[1129,11093,11095,11098],{"className":11094},[1187],[1129,11096,6646],{"className":11097,"style":2603},[1187,1191],[1129,11099,11101],{"className":11100},[1196],[1129,11102,11104,11125],{"className":11103},[1200,1201],[1129,11105,11107,11122],{"className":11106},[1205],[1129,11108,11110],{"className":11109,"style":7442},[1209],[1129,11111,11113,11116],{"style":11112},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1129,11114],{"className":11115,"style":1218},[1217],[1129,11117,11119],{"className":11118},[1222,1223,1224,1225],[1129,11120,1158],{"className":11121,"style":1232},[1187,1191,1225],[1129,11123,1254],{"className":11124},[1253],[1129,11126,11128],{"className":11127},[1205],[1129,11129,11131],{"className":11130,"style":7463},[1209],[1129,11132],{},[1129,11134],{"className":11135,"style":2061},[1368],[1129,11137,6649],{"className":11138},[2014],[1129,11140],{"className":11141,"style":2061},[1368],[1129,11143,11145,11148],{"className":11144},[1187],[1129,11146,1586],{"className":11147},[1187,1191],[1129,11149,11151],{"className":11150},[1196],[1129,11152,11154,11185],{"className":11153},[1200,1201],[1129,11155,11157,11182],{"className":11156},[1205],[1129,11158,11160,11171],{"className":11159,"style":2488},[1209],[1129,11161,11162,11165],{"style":1474},[1129,11163],{"className":11164,"style":1218},[1217],[1129,11166,11168],{"className":11167},[1222,1223,1224,1225],[1129,11169,1158],{"className":11170,"style":1232},[1187,1191,1225],[1129,11172,11173,11176],{"style":1239},[1129,11174],{"className":11175,"style":1218},[1217],[1129,11177,11179],{"className":11178},[1222,1223,1224,1225],[1129,11180,2437],{"className":11181},[1187,1191,1225],[1129,11183,1254],{"className":11184},[1253],[1129,11186,11188],{"className":11187},[1205],[1129,11189,11191],{"className":11190,"style":1504},[1209],[1129,11192],{},[1129,11194],{"className":11195,"style":1369},[1368],[1129,11197,1921],{"className":11198},[1373],[1129,11200],{"className":11201,"style":1369},[1368],[1129,11203,2466],{"className":11204},[2634],[1129,11206,1348],{"className":11207},[1187],[1129,11209],{"className":11210,"style":1369},[1368],[1129,11212,1344],{"className":11213},[1373],[1129,11215],{"className":11216,"style":1369},[1368],[1129,11218,11220,11223],{"className":11219},[1187],[1129,11221,6646],{"className":11222,"style":2603},[1187,1191],[1129,11224,11226],{"className":11225},[1196],[1129,11227,11229,11249],{"className":11228},[1200,1201],[1129,11230,11232,11246],{"className":11231},[1205],[1129,11233,11235],{"className":11234,"style":7442},[1209],[1129,11236,11237,11240],{"style":11112},[1129,11238],{"className":11239,"style":1218},[1217],[1129,11241,11243],{"className":11242},[1222,1223,1224,1225],[1129,11244,1158],{"className":11245,"style":1232},[1187,1191,1225],[1129,11247,1254],{"className":11248},[1253],[1129,11250,11252],{"className":11251},[1205],[1129,11253,11255],{"className":11254,"style":7463},[1209],[1129,11256],{},[1129,11258,2475],{"className":11259},[2667],[1129,11261],{"className":11262,"style":2061},[1368],[1129,11264,6649],{"className":11265},[2014],[1129,11267,2466],{"className":11268},[2634],[1129,11270,1348],{"className":11271},[1187],[1129,11273],{"className":11274,"style":1369},[1368],[1129,11276,1344],{"className":11277},[1373],[1129,11279],{"className":11280,"style":1369},[1368],[1129,11282,11284,11287],{"className":11283},[1187],[1129,11285,1586],{"className":11286},[1187,1191],[1129,11288,11290],{"className":11289},[1196],[1129,11291,11293,11324],{"className":11292},[1200,1201],[1129,11294,11296,11321],{"className":11295},[1205],[1129,11297,11299,11310],{"className":11298,"style":2488},[1209],[1129,11300,11301,11304],{"style":1474},[1129,11302],{"className":11303,"style":1218},[1217],[1129,11305,11307],{"className":11306},[1222,1223,1224,1225],[1129,11308,1158],{"className":11309,"style":1232},[1187,1191,1225],[1129,11311,11312,11315],{"style":1239},[1129,11313],{"className":11314,"style":1218},[1217],[1129,11316,11318],{"className":11317},[1222,1223,1224,1225],[1129,11319,2437],{"className":11320},[1187,1191,1225],[1129,11322,1254],{"className":11323},[1253],[1129,11325,11327],{"className":11326},[1205],[1129,11328,11330],{"className":11329,"style":1504},[1209],[1129,11331],{},[1129,11333,2475],{"className":11334},[2667],[1129,11336,11338],{"className":11337,"style":6843},[2667,6842],[1129,11339,6683],{"className":11340},[8158,3129],[1101,11342,6921,11343,11371],{},[1129,11344,11346,11359],{"className":11345},[1132],[1129,11347,11349],{"className":11348},[1136],[1138,11350,11351],{"xmlns":1140},[1142,11352,11353,11357],{},[1145,11354,11355],{},[1151,11356,1158],{},[1166,11358,1158],{"encoding":1168},[1129,11360,11362],{"className":11361,"ariaHidden":1174},[1173],[1129,11363,11365,11368],{"className":11364},[1178],[1129,11366],{"className":11367,"style":1322},[1182],[1129,11369,1158],{"className":11370,"style":1232},[1187,1191]," 遍历输出层所有神经元。",[5907,11373],{},[1091,11375,11377],{"id":11376},"三softmax-与对数似然","三、Softmax 与对数似然",[1096,11379,11381],{"id":11380},"_31-softmax-输出层","3.1 Softmax 输出层",[1101,11383,11384,11385,11388,11389,11473,11474],{},"Softmax 是一种",[2405,11386,11387],{},"输出层激活函数","，用来替代 sigmoid。它把输出层的原始值 ",[1129,11390,11392,11412],{"className":11391},[1132],[1129,11393,11395],{"className":11394},[1136],[1138,11396,11397],{"xmlns":1140},[1142,11398,11399,11409],{},[1145,11400,11401],{},[1148,11402,11403,11405,11407],{},[1151,11404,1733],{},[1151,11406,1158],{},[1151,11408,2437],{},[1166,11410,11411],{"encoding":1168},"z^L_j",[1129,11413,11415],{"className":11414,"ariaHidden":1174},[1173],[1129,11416,11418,11422],{"className":11417},[1178],[1129,11419],{"className":11420,"style":11421},[1182],"height:1.2361em;vertical-align:-0.3948em;",[1129,11423,11425,11428],{"className":11424},[1187],[1129,11426,1733],{"className":11427,"style":1756},[1187,1191],[1129,11429,11431],{"className":11430},[1196],[1129,11432,11434,11465],{"className":11433},[1200,1201],[1129,11435,11437,11462],{"className":11436},[1205],[1129,11438,11440,11451],{"className":11439,"style":2488},[1209],[1129,11441,11442,11445],{"style":1771},[1129,11443],{"className":11444,"style":1218},[1217],[1129,11446,11448],{"className":11447},[1222,1223,1224,1225],[1129,11449,1158],{"className":11450,"style":1232},[1187,1191,1225],[1129,11452,11453,11456],{"style":1239},[1129,11454],{"className":11455,"style":1218},[1217],[1129,11457,11459],{"className":11458},[1222,1223,1224,1225],[1129,11460,2437],{"className":11461},[1187,1191,1225],[1129,11463,1254],{"className":11464},[1253],[1129,11466,11468],{"className":11467},[1205],[1129,11469,11471],{"className":11470,"style":1504},[1209],[1129,11472],{}," 转换成",[2405,11475,11476],{},"概率分布",[1101,11478,11479],{},[1129,11480,11482,11539],{"className":11481},[1132],[1129,11483,11485],{"className":11484},[1136],[1138,11486,11487],{"xmlns":1140},[1142,11488,11489,11536],{},[1145,11490,11491,11499,11501],{},[1148,11492,11493,11495,11497],{},[1151,11494,1586],{},[1151,11496,1158],{},[1151,11498,2437],{},[1342,11500,1884],{},[3018,11502,11503,11516],{},[2431,11504,11505,11508],{},[1151,11506,11507],{},"e",[1148,11509,11510,11512,11514],{},[1151,11511,1733],{},[1151,11513,1158],{},[1151,11515,2437],{},[1145,11517,11518,11524],{},[1886,11519,11520,11522],{},[1342,11521,1890],{},[1151,11523,1161],{},[2431,11525,11526,11528],{},[1151,11527,11507],{},[1148,11529,11530,11532,11534],{},[1151,11531,1733],{},[1151,11533,1161],{},[1151,11535,2437],{},[1166,11537,11538],{"encoding":1168},"a^L_j = \\frac{e^{z^L_j}}{\\sum_{k} e^{z^L_k}}",[1129,11540,11542,11608],{"className":11541,"ariaHidden":1174},[1173],[1129,11543,11545,11548,11599,11602,11605],{"className":11544},[1178],[1129,11546],{"className":11547,"style":11421},[1182],[1129,11549,11551,11554],{"className":11550},[1187],[1129,11552,1586],{"className":11553},[1187,1191],[1129,11555,11557],{"className":11556},[1196],[1129,11558,11560,11591],{"className":11559},[1200,1201],[1129,11561,11563,11588],{"className":11562},[1205],[1129,11564,11566,11577],{"className":11565,"style":2488},[1209],[1129,11567,11568,11571],{"style":1474},[1129,11569],{"className":11570,"style":1218},[1217],[1129,11572,11574],{"className":11573},[1222,1223,1224,1225],[1129,11575,1158],{"className":11576,"style":1232},[1187,1191,1225],[1129,11578,11579,11582],{"style":1239},[1129,11580],{"className":11581,"style":1218},[1217],[1129,11583,11585],{"className":11584},[1222,1223,1224,1225],[1129,11586,2437],{"className":11587},[1187,1191,1225],[1129,11589,1254],{"className":11590},[1253],[1129,11592,11594],{"className":11593},[1205],[1129,11595,11597],{"className":11596,"style":1504},[1209],[1129,11598],{},[1129,11600],{"className":11601,"style":1996},[1368],[1129,11603,1884],{"className":11604},[2000],[1129,11606],{"className":11607,"style":1996},[1368],[1129,11609,11611,11615],{"className":11610},[1178],[1129,11612],{"className":11613,"style":11614},[1182],"height:2.2334em;vertical-align:-0.8973em;",[1129,11616,11618,11621,11891],{"className":11617},[1187],[1129,11619],{"className":11620},[2634,3068],[1129,11622,11624],{"className":11623},[3018],[1129,11625,11627,11882],{"className":11626},[1200,1201],[1129,11628,11630,11879],{"className":11629},[1205],[1129,11631,11634,11778,11786],{"className":11632,"style":11633},[1209],"height:1.3361em;",[1129,11635,11637,11640],{"style":11636},"top:-2.3277em;",[1129,11638],{"className":11639,"style":3088},[1217],[1129,11641,11643],{"className":11642},[1222,1223,1224,1225],[1129,11644,11646,11692,11696],{"className":11645},[1187,1225],[1129,11647,11649,11652],{"className":11648},[2014,1225],[1129,11650,1890],{"className":11651,"style":2020},[2014,2018,2019,1225],[1129,11653,11655],{"className":11654},[1196],[1129,11656,11658,11683],{"className":11657},[1200,1201],[1129,11659,11661,11680],{"className":11660},[1205],[1129,11662,11665],{"className":11663,"style":11664},[1209],"height:0.1746em;",[1129,11666,11668,11671],{"style":11667},"top:-2.1786em;margin-left:0em;margin-right:0.0714em;",[1129,11669],{"className":11670,"style":3124},[1217],[1129,11672,11674],{"className":11673},[1222,3128,3129,1225],[1129,11675,11677],{"className":11676},[1187,1225],[1129,11678,1161],{"className":11679,"style":1236},[1187,1191,1225],[1129,11681,1254],{"className":11682},[1253],[1129,11684,11686],{"className":11685},[1205],[1129,11687,11690],{"className":11688,"style":11689},[1209],"height:0.3214em;",[1129,11691],{},[1129,11693],{"className":11694,"style":11695},[1368,1225],"margin-right:0.1952em;",[1129,11697,11699,11702],{"className":11698},[1187,1225],[1129,11700,11507],{"className":11701},[1187,1191,1225],[1129,11703,11705],{"className":11704},[1196],[1129,11706,11708],{"className":11707},[1200],[1129,11709,11711],{"className":11710},[1205],[1129,11712,11715],{"className":11713,"style":11714},[1209],"height:1.2319em;",[1129,11716,11718,11722],{"style":11717},"top:-3.2319em;margin-right:0.0714em;",[1129,11719],{"className":11720,"style":11721},[1217],"height:2.7344em;",[1129,11723,11725],{"className":11724},[1222,3128,3129,1225],[1129,11726,11728],{"className":11727},[1187,1225],[1129,11729,11731,11734],{"className":11730},[1187,1225],[1129,11732,1733],{"className":11733,"style":1756},[1187,1191,1225],[1129,11735,11737],{"className":11736},[1196],[1129,11738,11740,11769],{"className":11739},[1200,1201],[1129,11741,11743,11766],{"className":11742},[1205],[1129,11744,11747,11757],{"className":11745,"style":11746},[1209],"height:1.0281em;",[1129,11748,11750,11754],{"style":11749},"top:-2.1488em;margin-left:-0.044em;margin-right:0.1em;",[1129,11751],{"className":11752,"style":11753},[1217],"height:2.6944em;",[1129,11755,1161],{"className":11756,"style":1236},[1187,1191,1225],[1129,11758,11760,11763],{"style":11759},"top:-3.0392em;margin-right:0.1em;",[1129,11761],{"className":11762,"style":11753},[1217],[1129,11764,2437],{"className":11765},[1187,1191,1225],[1129,11767,1254],{"className":11768},[1253],[1129,11770,11772],{"className":11771},[1205],[1129,11773,11776],{"className":11774,"style":11775},[1209],"height:0.5456em;",[1129,11777],{},[1129,11779,11780,11783],{"style":3159},[1129,11781],{"className":11782,"style":3088},[1217],[1129,11784],{"className":11785,"style":3167},[3166],[1129,11787,11788,11791],{"style":3170},[1129,11789],{"className":11790,"style":3088},[1217],[1129,11792,11794],{"className":11793},[1222,1223,1224,1225],[1129,11795,11797],{"className":11796},[1187,1225],[1129,11798,11800,11803],{"className":11799},[1187,1225],[1129,11801,11507],{"className":11802},[1187,1191,1225],[1129,11804,11806],{"className":11805},[1196],[1129,11807,11809],{"className":11808},[1200],[1129,11810,11812],{"className":11811},[1205],[1129,11813,11816],{"className":11814,"style":11815},[1209],"height:1.3458em;",[1129,11817,11819,11823],{"style":11818},"top:-3.3458em;margin-right:0.0714em;",[1129,11820],{"className":11821,"style":11822},[1217],"height:2.7767em;",[1129,11824,11826],{"className":11825},[1222,3128,3129,1225],[1129,11827,11829],{"className":11828},[1187,1225],[1129,11830,11832,11835],{"className":11831},[1187,1225],[1129,11833,1733],{"className":11834,"style":1756},[1187,1191,1225],[1129,11836,11838],{"className":11837},[1196],[1129,11839,11841,11870],{"className":11840},[1200,1201],[1129,11842,11844,11867],{"className":11843},[1205],[1129,11845,11848,11858],{"className":11846,"style":11847},[1209],"height:1.0873em;",[1129,11849,11851,11855],{"style":11850},"top:-2.2318em;margin-left:-0.044em;margin-right:0.1em;",[1129,11852],{"className":11853,"style":11854},[1217],"height:2.6833em;",[1129,11856,1158],{"className":11857,"style":1232},[1187,1191,1225],[1129,11859,11861,11864],{"style":11860},"top:-3.0873em;margin-right:0.1em;",[1129,11862],{"className":11863,"style":11854},[1217],[1129,11865,2437],{"className":11866},[1187,1191,1225],[1129,11868,1254],{"className":11869},[1253],[1129,11871,11873],{"className":11872},[1205],[1129,11874,11877],{"className":11875,"style":11876},[1209],"height:0.646em;",[1129,11878],{},[1129,11880,1254],{"className":11881},[1253],[1129,11883,11885],{"className":11884},[1205],[1129,11886,11889],{"className":11887,"style":11888},[1209],"height:0.8973em;",[1129,11890],{},[1129,11892],{"className":11893},[2667,3068],[1101,11895,11896,11897],{},"输出范围：每个 ",[1129,11898,11900,11933],{"className":11899},[1132],[1129,11901,11903],{"className":11902},[1136],[1138,11904,11905],{"xmlns":1140},[1142,11906,11907,11930],{},[1145,11908,11909,11917,11920,11922,11924,11926,11928],{},[1148,11910,11911,11913,11915],{},[1151,11912,1586],{},[1151,11914,1158],{},[1151,11916,2437],{},[1342,11918,11919],{},"∈",[1342,11921,2466],{"stretchy":2465},[1346,11923,6526],{},[1342,11925,3727],{"separator":1174},[1346,11927,1348],{},[1342,11929,2475],{"stretchy":2465},[1166,11931,11932],{"encoding":1168},"a^L_j \\in (0, 1)",[1129,11934,11936,12002],{"className":11935,"ariaHidden":1174},[1173],[1129,11937,11939,11942,11993,11996,11999],{"className":11938},[1178],[1129,11940],{"className":11941,"style":11421},[1182],[1129,11943,11945,11948],{"className":11944},[1187],[1129,11946,1586],{"className":11947},[1187,1191],[1129,11949,11951],{"className":11950},[1196],[1129,11952,11954,11985],{"className":11953},[1200,1201],[1129,11955,11957,11982],{"className":11956},[1205],[1129,11958,11960,11971],{"className":11959,"style":2488},[1209],[1129,11961,11962,11965],{"style":1474},[1129,11963],{"className":11964,"style":1218},[1217],[1129,11966,11968],{"className":11967},[1222,1223,1224,1225],[1129,11969,1158],{"className":11970,"style":1232},[1187,1191,1225],[1129,11972,11973,11976],{"style":1239},[1129,11974],{"className":11975,"style":1218},[1217],[1129,11977,11979],{"className":11978},[1222,1223,1224,1225],[1129,11980,2437],{"className":11981},[1187,1191,1225],[1129,11983,1254],{"className":11984},[1253],[1129,11986,11988],{"className":11987},[1205],[1129,11989,11991],{"className":11990,"style":1504},[1209],[1129,11992],{},[1129,11994],{"className":11995,"style":1996},[1368],[1129,11997,11919],{"className":11998},[2000],[1129,12000],{"className":12001,"style":1996},[1368],[1129,12003,12005,12008,12011,12014,12017,12020,12023],{"className":12004},[1178],[1129,12006],{"className":12007,"style":6081},[1182],[1129,12009,2466],{"className":12010},[2634],[1129,12012,6526],{"className":12013},[1187],[1129,12015,3727],{"className":12016},[3777],[1129,12018],{"className":12019,"style":2061},[1368],[1129,12021,1348],{"className":12022},[1187],[1129,12024,2475],{"className":12025},[2667],[1101,12027,12028,12029,12184],{},"和为 1：",[1129,12030,12032,12062],{"className":12031},[1132],[1129,12033,12035],{"className":12034},[1136],[1138,12036,12037],{"xmlns":1140},[1142,12038,12039,12059],{},[1145,12040,12041,12047,12055,12057],{},[1886,12042,12043,12045],{},[1342,12044,1890],{},[1151,12046,1158],{},[1148,12048,12049,12051,12053],{},[1151,12050,1586],{},[1151,12052,1158],{},[1151,12054,2437],{},[1342,12056,1884],{},[1346,12058,1348],{},[1166,12060,12061],{"encoding":1168},"\\sum_j a^L_j = 1",[1129,12063,12065,12175],{"className":12064,"ariaHidden":1174},[1173],[1129,12066,12068,12072,12112,12115,12166,12169,12172],{"className":12067},[1178],[1129,12069],{"className":12070,"style":12071},[1182],"height:1.2771em;vertical-align:-0.4358em;",[1129,12073,12075,12078],{"className":12074},[2014],[1129,12076,1890],{"className":12077,"style":2020},[2014,2018,2019],[1129,12079,12081],{"className":12080},[1196],[1129,12082,12084,12104],{"className":12083},[1200,1201],[1129,12085,12087,12101],{"className":12086},[1205],[1129,12088,12090],{"className":12089,"style":11057},[1209],[1129,12091,12092,12095],{"style":2036},[1129,12093],{"className":12094,"style":1218},[1217],[1129,12096,12098],{"className":12097},[1222,1223,1224,1225],[1129,12099,1158],{"className":12100,"style":1232},[1187,1191,1225],[1129,12102,1254],{"className":12103},[1253],[1129,12105,12107],{"className":12106},[1205],[1129,12108,12110],{"className":12109,"style":5696},[1209],[1129,12111],{},[1129,12113],{"className":12114,"style":2061},[1368],[1129,12116,12118,12121],{"className":12117},[1187],[1129,12119,1586],{"className":12120},[1187,1191],[1129,12122,12124],{"className":12123},[1196],[1129,12125,12127,12158],{"className":12126},[1200,1201],[1129,12128,12130,12155],{"className":12129},[1205],[1129,12131,12133,12144],{"className":12132,"style":2488},[1209],[1129,12134,12135,12138],{"style":1474},[1129,12136],{"className":12137,"style":1218},[1217],[1129,12139,12141],{"className":12140},[1222,1223,1224,1225],[1129,12142,1158],{"className":12143,"style":1232},[1187,1191,1225],[1129,12145,12146,12149],{"style":1239},[1129,12147],{"className":12148,"style":1218},[1217],[1129,12150,12152],{"className":12151},[1222,1223,1224,1225],[1129,12153,2437],{"className":12154},[1187,1191,1225],[1129,12156,1254],{"className":12157},[1253],[1129,12159,12161],{"className":12160},[1205],[1129,12162,12164],{"className":12163,"style":1504},[1209],[1129,12165],{},[1129,12167],{"className":12168,"style":1996},[1368],[1129,12170,1884],{"className":12171},[2000],[1129,12173],{"className":12174,"style":1996},[1368],[1129,12176,12178,12181],{"className":12177},[1178],[1129,12179],{"className":12180,"style":1383},[1182],[1129,12182,1348],{"className":12183},[1187],"（天然是概率分布）",[1101,12186,12187,12188,12216],{},"放大差异：",[1129,12189,12191,12204],{"className":12190},[1132],[1129,12192,12194],{"className":12193},[1136],[1138,12195,12196],{"xmlns":1140},[1142,12197,12198,12202],{},[1145,12199,12200],{},[1151,12201,1733],{},[1166,12203,1733],{"encoding":1168},[1129,12205,12207],{"className":12206,"ariaHidden":1174},[1173],[1129,12208,12210,12213],{"className":12209},[1178],[1129,12211],{"className":12212,"style":3696},[1182],[1129,12214,1733],{"className":12215,"style":1756},[1187,1191]," 最大的那个类别会得到最大的概率",[1101,12218,12219],{},"假设输出层有 3 个神经元（3 分类），加权输入为：",[1101,12221,12222],{},[1129,12223,12225,12266],{"className":12224},[1132],[1129,12226,12228],{"className":12227},[1136],[1138,12229,12230],{"xmlns":1140},[1142,12231,12232,12263],{},[1145,12233,12234,12240,12242,12244,12246,12248,12251,12254,12256,12258,12261],{},[2431,12235,12236,12238],{},[1151,12237,1733],{},[1151,12239,2437],{},[1342,12241,1884],{},[1342,12243,2466],{"stretchy":2465},[1346,12245,6197],{},[1342,12247,3727],{"separator":1174},[5470,12249,12250],{}," ",[1346,12252,12253],{},"1.0",[1342,12255,3727],{"separator":1174},[5470,12257,12250],{},[1346,12259,12260],{},"0.5",[1342,12262,2475],{"stretchy":2465},[1166,12264,12265],{"encoding":1168},"z^L = (2.0, \\ 1.0, \\ 0.5)",[1129,12267,12269,12313],{"className":12268,"ariaHidden":1174},[1173],[1129,12270,12272,12275,12304,12307,12310],{"className":12271},[1178],[1129,12273],{"className":12274,"style":2488},[1182],[1129,12276,12278,12281],{"className":12277},[1187],[1129,12279,1733],{"className":12280,"style":1756},[1187,1191],[1129,12282,12284],{"className":12283},[1196],[1129,12285,12287],{"className":12286},[1200],[1129,12288,12290],{"className":12289},[1205],[1129,12291,12293],{"className":12292,"style":2488},[1209],[1129,12294,12295,12298],{"style":1239},[1129,12296],{"className":12297,"style":1218},[1217],[1129,12299,12301],{"className":12300},[1222,1223,1224,1225],[1129,12302,2437],{"className":12303},[1187,1191,1225],[1129,12305],{"className":12306,"style":1996},[1368],[1129,12308,1884],{"className":12309},[2000],[1129,12311],{"className":12312,"style":1996},[1368],[1129,12314,12316,12319,12322,12325,12328,12331,12334,12337,12340,12343,12346,12349],{"className":12315},[1178],[1129,12317],{"className":12318,"style":6081},[1182],[1129,12320,2466],{"className":12321},[2634],[1129,12323,6197],{"className":12324},[1187],[1129,12326,3727],{"className":12327},[3777],[1129,12329,12250],{"className":12330},[1368],[1129,12332],{"className":12333,"style":2061},[1368],[1129,12335,12253],{"className":12336},[1187],[1129,12338,3727],{"className":12339},[3777],[1129,12341,12250],{"className":12342},[1368],[1129,12344],{"className":12345,"style":2061},[1368],[1129,12347,12260],{"className":12348},[1187],[1129,12350,2475],{"className":12351},[2667],[1101,12353,12354],{},"计算 softmax：",[1101,12356,12357],{},[1129,12358,12360,12434],{"className":12359},[1132],[1129,12361,12363],{"className":12362},[1136],[1138,12364,12365],{"xmlns":1140},[1142,12366,12367,12431],{},[1145,12368,12369,12375,12387,12389,12395,12397,12403,12405,12411,12413,12416,12418,12421,12423,12426,12428],{},[1886,12370,12371,12373],{},[1342,12372,1890],{},[1151,12374,1161],{},[2431,12376,12377,12379],{},[1151,12378,11507],{},[1148,12380,12381,12383,12385],{},[1151,12382,1733],{},[1151,12384,1161],{},[1151,12386,2437],{},[1342,12388,1884],{},[2431,12390,12391,12393],{},[1151,12392,11507],{},[1346,12394,6197],{},[1342,12396,1921],{},[2431,12398,12399,12401],{},[1151,12400,11507],{},[1346,12402,12253],{},[1342,12404,1921],{},[2431,12406,12407,12409],{},[1151,12408,11507],{},[1346,12410,12260],{},[1342,12412,1884],{},[1346,12414,12415],{},"7.389",[1342,12417,1921],{},[1346,12419,12420],{},"2.718",[1342,12422,1921],{},[1346,12424,12425],{},"1.649",[1342,12427,1884],{},[1346,12429,12430],{},"11.756",[1166,12432,12433],{"encoding":1168},"\\sum_k e^{z^L_k} = e^{2.0} + e^{1.0} + e^{0.5} = 7.389 + 2.718 + 1.649 = 11.756",[1129,12435,12437,12581,12629,12676,12723,12741,12759,12777],{"className":12436,"ariaHidden":1174},[1173],[1129,12438,12440,12444,12484,12487,12572,12575,12578],{"className":12439},[1178],[1129,12441],{"className":12442,"style":12443},[1182],"height:1.3061em;vertical-align:-0.2997em;",[1129,12445,12447,12450],{"className":12446},[2014],[1129,12448,1890],{"className":12449,"style":2020},[2014,2018,2019],[1129,12451,12453],{"className":12452},[1196],[1129,12454,12456,12476],{"className":12455},[1200,1201],[1129,12457,12459,12473],{"className":12458},[1205],[1129,12460,12462],{"className":12461,"style":2033},[1209],[1129,12463,12464,12467],{"style":2036},[1129,12465],{"className":12466,"style":1218},[1217],[1129,12468,12470],{"className":12469},[1222,1223,1224,1225],[1129,12471,1161],{"className":12472,"style":1236},[1187,1191,1225],[1129,12474,1254],{"className":12475},[1253],[1129,12477,12479],{"className":12478},[1205],[1129,12480,12482],{"className":12481,"style":2055},[1209],[1129,12483],{},[1129,12485],{"className":12486,"style":2061},[1368],[1129,12488,12490,12493],{"className":12489},[1187],[1129,12491,11507],{"className":12492},[1187,1191],[1129,12494,12496],{"className":12495},[1196],[1129,12497,12499],{"className":12498},[1200],[1129,12500,12502],{"className":12501},[1205],[1129,12503,12506],{"className":12504,"style":12505},[1209],"height:1.0064em;",[1129,12507,12508,12511],{"style":1239},[1129,12509],{"className":12510,"style":1218},[1217],[1129,12512,12514],{"className":12513},[1222,1223,1224,1225],[1129,12515,12517],{"className":12516},[1187,1225],[1129,12518,12520,12523],{"className":12519},[1187,1225],[1129,12521,1733],{"className":12522,"style":1756},[1187,1191,1225],[1129,12524,12526],{"className":12525},[1196],[1129,12527,12529,12563],{"className":12528},[1200,1201],[1129,12530,12532,12560],{"className":12531},[1205],[1129,12533,12536,12548],{"className":12534,"style":12535},[1209],"height:0.9191em;",[1129,12537,12539,12542],{"style":12538},"top:-2.214em;margin-left:-0.044em;margin-right:0.0714em;",[1129,12540],{"className":12541,"style":3124},[1217],[1129,12543,12545],{"className":12544},[1222,3128,3129,1225],[1129,12546,1161],{"className":12547,"style":1236},[1187,1191,1225],[1129,12549,12551,12554],{"style":12550},"top:-2.931em;margin-right:0.0714em;",[1129,12552],{"className":12553,"style":3124},[1217],[1129,12555,12557],{"className":12556},[1222,3128,3129,1225],[1129,12558,2437],{"className":12559},[1187,1191,1225],[1129,12561,1254],{"className":12562},[1253],[1129,12564,12566],{"className":12565},[1205],[1129,12567,12570],{"className":12568,"style":12569},[1209],"height:0.286em;",[1129,12571],{},[1129,12573],{"className":12574,"style":1996},[1368],[1129,12576,1884],{"className":12577},[2000],[1129,12579],{"className":12580,"style":1996},[1368],[1129,12582,12584,12588,12620,12623,12626],{"className":12583},[1178],[1129,12585],{"className":12586,"style":12587},[1182],"height:0.8974em;vertical-align:-0.0833em;",[1129,12589,12591,12594],{"className":12590},[1187],[1129,12592,11507],{"className":12593},[1187,1191],[1129,12595,12597],{"className":12596},[1196],[1129,12598,12600],{"className":12599},[1200],[1129,12601,12603],{"className":12602},[1205],[1129,12604,12606],{"className":12605,"style":3651},[1209],[1129,12607,12608,12611],{"style":1239},[1129,12609],{"className":12610,"style":1218},[1217],[1129,12612,12614],{"className":12613},[1222,1223,1224,1225],[1129,12615,12617],{"className":12616},[1187,1225],[1129,12618,6197],{"className":12619},[1187,1225],[1129,12621],{"className":12622,"style":1369},[1368],[1129,12624,1921],{"className":12625},[1373],[1129,12627],{"className":12628,"style":1369},[1368],[1129,12630,12632,12635,12667,12670,12673],{"className":12631},[1178],[1129,12633],{"className":12634,"style":12587},[1182],[1129,12636,12638,12641],{"className":12637},[1187],[1129,12639,11507],{"className":12640},[1187,1191],[1129,12642,12644],{"className":12643},[1196],[1129,12645,12647],{"className":12646},[1200],[1129,12648,12650],{"className":12649},[1205],[1129,12651,12653],{"className":12652,"style":3651},[1209],[1129,12654,12655,12658],{"style":1239},[1129,12656],{"className":12657,"style":1218},[1217],[1129,12659,12661],{"className":12660},[1222,1223,1224,1225],[1129,12662,12664],{"className":12663},[1187,1225],[1129,12665,12253],{"className":12666},[1187,1225],[1129,12668],{"className":12669,"style":1369},[1368],[1129,12671,1921],{"className":12672},[1373],[1129,12674],{"className":12675,"style":1369},[1368],[1129,12677,12679,12682,12714,12717,12720],{"className":12678},[1178],[1129,12680],{"className":12681,"style":3651},[1182],[1129,12683,12685,12688],{"className":12684},[1187],[1129,12686,11507],{"className":12687},[1187,1191],[1129,12689,12691],{"className":12690},[1196],[1129,12692,12694],{"className":12693},[1200],[1129,12695,12697],{"className":12696},[1205],[1129,12698,12700],{"className":12699,"style":3651},[1209],[1129,12701,12702,12705],{"style":1239},[1129,12703],{"className":12704,"style":1218},[1217],[1129,12706,12708],{"className":12707},[1222,1223,1224,1225],[1129,12709,12711],{"className":12710},[1187,1225],[1129,12712,12260],{"className":12713},[1187,1225],[1129,12715],{"className":12716,"style":1996},[1368],[1129,12718,1884],{"className":12719},[2000],[1129,12721],{"className":12722,"style":1996},[1368],[1129,12724,12726,12729,12732,12735,12738],{"className":12725},[1178],[1129,12727],{"className":12728,"style":6106},[1182],[1129,12730,12415],{"className":12731},[1187],[1129,12733],{"className":12734,"style":1369},[1368],[1129,12736,1921],{"className":12737},[1373],[1129,12739],{"className":12740,"style":1369},[1368],[1129,12742,12744,12747,12750,12753,12756],{"className":12743},[1178],[1129,12745],{"className":12746,"style":6106},[1182],[1129,12748,12420],{"className":12749},[1187],[1129,12751],{"className":12752,"style":1369},[1368],[1129,12754,1921],{"className":12755},[1373],[1129,12757],{"className":12758,"style":1369},[1368],[1129,12760,12762,12765,12768,12771,12774],{"className":12761},[1178],[1129,12763],{"className":12764,"style":1383},[1182],[1129,12766,12425],{"className":12767},[1187],[1129,12769],{"className":12770,"style":1996},[1368],[1129,12772,1884],{"className":12773},[2000],[1129,12775],{"className":12776,"style":1996},[1368],[1129,12778,12780,12783],{"className":12779},[1178],[1129,12781],{"className":12782,"style":1383},[1182],[1129,12784,12430],{"className":12785},[1187],[1105,12787,12788,13089],{},[1108,12789,12790],{},[1111,12791,12792,12795,12879,13000,13086],{},[1114,12793,12794],{},"神经元",[1114,12796,12797],{},[1129,12798,12800,12819],{"className":12799},[1132],[1129,12801,12803],{"className":12802},[1136],[1138,12804,12805],{"xmlns":1140},[1142,12806,12807,12817],{},[1145,12808,12809],{},[1148,12810,12811,12813,12815],{},[1151,12812,1733],{},[1151,12814,1158],{},[1151,12816,2437],{},[1166,12818,11411],{"encoding":1168},[1129,12820,12822],{"className":12821,"ariaHidden":1174},[1173],[1129,12823,12825,12828],{"className":12824},[1178],[1129,12826],{"className":12827,"style":11421},[1182],[1129,12829,12831,12834],{"className":12830},[1187],[1129,12832,1733],{"className":12833,"style":1756},[1187,1191],[1129,12835,12837],{"className":12836},[1196],[1129,12838,12840,12871],{"className":12839},[1200,1201],[1129,12841,12843,12868],{"className":12842},[1205],[1129,12844,12846,12857],{"className":12845,"style":2488},[1209],[1129,12847,12848,12851],{"style":1771},[1129,12849],{"className":12850,"style":1218},[1217],[1129,12852,12854],{"className":12853},[1222,1223,1224,1225],[1129,12855,1158],{"className":12856,"style":1232},[1187,1191,1225],[1129,12858,12859,12862],{"style":1239},[1129,12860],{"className":12861,"style":1218},[1217],[1129,12863,12865],{"className":12864},[1222,1223,1224,1225],[1129,12866,2437],{"className":12867},[1187,1191,1225],[1129,12869,1254],{"className":12870},[1253],[1129,12872,12874],{"className":12873},[1205],[1129,12875,12877],{"className":12876,"style":1504},[1209],[1129,12878],{},[1114,12880,12881],{},[1129,12882,12884,12908],{"className":12883},[1132],[1129,12885,12887],{"className":12886},[1136],[1138,12888,12889],{"xmlns":1140},[1142,12890,12891,12905],{},[1145,12892,12893],{},[2431,12894,12895,12897],{},[1151,12896,11507],{},[1148,12898,12899,12901,12903],{},[1151,12900,1733],{},[1151,12902,1158],{},[1151,12904,2437],{},[1166,12906,12907],{"encoding":1168},"e^{z^L_j}",[1129,12909,12911],{"className":12910,"ariaHidden":1174},[1173],[1129,12912,12914,12918],{"className":12913},[1178],[1129,12915],{"className":12916,"style":12917},[1182],"height:1.0485em;",[1129,12919,12921,12924],{"className":12920},[1187],[1129,12922,11507],{"className":12923},[1187,1191],[1129,12925,12927],{"className":12926},[1196],[1129,12928,12930],{"className":12929},[1200],[1129,12931,12933],{"className":12932},[1205],[1129,12934,12936],{"className":12935,"style":12917},[1209],[1129,12937,12939,12942],{"style":12938},"top:-3.1052em;margin-right:0.05em;",[1129,12940],{"className":12941,"style":1218},[1217],[1129,12943,12945],{"className":12944},[1222,1223,1224,1225],[1129,12946,12948],{"className":12947},[1187,1225],[1129,12949,12951,12954],{"className":12950},[1187,1225],[1129,12952,1733],{"className":12953,"style":1756},[1187,1191,1225],[1129,12955,12957],{"className":12956},[1196],[1129,12958,12960,12991],{"className":12959},[1200,1201],[1129,12961,12963,12988],{"className":12962},[1205],[1129,12964,12966,12977],{"className":12965,"style":12535},[1209],[1129,12967,12968,12971],{"style":12538},[1129,12969],{"className":12970,"style":3124},[1217],[1129,12972,12974],{"className":12973},[1222,3128,3129,1225],[1129,12975,1158],{"className":12976,"style":1232},[1187,1191,1225],[1129,12978,12979,12982],{"style":12550},[1129,12980],{"className":12981,"style":3124},[1217],[1129,12983,12985],{"className":12984},[1222,3128,3129,1225],[1129,12986,2437],{"className":12987},[1187,1191,1225],[1129,12989,1254],{"className":12990},[1253],[1129,12992,12994],{"className":12993},[1205],[1129,12995,12998],{"className":12996,"style":12997},[1209],"height:0.4249em;",[1129,12999],{},[1114,13001,13002,13085],{},[1129,13003,13005,13025],{"className":13004},[1132],[1129,13006,13008],{"className":13007},[1136],[1138,13009,13010],{"xmlns":1140},[1142,13011,13012,13022],{},[1145,13013,13014],{},[1148,13015,13016,13018,13020],{},[1151,13017,1586],{},[1151,13019,1158],{},[1151,13021,2437],{},[1166,13023,13024],{"encoding":1168},"a^L_j",[1129,13026,13028],{"className":13027,"ariaHidden":1174},[1173],[1129,13029,13031,13034],{"className":13030},[1178],[1129,13032],{"className":13033,"style":11421},[1182],[1129,13035,13037,13040],{"className":13036},[1187],[1129,13038,1586],{"className":13039},[1187,1191],[1129,13041,13043],{"className":13042},[1196],[1129,13044,13046,13077],{"className":13045},[1200,1201],[1129,13047,13049,13074],{"className":13048},[1205],[1129,13050,13052,13063],{"className":13051,"style":2488},[1209],[1129,13053,13054,13057],{"style":1474},[1129,13055],{"className":13056,"style":1218},[1217],[1129,13058,13060],{"className":13059},[1222,1223,1224,1225],[1129,13061,1158],{"className":13062,"style":1232},[1187,1191,1225],[1129,13064,13065,13068],{"style":1239},[1129,13066],{"className":13067,"style":1218},[1217],[1129,13069,13071],{"className":13070},[1222,1223,1224,1225],[1129,13072,2437],{"className":13073},[1187,1191,1225],[1129,13075,1254],{"className":13076},[1253],[1129,13078,13080],{"className":13079},[1205],[1129,13081,13083],{"className":13082,"style":1504},[1209],[1129,13084],{},"（softmax 输出）",[1114,13087,13088],{},"解释",[1121,13090,13091,13109,13126],{},[1111,13092,13093,13096,13098,13100,13106],{},[1126,13094,13095],{},"j=1",[1126,13097,6197],{},[1126,13099,12415],{},[1126,13101,13102,13103],{},"7.389\u002F11.756 = ",[2405,13104,13105],{},"0.629",[1126,13107,13108],{},"最大 → 最高概率",[1111,13110,13111,13114,13116,13118,13124],{},[1126,13112,13113],{},"j=2",[1126,13115,12253],{},[1126,13117,12420],{},[1126,13119,13120,13121],{},"2.718\u002F11.756 = ",[2405,13122,13123],{},"0.231",[1126,13125],{},[1111,13127,13128,13131,13133,13135,13141],{},[1126,13129,13130],{},"j=3",[1126,13132,12260],{},[1126,13134,12425],{},[1126,13136,13137,13138],{},"1.649\u002F11.756 = ",[2405,13139,13140],{},"0.140",[1126,13142],{},[1101,13144,13145,13146,13211],{},"输出 ",[1129,13147,13149,13175],{"className":13148},[1132],[1129,13150,13152],{"className":13151},[1136],[1138,13153,13154],{"xmlns":1140},[1142,13155,13156,13172],{},[1145,13157,13158,13160,13162,13164,13166,13168,13170],{},[1342,13159,2466],{"stretchy":2465},[1346,13161,13105],{},[1342,13163,3727],{"separator":1174},[1346,13165,13123],{},[1342,13167,3727],{"separator":1174},[1346,13169,13140],{},[1342,13171,2475],{"stretchy":2465},[1166,13173,13174],{"encoding":1168},"(0.629, 0.231, 0.140)",[1129,13176,13178],{"className":13177,"ariaHidden":1174},[1173],[1129,13179,13181,13184,13187,13190,13193,13196,13199,13202,13205,13208],{"className":13180},[1178],[1129,13182],{"className":13183,"style":6081},[1182],[1129,13185,2466],{"className":13186},[2634],[1129,13188,13105],{"className":13189},[1187],[1129,13191,3727],{"className":13192},[3777],[1129,13194],{"className":13195,"style":2061},[1368],[1129,13197,13123],{"className":13198},[1187],[1129,13200,3727],{"className":13201},[3777],[1129,13203],{"className":13204,"style":2061},[1368],[1129,13206,13140],{"className":13207},[1187],[1129,13209,2475],{"className":13210},[2667],"，和为 1",[1101,13213,13214],{},"网络预测：最可能是第 1 类（概率 62.9%）",[5907,13216],{},[1096,13218,13220],{"id":13219},"_32-对数似然代价函数","3.2 对数似然代价函数",[1101,13222,13223,13224,2417,13227],{},"Softmax 通常搭配",[2405,13225,13226],{},"对数似然代价函数（Log-likelihood cost）",[1129,13228,13230,13260],{"className":13229},[1132],[1129,13231,13233],{"className":13232},[1136],[1138,13234,13235],{"xmlns":1140},[1142,13236,13237,13257],{},[1145,13238,13239,13241,13243,13245,13247,13249],{},[1151,13240,2450],{},[1342,13242,1884],{},[1342,13244,1344],{},[1151,13246,6649],{},[1342,13248,6652],{},[1148,13250,13251,13253,13255],{},[1151,13252,1586],{},[1151,13254,6646],{},[1151,13256,2437],{},[1166,13258,13259],{"encoding":1168},"C = -\\ln a^L_y",[1129,13261,13263,13281],{"className":13262,"ariaHidden":1174},[1173],[1129,13264,13266,13269,13272,13275,13278],{"className":13265},[1178],[1129,13267],{"className":13268,"style":5901},[1182],[1129,13270,2450],{"className":13271,"style":2580},[1187,1191],[1129,13273],{"className":13274,"style":1996},[1368],[1129,13276,1884],{"className":13277},[2000],[1129,13279],{"className":13280,"style":1996},[1368],[1129,13282,13284,13288,13291,13294,13297,13300],{"className":13283},[1178],[1129,13285],{"className":13286,"style":13287},[1182],"height:1.2244em;vertical-align:-0.3831em;",[1129,13289,1344],{"className":13290},[1187],[1129,13292],{"className":13293,"style":2061},[1368],[1129,13295,6649],{"className":13296},[2014],[1129,13298],{"className":13299,"style":2061},[1368],[1129,13301,13303,13306],{"className":13302},[1187],[1129,13304,1586],{"className":13305},[1187,1191],[1129,13307,13309],{"className":13308},[1196],[1129,13310,13312,13344],{"className":13311},[1200,1201],[1129,13313,13315,13341],{"className":13314},[1205],[1129,13316,13318,13330],{"className":13317,"style":2488},[1209],[1129,13319,13321,13324],{"style":13320},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[1129,13322],{"className":13323,"style":1218},[1217],[1129,13325,13327],{"className":13326},[1222,1223,1224,1225],[1129,13328,6646],{"className":13329,"style":2603},[1187,1191,1225],[1129,13331,13332,13335],{"style":1239},[1129,13333],{"className":13334,"style":1218},[1217],[1129,13336,13338],{"className":13337},[1222,1223,1224,1225],[1129,13339,2437],{"className":13340},[1187,1191,1225],[1129,13342,1254],{"className":13343},[1253],[1129,13345,13347],{"className":13346},[1205],[1129,13348,13351],{"className":13349,"style":13350},[1209],"height:0.3831em;",[1129,13352],{},[1101,13354,6921,13355,13383],{},[1129,13356,13358,13371],{"className":13357},[1132],[1129,13359,13361],{"className":13360},[1136],[1138,13362,13363],{"xmlns":1140},[1142,13364,13365,13369],{},[1145,13366,13367],{},[1151,13368,6646],{},[1166,13370,6646],{"encoding":1168},[1129,13372,13374],{"className":13373,"ariaHidden":1174},[1173],[1129,13375,13377,13380],{"className":13376},[1178],[1129,13378],{"className":13379,"style":7005},[1182],[1129,13381,6646],{"className":13382,"style":2603},[1187,1191]," 是正确类别的索引。当网络对正确类别预测的概率越高，代价越低。",[1101,13385,13386],{},[2405,13387,13388],{},"也就是只关注\"正确类别的概率\"有多大",[1105,13390,13391,13607],{},[1108,13392,13393],{},[1111,13394,13395,13481,13605],{},[1114,13396,13397,13480],{},[1129,13398,13400,13420],{"className":13399},[1132],[1129,13401,13403],{"className":13402},[1136],[1138,13404,13405],{"xmlns":1140},[1142,13406,13407,13417],{},[1145,13408,13409],{},[1148,13410,13411,13413,13415],{},[1151,13412,1586],{},[1151,13414,6646],{},[1151,13416,2437],{},[1166,13418,13419],{"encoding":1168},"a^L_y",[1129,13421,13423],{"className":13422,"ariaHidden":1174},[1173],[1129,13424,13426,13429],{"className":13425},[1178],[1129,13427],{"className":13428,"style":13287},[1182],[1129,13430,13432,13435],{"className":13431},[1187],[1129,13433,1586],{"className":13434},[1187,1191],[1129,13436,13438],{"className":13437},[1196],[1129,13439,13441,13472],{"className":13440},[1200,1201],[1129,13442,13444,13469],{"className":13443},[1205],[1129,13445,13447,13458],{"className":13446,"style":2488},[1209],[1129,13448,13449,13452],{"style":13320},[1129,13450],{"className":13451,"style":1218},[1217],[1129,13453,13455],{"className":13454},[1222,1223,1224,1225],[1129,13456,6646],{"className":13457,"style":2603},[1187,1191,1225],[1129,13459,13460,13463],{"style":1239},[1129,13461],{"className":13462,"style":1218},[1217],[1129,13464,13466],{"className":13465},[1222,1223,1224,1225],[1129,13467,2437],{"className":13468},[1187,1191,1225],[1129,13470,1254],{"className":13471},[1253],[1129,13473,13475],{"className":13474},[1205],[1129,13476,13478],{"className":13477,"style":13350},[1209],[1129,13479],{},"（正确类别的概率）",[1114,13482,13483],{},[1129,13484,13486,13515],{"className":13485},[1132],[1129,13487,13489],{"className":13488},[1136],[1138,13490,13491],{"xmlns":1140},[1142,13492,13493,13513],{},[1145,13494,13495,13497,13499,13501,13503,13505],{},[1151,13496,2450],{},[1342,13498,1884],{},[1342,13500,1344],{},[1151,13502,6649],{},[1342,13504,6652],{},[1148,13506,13507,13509,13511],{},[1151,13508,1586],{},[1151,13510,6646],{},[1151,13512,2437],{},[1166,13514,13259],{"encoding":1168},[1129,13516,13518,13536],{"className":13517,"ariaHidden":1174},[1173],[1129,13519,13521,13524,13527,13530,13533],{"className":13520},[1178],[1129,13522],{"className":13523,"style":5901},[1182],[1129,13525,2450],{"className":13526,"style":2580},[1187,1191],[1129,13528],{"className":13529,"style":1996},[1368],[1129,13531,1884],{"className":13532},[2000],[1129,13534],{"className":13535,"style":1996},[1368],[1129,13537,13539,13542,13545,13548,13551,13554],{"className":13538},[1178],[1129,13540],{"className":13541,"style":13287},[1182],[1129,13543,1344],{"className":13544},[1187],[1129,13546],{"className":13547,"style":2061},[1368],[1129,13549,6649],{"className":13550},[2014],[1129,13552],{"className":13553,"style":2061},[1368],[1129,13555,13557,13560],{"className":13556},[1187],[1129,13558,1586],{"className":13559},[1187,1191],[1129,13561,13563],{"className":13562},[1196],[1129,13564,13566,13597],{"className":13565},[1200,1201],[1129,13567,13569,13594],{"className":13568},[1205],[1129,13570,13572,13583],{"className":13571,"style":2488},[1209],[1129,13573,13574,13577],{"style":13320},[1129,13575],{"className":13576,"style":1218},[1217],[1129,13578,13580],{"className":13579},[1222,1223,1224,1225],[1129,13581,6646],{"className":13582,"style":2603},[1187,1191,1225],[1129,13584,13585,13588],{"style":1239},[1129,13586],{"className":13587,"style":1218},[1217],[1129,13589,13591],{"className":13590},[1222,1223,1224,1225],[1129,13592,2437],{"className":13593},[1187,1191,1225],[1129,13595,1254],{"className":13596},[1253],[1129,13598,13600],{"className":13599},[1205],[1129,13601,13603],{"className":13602,"style":13350},[1209],[1129,13604],{},[1114,13606],{},[1121,13608,13609,13619,13629,13640],{},[1111,13610,13611,13613,13616],{},[1126,13612,5960],{},[1126,13614,13615],{},"0.105",[1126,13617,13618],{},"很自信且正确 → 损失小",[1111,13620,13621,13623,13626],{},[1126,13622,12260],{},[1126,13624,13625],{},"0.693",[1126,13627,13628],{},"不太确定 → 损失中等",[1111,13630,13631,13634,13637],{},[1126,13632,13633],{},"0.1",[1126,13635,13636],{},"2.303",[1126,13638,13639],{},"把正确答案排很低 → 损失很大",[1111,13641,13642,13645,13648],{},[1126,13643,13644],{},"→ 0",[1126,13646,13647],{},"→ ∞",[1126,13649,13650],{},"完全错误 → 惩罚趋于无穷",[1096,13652,13654],{"id":13653},"_33-梯度推导","3.3 梯度推导",[1101,13656,13657],{},"Softmax + 对数似然的梯度同样具有简洁的形式：",[1101,13659,13660],{},[1129,13661,13663,13735],{"className":13662},[1132],[1129,13664,13666],{"className":13665},[1136],[1138,13667,13668],{"xmlns":1140},[1142,13669,13670,13732],{},[1145,13671,13672,13696,13698,13712,13714,13722,13724,13730],{},[3018,13673,13674,13680],{},[1145,13675,13676,13678],{},[1151,13677,3024],{"mathvariant":2444},[1151,13679,2450],{},[1145,13681,13682,13684],{},[1151,13683,3024],{"mathvariant":2444},[1148,13685,13686,13688,13694],{},[1151,13687,1153],{},[1145,13689,13690,13692],{},[1151,13691,1158],{},[1151,13693,1161],{},[1151,13695,2437],{},[1342,13697,1884],{},[1148,13699,13700,13702,13704],{},[1151,13701,1586],{},[1151,13703,1161],{},[1145,13705,13706,13708,13710],{},[1151,13707,1164],{},[1342,13709,1344],{},[1346,13711,1348],{},[1342,13713,2466],{"stretchy":2465},[1148,13715,13716,13718,13720],{},[1151,13717,1586],{},[1151,13719,1158],{},[1151,13721,2437],{},[1342,13723,1344],{},[1886,13725,13726,13728],{},[1151,13727,6646],{},[1151,13729,1158],{},[1342,13731,2475],{"stretchy":2465},[1166,13733,13734],{"encoding":1168},"\\frac{\\partial C}{\\partial w^L_{jk}} = a^{l-1}_k (a^L_j - y_j)",[1129,13736,13738,13885,14014],{"className":13737,"ariaHidden":1174},[1173],[1129,13739,13741,13745,13876,13879,13882],{"className":13740},[1178],[1129,13742],{"className":13743,"style":13744},[1182],"height:1.6134em;vertical-align:-0.7333em;",[1129,13746,13748,13751,13873],{"className":13747},[1187],[1129,13749],{"className":13750},[2634,3068],[1129,13752,13754],{"className":13753},[3018],[1129,13755,13757,13864],{"className":13756},[1200,1201],[1129,13758,13760,13861],{"className":13759},[1205],[1129,13761,13763,13836,13844],{"className":13762,"style":3081},[1209],[1129,13764,13766,13769],{"style":13765},"top:-2.607em;",[1129,13767],{"className":13768,"style":3088},[1217],[1129,13770,13772],{"className":13771},[1222,1223,1224,1225],[1129,13773,13775,13778],{"className":13774},[1187,1225],[1129,13776,3024],{"className":13777,"style":3098},[1187,1225],[1129,13779,13781,13784],{"className":13780},[1187,1225],[1129,13782,1153],{"className":13783,"style":1192},[1187,1191,1225],[1129,13785,13787],{"className":13786},[1196],[1129,13788,13790,13828],{"className":13789},[1200,1201],[1129,13791,13793,13825],{"className":13792},[1205],[1129,13794,13797,13814],{"className":13795,"style":13796},[1209],"height:0.8329em;",[1129,13798,13799,13802],{"style":3397},[1129,13800],{"className":13801,"style":3124},[1217],[1129,13803,13805],{"className":13804},[1222,3128,3129,1225],[1129,13806,13808,13811],{"className":13807},[1187,1225],[1129,13809,1158],{"className":13810,"style":1232},[1187,1191,1225],[1129,13812,1161],{"className":13813,"style":1236},[1187,1191,1225],[1129,13815,13816,13819],{"style":3135},[1129,13817],{"className":13818,"style":3124},[1217],[1129,13820,13822],{"className":13821},[1222,3128,3129,1225],[1129,13823,2437],{"className":13824},[1187,1191,1225],[1129,13826,1254],{"className":13827},[1253],[1129,13829,13831],{"className":13830},[1205],[1129,13832,13834],{"className":13833,"style":3433},[1209],[1129,13835],{},[1129,13837,13838,13841],{"style":3159},[1129,13839],{"className":13840,"style":3088},[1217],[1129,13842],{"className":13843,"style":3167},[3166],[1129,13845,13846,13849],{"style":3170},[1129,13847],{"className":13848,"style":3088},[1217],[1129,13850,13852],{"className":13851},[1222,1223,1224,1225],[1129,13853,13855,13858],{"className":13854},[1187,1225],[1129,13856,3024],{"className":13857,"style":3098},[1187,1225],[1129,13859,2450],{"className":13860,"style":2580},[1187,1191,1225],[1129,13862,1254],{"className":13863},[1253],[1129,13865,13867],{"className":13866},[1205],[1129,13868,13871],{"className":13869,"style":13870},[1209],"height:0.7333em;",[1129,13872],{},[1129,13874],{"className":13875},[2667,3068],[1129,13877],{"className":13878,"style":1996},[1368],[1129,13880,1884],{"className":13881},[2000],[1129,13883],{"className":13884,"style":1996},[1368],[1129,13886,13888,13891,13951,13954,14005,14008,14011],{"className":13887},[1178],[1129,13889],{"className":13890,"style":3491},[1182],[1129,13892,13894,13897],{"className":13893},[1187],[1129,13895,1586],{"className":13896},[1187,1191],[1129,13898,13900],{"className":13899},[1196],[1129,13901,13903,13943],{"className":13902},[1200,1201],[1129,13904,13906,13940],{"className":13905},[1205],[1129,13907,13909,13920],{"className":13908,"style":2137},[1209],[1129,13910,13911,13914],{"style":2140},[1129,13912],{"className":13913,"style":1218},[1217],[1129,13915,13917],{"className":13916},[1222,1223,1224,1225],[1129,13918,1161],{"className":13919,"style":1236},[1187,1191,1225],[1129,13921,13922,13925],{"style":2152},[1129,13923],{"className":13924,"style":1218},[1217],[1129,13926,13928],{"className":13927},[1222,1223,1224,1225],[1129,13929,13931,13934,13937],{"className":13930},[1187,1225],[1129,13932,1164],{"className":13933,"style":1249},[1187,1191,1225],[1129,13935,1344],{"className":13936},[1373,1225],[1129,13938,1348],{"className":13939},[1187,1225],[1129,13941,1254],{"className":13942},[1253],[1129,13944,13946],{"className":13945},[1205],[1129,13947,13949],{"className":13948,"style":2180},[1209],[1129,13950],{},[1129,13952,2466],{"className":13953},[2634],[1129,13955,13957,13960],{"className":13956},[1187],[1129,13958,1586],{"className":13959},[1187,1191],[1129,13961,13963],{"className":13962},[1196],[1129,13964,13966,13997],{"className":13965},[1200,1201],[1129,13967,13969,13994],{"className":13968},[1205],[1129,13970,13972,13983],{"className":13971,"style":2488},[1209],[1129,13973,13974,13977],{"style":1474},[1129,13975],{"className":13976,"style":1218},[1217],[1129,13978,13980],{"className":13979},[1222,1223,1224,1225],[1129,13981,1158],{"className":13982,"style":1232},[1187,1191,1225],[1129,13984,13985,13988],{"style":1239},[1129,13986],{"className":13987,"style":1218},[1217],[1129,13989,13991],{"className":13990},[1222,1223,1224,1225],[1129,13992,2437],{"className":13993},[1187,1191,1225],[1129,13995,1254],{"className":13996},[1253],[1129,13998,14000],{"className":13999},[1205],[1129,14001,14003],{"className":14002,"style":1504},[1209],[1129,14004],{},[1129,14006],{"className":14007,"style":1369},[1368],[1129,14009,1344],{"className":14010},[1373],[1129,14012],{"className":14013,"style":1369},[1368],[1129,14015,14017,14021,14061],{"className":14016},[1178],[1129,14018],{"className":14019,"style":14020},[1182],"height:1.0361em;vertical-align:-0.2861em;",[1129,14022,14024,14027],{"className":14023},[1187],[1129,14025,6646],{"className":14026,"style":2603},[1187,1191],[1129,14028,14030],{"className":14029},[1196],[1129,14031,14033,14053],{"className":14032},[1200,1201],[1129,14034,14036,14050],{"className":14035},[1205],[1129,14037,14039],{"className":14038,"style":7442},[1209],[1129,14040,14041,14044],{"style":11112},[1129,14042],{"className":14043,"style":1218},[1217],[1129,14045,14047],{"className":14046},[1222,1223,1224,1225],[1129,14048,1158],{"className":14049,"style":1232},[1187,1191,1225],[1129,14051,1254],{"className":14052},[1253],[1129,14054,14056],{"className":14055},[1205],[1129,14057,14059],{"className":14058,"style":7463},[1209],[1129,14060],{},[1129,14062,2475],{"className":14063},[2667],[1101,14065,14066],{},[1129,14067,14069,14119],{"className":14068},[1132],[1129,14070,14072],{"className":14071},[1136],[1138,14073,14074],{"xmlns":1140},[1142,14075,14076,14116],{},[1145,14077,14078,14098,14100,14108,14110],{},[3018,14079,14080,14086],{},[1145,14081,14082,14084],{},[1151,14083,3024],{"mathvariant":2444},[1151,14085,2450],{},[1145,14087,14088,14090],{},[1151,14089,3024],{"mathvariant":2444},[1148,14091,14092,14094,14096],{},[1151,14093,1436],{},[1151,14095,1158],{},[1151,14097,2437],{},[1342,14099,1884],{},[1148,14101,14102,14104,14106],{},[1151,14103,1586],{},[1151,14105,1158],{},[1151,14107,2437],{},[1342,14109,1344],{},[1886,14111,14112,14114],{},[1151,14113,6646],{},[1151,14115,1158],{},[1166,14117,14118],{"encoding":1168},"\\frac{\\partial C}{\\partial b^L_j} = a^L_j - y_j",[1129,14120,14122,14261,14327],{"className":14121,"ariaHidden":1174},[1173],[1129,14123,14125,14129,14252,14255,14258],{"className":14124},[1178],[1129,14126],{"className":14127,"style":14128},[1182],"height:1.596em;vertical-align:-0.7158em;",[1129,14130,14132,14135,14249],{"className":14131},[1187],[1129,14133],{"className":14134},[2634,3068],[1129,14136,14138],{"className":14137},[3018],[1129,14139,14141,14240],{"className":14140},[1200,1201],[1129,14142,14144,14237],{"className":14143},[1205],[1129,14145,14147,14212,14220],{"className":14146,"style":3081},[1209],[1129,14148,14149,14152],{"style":13765},[1129,14150],{"className":14151,"style":3088},[1217],[1129,14153,14155],{"className":14154},[1222,1223,1224,1225],[1129,14156,14158,14161],{"className":14157},[1187,1225],[1129,14159,3024],{"className":14160,"style":3098},[1187,1225],[1129,14162,14164,14167],{"className":14163},[1187,1225],[1129,14165,1436],{"className":14166},[1187,1191,1225],[1129,14168,14170],{"className":14169},[1196],[1129,14171,14173,14204],{"className":14172},[1200,1201],[1129,14174,14176,14201],{"className":14175},[1205],[1129,14177,14179,14190],{"className":14178,"style":13796},[1209],[1129,14180,14181,14184],{"style":3120},[1129,14182],{"className":14183,"style":3124},[1217],[1129,14185,14187],{"className":14186},[1222,3128,3129,1225],[1129,14188,1158],{"className":14189,"style":1232},[1187,1191,1225],[1129,14191,14192,14195],{"style":3135},[1129,14193],{"className":14194,"style":3124},[1217],[1129,14196,14198],{"className":14197},[1222,3128,3129,1225],[1129,14199,2437],{"className":14200},[1187,1191,1225],[1129,14202,1254],{"className":14203},[1253],[1129,14205,14207],{"className":14206},[1205],[1129,14208,14210],{"className":14209,"style":3154},[1209],[1129,14211],{},[1129,14213,14214,14217],{"style":3159},[1129,14215],{"className":14216,"style":3088},[1217],[1129,14218],{"className":14219,"style":3167},[3166],[1129,14221,14222,14225],{"style":3170},[1129,14223],{"className":14224,"style":3088},[1217],[1129,14226,14228],{"className":14227},[1222,1223,1224,1225],[1129,14229,14231,14234],{"className":14230},[1187,1225],[1129,14232,3024],{"className":14233,"style":3098},[1187,1225],[1129,14235,2450],{"className":14236,"style":2580},[1187,1191,1225],[1129,14238,1254],{"className":14239},[1253],[1129,14241,14243],{"className":14242},[1205],[1129,14244,14247],{"className":14245,"style":14246},[1209],"height:0.7158em;",[1129,14248],{},[1129,14250],{"className":14251},[2667,3068],[1129,14253],{"className":14254,"style":1996},[1368],[1129,14256,1884],{"className":14257},[2000],[1129,14259],{"className":14260,"style":1996},[1368],[1129,14262,14264,14267,14318,14321,14324],{"className":14263},[1178],[1129,14265],{"className":14266,"style":11421},[1182],[1129,14268,14270,14273],{"className":14269},[1187],[1129,14271,1586],{"className":14272},[1187,1191],[1129,14274,14276],{"className":14275},[1196],[1129,14277,14279,14310],{"className":14278},[1200,1201],[1129,14280,14282,14307],{"className":14281},[1205],[1129,14283,14285,14296],{"className":14284,"style":2488},[1209],[1129,14286,14287,14290],{"style":1474},[1129,14288],{"className":14289,"style":1218},[1217],[1129,14291,14293],{"className":14292},[1222,1223,1224,1225],[1129,14294,1158],{"className":14295,"style":1232},[1187,1191,1225],[1129,14297,14298,14301],{"style":1239},[1129,14299],{"className":14300,"style":1218},[1217],[1129,14302,14304],{"className":14303},[1222,1223,1224,1225],[1129,14305,2437],{"className":14306},[1187,1191,1225],[1129,14308,1254],{"className":14309},[1253],[1129,14311,14313],{"className":14312},[1205],[1129,14314,14316],{"className":14315,"style":1504},[1209],[1129,14317],{},[1129,14319],{"className":14320,"style":1369},[1368],[1129,14322,1344],{"className":14323},[1373],[1129,14325],{"className":14326,"style":1369},[1368],[1129,14328,14330,14333],{"className":14329},[1178],[1129,14331],{"className":14332,"style":8416},[1182],[1129,14334,14336,14339],{"className":14335},[1187],[1129,14337,6646],{"className":14338,"style":2603},[1187,1191],[1129,14340,14342],{"className":14341},[1196],[1129,14343,14345,14365],{"className":14344},[1200,1201],[1129,14346,14348,14362],{"className":14347},[1205],[1129,14349,14351],{"className":14350,"style":7442},[1209],[1129,14352,14353,14356],{"style":11112},[1129,14354],{"className":14355,"style":1218},[1217],[1129,14357,14359],{"className":14358},[1222,1223,1224,1225],[1129,14360,1158],{"className":14361,"style":1232},[1187,1191,1225],[1129,14363,1254],{"className":14364},[1253],[1129,14366,14368],{"className":14367},[1205],[1129,14369,14371],{"className":14370,"style":7463},[1209],[1129,14372],{},[1101,14374,14375,14378,14379,14455,14456,14612],{},[2405,14376,14377],{},"与交叉熵相同的优势都是","梯度同样不含 ",[1129,14380,14382,14405],{"className":14381},[1132],[1129,14383,14385],{"className":14384},[1136],[1138,14386,14387],{"xmlns":1140},[1142,14388,14389,14403],{},[1145,14390,14391,14397,14399,14401],{},[2431,14392,14393,14395],{},[1151,14394,2458],{},[1342,14396,2462],{"mathvariant":2444,"lspace":2461,"rspace":2461},[1342,14398,2466],{"stretchy":2465},[1151,14400,1733],{},[1342,14402,2475],{"stretchy":2465},[1166,14404,6445],{"encoding":1168},[1129,14406,14408],{"className":14407,"ariaHidden":1174},[1173],[1129,14409,14411,14414,14446,14449,14452],{"className":14410},[1178],[1129,14412],{"className":14413,"style":6455},[1182],[1129,14415,14417,14420],{"className":14416},[1187],[1129,14418,2458],{"className":14419,"style":2603},[1187,1191],[1129,14421,14423],{"className":14422},[1196],[1129,14424,14426],{"className":14425},[1200],[1129,14427,14429],{"className":14428},[1205],[1129,14430,14432],{"className":14431,"style":2616},[1209],[1129,14433,14434,14437],{"style":1239},[1129,14435],{"className":14436,"style":1218},[1217],[1129,14438,14440],{"className":14439},[1222,1223,1224,1225],[1129,14441,14443],{"className":14442},[1187,1225],[1129,14444,2462],{"className":14445},[1187,1225],[1129,14447,2466],{"className":14448},[2634],[1129,14450,1733],{"className":14451,"style":1756},[1187,1191],[1129,14453,2475],{"className":14454},[2667],"，由误差 ",[1129,14457,14459,14491],{"className":14458},[1132],[1129,14460,14462],{"className":14461},[1136],[1138,14463,14464],{"xmlns":1140},[1142,14465,14466,14488],{},[1145,14467,14468,14470,14478,14480,14486],{},[1342,14469,2466],{"stretchy":2465},[1148,14471,14472,14474,14476],{},[1151,14473,1586],{},[1151,14475,1158],{},[1151,14477,2437],{},[1342,14479,1344],{},[1886,14481,14482,14484],{},[1151,14483,6646],{},[1151,14485,1158],{},[1342,14487,2475],{"stretchy":2465},[1166,14489,14490],{"encoding":1168},"(a^L_j - y_j)",[1129,14492,14494,14563],{"className":14493,"ariaHidden":1174},[1173],[1129,14495,14497,14500,14503,14554,14557,14560],{"className":14496},[1178],[1129,14498],{"className":14499,"style":11421},[1182],[1129,14501,2466],{"className":14502},[2634],[1129,14504,14506,14509],{"className":14505},[1187],[1129,14507,1586],{"className":14508},[1187,1191],[1129,14510,14512],{"className":14511},[1196],[1129,14513,14515,14546],{"className":14514},[1200,1201],[1129,14516,14518,14543],{"className":14517},[1205],[1129,14519,14521,14532],{"className":14520,"style":2488},[1209],[1129,14522,14523,14526],{"style":1474},[1129,14524],{"className":14525,"style":1218},[1217],[1129,14527,14529],{"className":14528},[1222,1223,1224,1225],[1129,14530,1158],{"className":14531,"style":1232},[1187,1191,1225],[1129,14533,14534,14537],{"style":1239},[1129,14535],{"className":14536,"style":1218},[1217],[1129,14538,14540],{"className":14539},[1222,1223,1224,1225],[1129,14541,2437],{"className":14542},[1187,1191,1225],[1129,14544,1254],{"className":14545},[1253],[1129,14547,14549],{"className":14548},[1205],[1129,14550,14552],{"className":14551,"style":1504},[1209],[1129,14553],{},[1129,14555],{"className":14556,"style":1369},[1368],[1129,14558,1344],{"className":14559},[1373],[1129,14561],{"className":14562,"style":1369},[1368],[1129,14564,14566,14569,14609],{"className":14565},[1178],[1129,14567],{"className":14568,"style":14020},[1182],[1129,14570,14572,14575],{"className":14571},[1187],[1129,14573,6646],{"className":14574,"style":2603},[1187,1191],[1129,14576,14578],{"className":14577},[1196],[1129,14579,14581,14601],{"className":14580},[1200,1201],[1129,14582,14584,14598],{"className":14583},[1205],[1129,14585,14587],{"className":14586,"style":7442},[1209],[1129,14588,14589,14592],{"style":11112},[1129,14590],{"className":14591,"style":1218},[1217],[1129,14593,14595],{"className":14594},[1222,1223,1224,1225],[1129,14596,1158],{"className":14597,"style":1232},[1187,1191,1225],[1129,14599,1254],{"className":14600},[1253],[1129,14602,14604],{"className":14603},[1205],[1129,14605,14607],{"className":14606,"style":7463},[1209],[1129,14608],{},[1129,14610,2475],{"className":14611},[2667]," 驱动，避免学习缓慢。",[1096,14614,14616],{"id":14615},"_34-交叉熵-vs-softmax对数似然-对比","3.4 交叉熵 vs Softmax+对数似然 对比",[1101,14618,14619],{},[2405,14620,14621],{},"Sigmoid + 交叉熵",[2409,14623,14624,14627,14895,14898],{},[2412,14625,14626],{},"输出层使用 Sigmoid",[2412,14628,14629,14630],{},"代价函数：",[1129,14631,14633,14697],{"className":14632},[1132],[1129,14634,14636],{"className":14635},[1136],[1138,14637,14638],{"xmlns":1140},[1142,14639,14640,14694],{},[1145,14641,14642,14644,14646,14648,14654,14656,14658,14660,14662,14664,14666,14668,14670,14672,14674,14676,14678,14680,14682,14684,14686,14688,14690,14692],{},[1151,14643,2450],{},[1342,14645,1884],{},[1342,14647,1344],{},[3018,14649,14650,14652],{},[1346,14651,1348],{},[1151,14653,6632],{},[1342,14655,1890],{},[1342,14657,6643],{"stretchy":2465},[1151,14659,6646],{},[1151,14661,6649],{},[1342,14663,6652],{},[1151,14665,1586],{},[1342,14667,1921],{},[1342,14669,2466],{"stretchy":2465},[1346,14671,1348],{},[1342,14673,1344],{},[1151,14675,6646],{},[1342,14677,2475],{"stretchy":2465},[1151,14679,6649],{},[1342,14681,6652],{},[1342,14683,2466],{"stretchy":2465},[1346,14685,1348],{},[1342,14687,1344],{},[1151,14689,1586],{},[1342,14691,2475],{"stretchy":2465},[1342,14693,6683],{"stretchy":2465},[1166,14695,14696],{"encoding":1168},"C = -\\frac{1}{n}\\sum[y\\ln a + (1-y)\\ln(1-a)]",[1129,14698,14700,14718,14828,14849,14882],{"className":14699,"ariaHidden":1174},[1173],[1129,14701,14703,14706,14709,14712,14715],{"className":14702},[1178],[1129,14704],{"className":14705,"style":5901},[1182],[1129,14707,2450],{"className":14708,"style":2580},[1187,1191],[1129,14710],{"className":14711,"style":1996},[1368],[1129,14713,1884],{"className":14714},[2000],[1129,14716],{"className":14717,"style":1996},[1368],[1129,14719,14721,14724,14727,14795,14798,14801,14804,14807,14810,14813,14816,14819,14822,14825],{"className":14720},[1178],[1129,14722],{"className":14723,"style":6714},[1182],[1129,14725,1344],{"className":14726},[1187],[1129,14728,14730,14733,14792],{"className":14729},[1187],[1129,14731],{"className":14732},[2634,3068],[1129,14734,14736],{"className":14735},[3018],[1129,14737,14739,14784],{"className":14738},[1200,1201],[1129,14740,14742,14781],{"className":14741},[1205],[1129,14743,14745,14759,14767],{"className":14744,"style":6736},[1209],[1129,14746,14747,14750],{"style":6739},[1129,14748],{"className":14749,"style":3088},[1217],[1129,14751,14753],{"className":14752},[1222,1223,1224,1225],[1129,14754,14756],{"className":14755},[1187,1225],[1129,14757,6632],{"className":14758},[1187,1191,1225],[1129,14760,14761,14764],{"style":3159},[1129,14762],{"className":14763,"style":3088},[1217],[1129,14765],{"className":14766,"style":3167},[3166],[1129,14768,14769,14772],{"style":3170},[1129,14770],{"className":14771,"style":3088},[1217],[1129,14773,14775],{"className":14774},[1222,1223,1224,1225],[1129,14776,14778],{"className":14777},[1187,1225],[1129,14779,1348],{"className":14780},[1187,1225],[1129,14782,1254],{"className":14783},[1253],[1129,14785,14787],{"className":14786},[1205],[1129,14788,14790],{"className":14789,"style":6783},[1209],[1129,14791],{},[1129,14793],{"className":14794},[2667,3068],[1129,14796],{"className":14797,"style":2061},[1368],[1129,14799,1890],{"className":14800,"style":2020},[2014,2018,2019],[1129,14802,6643],{"className":14803},[2634],[1129,14805,6646],{"className":14806,"style":2603},[1187,1191],[1129,14808],{"className":14809,"style":2061},[1368],[1129,14811,6649],{"className":14812},[2014],[1129,14814],{"className":14815,"style":2061},[1368],[1129,14817,1586],{"className":14818},[1187,1191],[1129,14820],{"className":14821,"style":1369},[1368],[1129,14823,1921],{"className":14824},[1373],[1129,14826],{"className":14827,"style":1369},[1368],[1129,14829,14831,14834,14837,14840,14843,14846],{"className":14830},[1178],[1129,14832],{"className":14833,"style":6081},[1182],[1129,14835,2466],{"className":14836},[2634],[1129,14838,1348],{"className":14839},[1187],[1129,14841],{"className":14842,"style":1369},[1368],[1129,14844,1344],{"className":14845},[1373],[1129,14847],{"className":14848,"style":1369},[1368],[1129,14850,14852,14855,14858,14861,14864,14867,14870,14873,14876,14879],{"className":14851},[1178],[1129,14853],{"className":14854,"style":6081},[1182],[1129,14856,6646],{"className":14857,"style":2603},[1187,1191],[1129,14859,2475],{"className":14860},[2667],[1129,14862],{"className":14863,"style":2061},[1368],[1129,14865,6649],{"className":14866},[2014],[1129,14868,2466],{"className":14869},[2634],[1129,14871,1348],{"className":14872},[1187],[1129,14874],{"className":14875,"style":1369},[1368],[1129,14877,1344],{"className":14878},[1373],[1129,14880],{"className":14881,"style":1369},[1368],[1129,14883,14885,14888,14891],{"className":14884},[1178],[1129,14886],{"className":14887,"style":6081},[1182],[1129,14889,1586],{"className":14890},[1187,1191],[1129,14892,14894],{"className":14893},[2667],")]",[2412,14896,14897],{},"适合二分类或多标签任务",[2412,14899,14900],{},"各输出独立",[1101,14902,14903],{},[2405,14904,14905],{},"Softmax + 对数似然",[2409,14907,14908,14911,15035,15038],{},[2412,14909,14910],{},"输出层使用 Softmax",[2412,14912,14629,14913],{},[1129,14914,14916,14945],{"className":14915},[1132],[1129,14917,14919],{"className":14918},[1136],[1138,14920,14921],{"xmlns":1140},[1142,14922,14923,14943],{},[1145,14924,14925,14927,14929,14931,14933,14935],{},[1151,14926,2450],{},[1342,14928,1884],{},[1342,14930,1344],{},[1151,14932,6649],{},[1342,14934,6652],{},[1148,14936,14937,14939,14941],{},[1151,14938,1586],{},[1151,14940,6646],{},[1151,14942,2437],{},[1166,14944,13259],{"encoding":1168},[1129,14946,14948,14966],{"className":14947,"ariaHidden":1174},[1173],[1129,14949,14951,14954,14957,14960,14963],{"className":14950},[1178],[1129,14952],{"className":14953,"style":5901},[1182],[1129,14955,2450],{"className":14956,"style":2580},[1187,1191],[1129,14958],{"className":14959,"style":1996},[1368],[1129,14961,1884],{"className":14962},[2000],[1129,14964],{"className":14965,"style":1996},[1368],[1129,14967,14969,14972,14975,14978,14981,14984],{"className":14968},[1178],[1129,14970],{"className":14971,"style":13287},[1182],[1129,14973,1344],{"className":14974},[1187],[1129,14976],{"className":14977,"style":2061},[1368],[1129,14979,6649],{"className":14980},[2014],[1129,14982],{"className":14983,"style":2061},[1368],[1129,14985,14987,14990],{"className":14986},[1187],[1129,14988,1586],{"className":14989},[1187,1191],[1129,14991,14993],{"className":14992},[1196],[1129,14994,14996,15027],{"className":14995},[1200,1201],[1129,14997,14999,15024],{"className":14998},[1205],[1129,15000,15002,15013],{"className":15001,"style":2488},[1209],[1129,15003,15004,15007],{"style":13320},[1129,15005],{"className":15006,"style":1218},[1217],[1129,15008,15010],{"className":15009},[1222,1223,1224,1225],[1129,15011,6646],{"className":15012,"style":2603},[1187,1191,1225],[1129,15014,15015,15018],{"style":1239},[1129,15016],{"className":15017,"style":1218},[1217],[1129,15019,15021],{"className":15020},[1222,1223,1224,1225],[1129,15022,2437],{"className":15023},[1187,1191,1225],[1129,15025,1254],{"className":15026},[1253],[1129,15028,15030],{"className":15029},[1205],[1129,15031,15033],{"className":15032,"style":13350},[1209],[1129,15034],{},[2412,15036,15037],{},"适合多分类（互斥）任务",[2412,15039,15040],{},"各输出竞争（和为 1）",[5907,15042],{},[1091,15044,15046],{"id":15045},"四过拟合问题","四、过拟合问题",[1096,15048,15050],{"id":15049},"_41-过拟合现象","4.1 过拟合现象",[1101,15052,15053],{},"当模型参数远多于训练数据时，网络会记住训练数据的噪声而非学习通用规律。",[1101,15055,15056],{},[2405,15057,15058],{},"实验示例",[1101,15060,15061],{},"使用 30 个隐藏神经元的网络（共 23860 个参数），仅用 1000 张图片训练：",[2409,15063,15064,15067,15070],{},[2412,15065,15066],{},"训练准确率持续上升（接近 100%）",[2412,15068,15069],{},"测试准确率很快达到平台期并停止提升",[2412,15071,15072],{},"训练代价持续下降，但测试代价开始上升",[1096,15074,15076],{"id":15075},"_42-检测过拟合","4.2 检测过拟合",[3608,15078,15079,15082,15089],{},[2412,15080,15081],{},"跟踪测试集（或验证集）上的准确率",[2412,15083,15084,15085,15088],{},"当测试准确率不再提升时，停止训练（",[2405,15086,15087],{},"早停法 Early Stopping","）",[2412,15090,15091],{},"观察训练代价与测试代价的差距是否持续增大",[1096,15093,15095],{"id":15094},"_43-最直接的解决方案增加训练数据","4.3 最直接的解决方案：增加训练数据",[1101,15097,15098],{},"将训练数据从 1000 张增加到 50000 张后，过拟合现象大幅缓解，测试准确率显著提升。",[1101,15100,15101],{},"更多的数据几乎总是比更复杂的模型更有效。但获取更多数据并非总是可行，因此需要正则化等技术。",[5907,15103],{},[1091,15105,15107],{"id":15106},"五正则化方法","五、正则化方法",[1101,15109,15110],{},"当网络参数太多、训练数据太少时，网络会过拟合—— 在训练集上表现很好，但在新数据上很差（相当于 \"死记硬背\" 而不是 \"学会规律\"）。",[1101,15112,15113],{},"正则化的核心思想是给代价函数加一个 \"惩罚项\"，让网络倾向于用更小、更简单的权重，从而避免过拟合。",[1096,15115,15117],{"id":15116},"_51-l1-正则化","5.1 L1 正则化",[1101,15119,15120],{},"L1 正则化使用权重的绝对值之和作为惩罚项：",[1101,15122,15123],{},[1129,15124,15126,15170],{"className":15125},[1132],[1129,15127,15129],{"className":15128},[1136],[1138,15130,15131],{"xmlns":1140},[1142,15132,15133,15167],{},[1145,15134,15135,15137,15139,15145,15147,15154,15160,15163,15165],{},[1151,15136,2450],{},[1342,15138,1884],{},[1886,15140,15141,15143],{},[1151,15142,2450],{},[1346,15144,6526],{},[1342,15146,1921],{},[3018,15148,15149,15152],{},[1151,15150,15151],{},"λ",[1151,15153,6632],{},[1886,15155,15156,15158],{},[1342,15157,1890],{},[1151,15159,1153],{},[1151,15161,15162],{"mathvariant":2444},"∣",[1151,15164,1153],{},[1151,15166,15162],{"mathvariant":2444},[1166,15168,15169],{"encoding":1168},"C = C_0 + \\frac{\\lambda}{n} \\sum_w |w|",[1129,15171,15173,15191,15248],{"className":15172,"ariaHidden":1174},[1173],[1129,15174,15176,15179,15182,15185,15188],{"className":15175},[1178],[1129,15177],{"className":15178,"style":5901},[1182],[1129,15180,2450],{"className":15181,"style":2580},[1187,1191],[1129,15183],{"className":15184,"style":1996},[1368],[1129,15186,1884],{"className":15187},[2000],[1129,15189],{"className":15190,"style":1996},[1368],[1129,15192,15194,15197,15239,15242,15245],{"className":15193},[1178],[1129,15195],{"className":15196,"style":2533},[1182],[1129,15198,15200,15203],{"className":15199},[1187],[1129,15201,2450],{"className":15202,"style":2580},[1187,1191],[1129,15204,15206],{"className":15205},[1196],[1129,15207,15209,15231],{"className":15208},[1200,1201],[1129,15210,15212,15228],{"className":15211},[1205],[1129,15213,15216],{"className":15214,"style":15215},[1209],"height:0.3011em;",[1129,15217,15219,15222],{"style":15218},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[1129,15220],{"className":15221,"style":1218},[1217],[1129,15223,15225],{"className":15224},[1222,1223,1224,1225],[1129,15226,6526],{"className":15227},[1187,1225],[1129,15229,1254],{"className":15230},[1253],[1129,15232,15234],{"className":15233},[1205],[1129,15235,15237],{"className":15236,"style":2574},[1209],[1129,15238],{},[1129,15240],{"className":15241,"style":1369},[1368],[1129,15243,1921],{"className":15244},[1373],[1129,15246],{"className":15247,"style":1369},[1368],[1129,15249,15251,15254,15322,15325,15365,15368,15371,15374],{"className":15250},[1178],[1129,15252],{"className":15253,"style":9888},[1182],[1129,15255,15257,15260,15319],{"className":15256},[1187],[1129,15258],{"className":15259},[2634,3068],[1129,15261,15263],{"className":15262},[3018],[1129,15264,15266,15311],{"className":15265},[1200,1201],[1129,15267,15269,15308],{"className":15268},[1205],[1129,15270,15272,15286,15294],{"className":15271,"style":3081},[1209],[1129,15273,15274,15277],{"style":6739},[1129,15275],{"className":15276,"style":3088},[1217],[1129,15278,15280],{"className":15279},[1222,1223,1224,1225],[1129,15281,15283],{"className":15282},[1187,1225],[1129,15284,6632],{"className":15285},[1187,1191,1225],[1129,15287,15288,15291],{"style":3159},[1129,15289],{"className":15290,"style":3088},[1217],[1129,15292],{"className":15293,"style":3167},[3166],[1129,15295,15296,15299],{"style":3170},[1129,15297],{"className":15298,"style":3088},[1217],[1129,15300,15302],{"className":15301},[1222,1223,1224,1225],[1129,15303,15305],{"className":15304},[1187,1225],[1129,15306,15151],{"className":15307},[1187,1191,1225],[1129,15309,1254],{"className":15310},[1253],[1129,15312,15314],{"className":15313},[1205],[1129,15315,15317],{"className":15316,"style":6783},[1209],[1129,15318],{},[1129,15320],{"className":15321},[2667,3068],[1129,15323],{"className":15324,"style":2061},[1368],[1129,15326,15328,15331],{"className":15327},[2014],[1129,15329,1890],{"className":15330,"style":2020},[2014,2018,2019],[1129,15332,15334],{"className":15333},[1196],[1129,15335,15337,15357],{"className":15336},[1200,1201],[1129,15338,15340,15354],{"className":15339},[1205],[1129,15341,15343],{"className":15342,"style":6810},[1209],[1129,15344,15345,15348],{"style":2036},[1129,15346],{"className":15347,"style":1218},[1217],[1129,15349,15351],{"className":15350},[1222,1223,1224,1225],[1129,15352,1153],{"className":15353,"style":1192},[1187,1191,1225],[1129,15355,1254],{"className":15356},[1253],[1129,15358,15360],{"className":15359},[1205],[1129,15361,15363],{"className":15362,"style":2055},[1209],[1129,15364],{},[1129,15366],{"className":15367,"style":2061},[1368],[1129,15369,15162],{"className":15370},[1187],[1129,15372,1153],{"className":15373,"style":1192},[1187,1191],[1129,15375,15162],{"className":15376},[1187],[1101,15378,6921,15379,15449,15450,15503],{},[1129,15380,15382,15400],{"className":15381},[1132],[1129,15383,15385],{"className":15384},[1136],[1138,15386,15387],{"xmlns":1140},[1142,15388,15389,15397],{},[1145,15390,15391],{},[1886,15392,15393,15395],{},[1151,15394,2450],{},[1346,15396,6526],{},[1166,15398,15399],{"encoding":1168},"C_0",[1129,15401,15403],{"className":15402,"ariaHidden":1174},[1173],[1129,15404,15406,15409],{"className":15405},[1178],[1129,15407],{"className":15408,"style":2533},[1182],[1129,15410,15412,15415],{"className":15411},[1187],[1129,15413,2450],{"className":15414,"style":2580},[1187,1191],[1129,15416,15418],{"className":15417},[1196],[1129,15419,15421,15441],{"className":15420},[1200,1201],[1129,15422,15424,15438],{"className":15423},[1205],[1129,15425,15427],{"className":15426,"style":15215},[1209],[1129,15428,15429,15432],{"style":15218},[1129,15430],{"className":15431,"style":1218},[1217],[1129,15433,15435],{"className":15434},[1222,1223,1224,1225],[1129,15436,6526],{"className":15437},[1187,1225],[1129,15439,1254],{"className":15440},[1253],[1129,15442,15444],{"className":15443},[1205],[1129,15445,15447],{"className":15446,"style":2574},[1209],[1129,15448],{}," 为原始代价函数，",[1129,15451,15453,15472],{"className":15452},[1132],[1129,15454,15456],{"className":15455},[1136],[1138,15457,15458],{"xmlns":1140},[1142,15459,15460,15469],{},[1145,15461,15462,15464,15467],{},[1151,15463,15151],{},[1342,15465,15466],{},">",[1346,15468,6526],{},[1166,15470,15471],{"encoding":1168},"\\lambda > 0",[1129,15473,15475,15494],{"className":15474,"ariaHidden":1174},[1173],[1129,15476,15478,15482,15485,15488,15491],{"className":15477},[1178],[1129,15479],{"className":15480,"style":15481},[1182],"height:0.7335em;vertical-align:-0.0391em;",[1129,15483,15151],{"className":15484},[1187,1191],[1129,15486],{"className":15487,"style":1996},[1368],[1129,15489,15466],{"className":15490},[2000],[1129,15492],{"className":15493,"style":1996},[1368],[1129,15495,15497,15500],{"className":15496},[1178],[1129,15498],{"className":15499,"style":1383},[1182],[1129,15501,6526],{"className":15502},[1187]," 为正则化参数，求和遍历网络中所有权重。",[15505,15506,15507],"h3",{"id":15507},"权重更新规则",[1101,15509,15510],{},[1129,15511,15513,15576],{"className":15512},[1132],[1129,15514,15516],{"className":15515},[1136],[1138,15517,15518],{"xmlns":1140},[1142,15519,15520,15573],{},[1145,15521,15522,15524,15527,15529,15531,15542,15545,15547,15549,15551,15553,15555],{},[1151,15523,1153],{},[1342,15525,15526],{},"→",[1151,15528,1153],{},[1342,15530,1344],{},[3018,15532,15533,15540],{},[1145,15534,15535,15538],{},[1151,15536,15537],{},"η",[1151,15539,15151],{},[1151,15541,6632],{},[5470,15543,15544],{},"sgn",[1342,15546,2466],{"stretchy":2465},[1151,15548,1153],{},[1342,15550,2475],{"stretchy":2465},[1342,15552,1344],{},[1151,15554,15537],{},[3018,15556,15557,15567],{},[1145,15558,15559,15561],{},[1151,15560,3024],{"mathvariant":2444},[1886,15562,15563,15565],{},[1151,15564,2450],{},[1346,15566,6526],{},[1145,15568,15569,15571],{},[1151,15570,3024],{"mathvariant":2444},[1151,15572,1153],{},[1166,15574,15575],{"encoding":1168},"w \\to w - \\frac{\\eta\\lambda}{n} \\text{sgn}(w) - \\eta \\frac{\\partial C_0}{\\partial w}",[1129,15577,15579,15597,15616,15719],{"className":15578,"ariaHidden":1174},[1173],[1129,15580,15582,15585,15588,15591,15594],{"className":15581},[1178],[1129,15583],{"className":15584,"style":3696},[1182],[1129,15586,1153],{"className":15587,"style":1192},[1187,1191],[1129,15589],{"className":15590,"style":1996},[1368],[1129,15592,15526],{"className":15593},[2000],[1129,15595],{"className":15596,"style":1996},[1368],[1129,15598,15600,15604,15607,15610,15613],{"className":15599},[1178],[1129,15601],{"className":15602,"style":15603},[1182],"height:0.6667em;vertical-align:-0.0833em;",[1129,15605,1153],{"className":15606,"style":1192},[1187,1191],[1129,15608],{"className":15609,"style":1369},[1368],[1129,15611,1344],{"className":15612},[1373],[1129,15614],{"className":15615,"style":1369},[1368],[1129,15617,15619,15623,15695,15701,15704,15707,15710,15713,15716],{"className":15618},[1178],[1129,15620],{"className":15621,"style":15622},[1182],"height:1.2772em;vertical-align:-0.345em;",[1129,15624,15626,15629,15692],{"className":15625},[1187],[1129,15627],{"className":15628},[2634,3068],[1129,15630,15632],{"className":15631},[3018],[1129,15633,15635,15684],{"className":15634},[1200,1201],[1129,15636,15638,15681],{"className":15637},[1205],[1129,15639,15642,15656,15664],{"className":15640,"style":15641},[1209],"height:0.9322em;",[1129,15643,15644,15647],{"style":6739},[1129,15645],{"className":15646,"style":3088},[1217],[1129,15648,15650],{"className":15649},[1222,1223,1224,1225],[1129,15651,15653],{"className":15652},[1187,1225],[1129,15654,6632],{"className":15655},[1187,1191,1225],[1129,15657,15658,15661],{"style":3159},[1129,15659],{"className":15660,"style":3088},[1217],[1129,15662],{"className":15663,"style":3167},[3166],[1129,15665,15666,15669],{"style":8212},[1129,15667],{"className":15668,"style":3088},[1217],[1129,15670,15672],{"className":15671},[1222,1223,1224,1225],[1129,15673,15675,15678],{"className":15674},[1187,1225],[1129,15676,15537],{"className":15677,"style":2603},[1187,1191,1225],[1129,15679,15151],{"className":15680},[1187,1191,1225],[1129,15682,1254],{"className":15683},[1253],[1129,15685,15687],{"className":15686},[1205],[1129,15688,15690],{"className":15689,"style":6783},[1209],[1129,15691],{},[1129,15693],{"className":15694},[2667,3068],[1129,15696,15698],{"className":15697},[1187,5683],[1129,15699,15544],{"className":15700},[1187],[1129,15702,2466],{"className":15703},[2634],[1129,15705,1153],{"className":15706,"style":1192},[1187,1191],[1129,15708,2475],{"className":15709},[2667],[1129,15711],{"className":15712,"style":1369},[1368],[1129,15714,1344],{"className":15715},[1373],[1129,15717],{"className":15718,"style":1369},[1368],[1129,15720,15722,15726,15729],{"className":15721},[1178],[1129,15723],{"className":15724,"style":15725},[1182],"height:1.2412em;vertical-align:-0.345em;",[1129,15727,15537],{"className":15728,"style":2603},[1187,1191],[1129,15730,15732,15735,15842],{"className":15731},[1187],[1129,15733],{"className":15734},[2634,3068],[1129,15736,15738],{"className":15737},[3018],[1129,15739,15741,15834],{"className":15740},[1200,1201],[1129,15742,15744,15831],{"className":15743},[1205],[1129,15745,15748,15765,15773],{"className":15746,"style":15747},[1209],"height:0.8962em;",[1129,15749,15750,15753],{"style":6739},[1129,15751],{"className":15752,"style":3088},[1217],[1129,15754,15756],{"className":15755},[1222,1223,1224,1225],[1129,15757,15759,15762],{"className":15758},[1187,1225],[1129,15760,3024],{"className":15761,"style":3098},[1187,1225],[1129,15763,1153],{"className":15764,"style":1192},[1187,1191,1225],[1129,15766,15767,15770],{"style":3159},[1129,15768],{"className":15769,"style":3088},[1217],[1129,15771],{"className":15772,"style":3167},[3166],[1129,15774,15776,15779],{"style":15775},"top:-3.4101em;",[1129,15777],{"className":15778,"style":3088},[1217],[1129,15780,15782],{"className":15781},[1222,1223,1224,1225],[1129,15783,15785,15788],{"className":15784},[1187,1225],[1129,15786,3024],{"className":15787,"style":3098},[1187,1225],[1129,15789,15791,15794],{"className":15790},[1187,1225],[1129,15792,2450],{"className":15793,"style":2580},[1187,1191,1225],[1129,15795,15797],{"className":15796},[1196],[1129,15798,15800,15822],{"className":15799},[1200,1201],[1129,15801,15803,15819],{"className":15802},[1205],[1129,15804,15807],{"className":15805,"style":15806},[1209],"height:0.3173em;",[1129,15808,15810,15813],{"style":15809},"top:-2.357em;margin-left:-0.0715em;margin-right:0.0714em;",[1129,15811],{"className":15812,"style":3124},[1217],[1129,15814,15816],{"className":15815},[1222,3128,3129,1225],[1129,15817,6526],{"className":15818},[1187,1225],[1129,15820,1254],{"className":15821},[1253],[1129,15823,15825],{"className":15824},[1205],[1129,15826,15829],{"className":15827,"style":15828},[1209],"height:0.143em;",[1129,15830],{},[1129,15832,1254],{"className":15833},[1253],[1129,15835,15837],{"className":15836},[1205],[1129,15838,15840],{"className":15839,"style":6783},[1209],[1129,15841],{},[1129,15843],{"className":15844},[2667,3068],[1101,15846,15847],{},"sgn 是符号函数（Sign Function）",[1096,15849,15851],{"id":15850},"_52-l2-正则化权重衰减","5.2 L2 正则化（权重衰减）",[1101,15853,15854],{},"在原始代价函数基础上添加权重惩罚项：",[1101,15856,15857],{},[1129,15858,15860,15906],{"className":15859},[1132],[1129,15861,15863],{"className":15862},[1136],[1138,15864,15865],{"xmlns":1140},[1142,15866,15867,15903],{},[1145,15868,15869,15871,15873,15879,15881,15891,15897],{},[1151,15870,2450],{},[1342,15872,1884],{},[1886,15874,15875,15877],{},[1151,15876,2450],{},[1346,15878,6526],{},[1342,15880,1921],{},[3018,15882,15883,15885],{},[1151,15884,15151],{},[1145,15886,15887,15889],{},[1346,15888,3724],{},[1151,15890,6632],{},[1886,15892,15893,15895],{},[1342,15894,1890],{},[1151,15896,1153],{},[2431,15898,15899,15901],{},[1151,15900,1153],{},[1346,15902,3724],{},[1166,15904,15905],{"encoding":1168},"C = C_0 + \\frac{\\lambda}{2n} \\sum_w w^2",[1129,15907,15909,15927,15982],{"className":15908,"ariaHidden":1174},[1173],[1129,15910,15912,15915,15918,15921,15924],{"className":15911},[1178],[1129,15913],{"className":15914,"style":5901},[1182],[1129,15916,2450],{"className":15917,"style":2580},[1187,1191],[1129,15919],{"className":15920,"style":1996},[1368],[1129,15922,1884],{"className":15923},[2000],[1129,15925],{"className":15926,"style":1996},[1368],[1129,15928,15930,15933,15973,15976,15979],{"className":15929},[1178],[1129,15931],{"className":15932,"style":2533},[1182],[1129,15934,15936,15939],{"className":15935},[1187],[1129,15937,2450],{"className":15938,"style":2580},[1187,1191],[1129,15940,15942],{"className":15941},[1196],[1129,15943,15945,15965],{"className":15944},[1200,1201],[1129,15946,15948,15962],{"className":15947},[1205],[1129,15949,15951],{"className":15950,"style":15215},[1209],[1129,15952,15953,15956],{"style":15218},[1129,15954],{"className":15955,"style":1218},[1217],[1129,15957,15959],{"className":15958},[1222,1223,1224,1225],[1129,15960,6526],{"className":15961},[1187,1225],[1129,15963,1254],{"className":15964},[1253],[1129,15966,15968],{"className":15967},[1205],[1129,15969,15971],{"className":15970,"style":2574},[1209],[1129,15972],{},[1129,15974],{"className":15975,"style":1369},[1368],[1129,15977,1921],{"className":15978},[1373],[1129,15980],{"className":15981,"style":1369},[1368],[1129,15983,15985,15988,16059,16062,16102,16105],{"className":15984},[1178],[1129,15986],{"className":15987,"style":9888},[1182],[1129,15989,15991,15994,16056],{"className":15990},[1187],[1129,15992],{"className":15993},[2634,3068],[1129,15995,15997],{"className":15996},[3018],[1129,15998,16000,16048],{"className":15999},[1200,1201],[1129,16001,16003,16045],{"className":16002},[1205],[1129,16004,16006,16023,16031],{"className":16005,"style":3081},[1209],[1129,16007,16008,16011],{"style":6739},[1129,16009],{"className":16010,"style":3088},[1217],[1129,16012,16014],{"className":16013},[1222,1223,1224,1225],[1129,16015,16017,16020],{"className":16016},[1187,1225],[1129,16018,3724],{"className":16019},[1187,1225],[1129,16021,6632],{"className":16022},[1187,1191,1225],[1129,16024,16025,16028],{"style":3159},[1129,16026],{"className":16027,"style":3088},[1217],[1129,16029],{"className":16030,"style":3167},[3166],[1129,16032,16033,16036],{"style":3170},[1129,16034],{"className":16035,"style":3088},[1217],[1129,16037,16039],{"className":16038},[1222,1223,1224,1225],[1129,16040,16042],{"className":16041},[1187,1225],[1129,16043,15151],{"className":16044},[1187,1191,1225],[1129,16046,1254],{"className":16047},[1253],[1129,16049,16051],{"className":16050},[1205],[1129,16052,16054],{"className":16053,"style":6783},[1209],[1129,16055],{},[1129,16057],{"className":16058},[2667,3068],[1129,16060],{"className":16061,"style":2061},[1368],[1129,16063,16065,16068],{"className":16064},[2014],[1129,16066,1890],{"className":16067,"style":2020},[2014,2018,2019],[1129,16069,16071],{"className":16070},[1196],[1129,16072,16074,16094],{"className":16073},[1200,1201],[1129,16075,16077,16091],{"className":16076},[1205],[1129,16078,16080],{"className":16079,"style":6810},[1209],[1129,16081,16082,16085],{"style":2036},[1129,16083],{"className":16084,"style":1218},[1217],[1129,16086,16088],{"className":16087},[1222,1223,1224,1225],[1129,16089,1153],{"className":16090,"style":1192},[1187,1191,1225],[1129,16092,1254],{"className":16093},[1253],[1129,16095,16097],{"className":16096},[1205],[1129,16098,16100],{"className":16099,"style":2055},[1209],[1129,16101],{},[1129,16103],{"className":16104,"style":2061},[1368],[1129,16106,16108,16111],{"className":16107},[1187],[1129,16109,1153],{"className":16110,"style":1192},[1187,1191],[1129,16112,16114],{"className":16113},[1196],[1129,16115,16117],{"className":16116},[1200],[1129,16118,16120],{"className":16119},[1205],[1129,16121,16123],{"className":16122,"style":3651},[1209],[1129,16124,16125,16128],{"style":1239},[1129,16126],{"className":16127,"style":1218},[1217],[1129,16129,16131],{"className":16130},[1222,1223,1224,1225],[1129,16132,3724],{"className":16133},[1187,1225],[1101,16135,6921,16136,15449,16205,15503],{},[1129,16137,16139,16156],{"className":16138},[1132],[1129,16140,16142],{"className":16141},[1136],[1138,16143,16144],{"xmlns":1140},[1142,16145,16146,16154],{},[1145,16147,16148],{},[1886,16149,16150,16152],{},[1151,16151,2450],{},[1346,16153,6526],{},[1166,16155,15399],{"encoding":1168},[1129,16157,16159],{"className":16158,"ariaHidden":1174},[1173],[1129,16160,16162,16165],{"className":16161},[1178],[1129,16163],{"className":16164,"style":2533},[1182],[1129,16166,16168,16171],{"className":16167},[1187],[1129,16169,2450],{"className":16170,"style":2580},[1187,1191],[1129,16172,16174],{"className":16173},[1196],[1129,16175,16177,16197],{"className":16176},[1200,1201],[1129,16178,16180,16194],{"className":16179},[1205],[1129,16181,16183],{"className":16182,"style":15215},[1209],[1129,16184,16185,16188],{"style":1521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",[1129,16278,16280,16293],{"className":16279},[1132],[1129,16281,16283],{"className":16282},[1136],[1138,16284,16285],{"xmlns":1140},[1142,16286,16287,16291],{},[1145,16288,16289],{},[1151,16290,1153],{},[1166,16292,1153],{"encoding":1168},[1129,16294,16296],{"className":16295,"ariaHidden":1174},[1173],[1129,16297,16299,16302],{"className":16298},[1178],[1129,16300],{"className":16301,"style":3696},[1182],[1129,16303,1153],{"className":16304,"style":1192},[1187,1191],[1126,16306,16307],{},[1129,16308,16310,16370],{"className":16309},[1132],[1129,16311,16313],{"className":16312},[1136],[1138,16314,16315],{"xmlns":1140},[1142,16316,16317,16367],{},[1145,16318,16319,16321,16323,16325,16345,16347,16349],{},[1151,16320,1153],{},[1342,16322,15526],{},[1151,16324,1153],{},[1145,16326,16327,16329,16331,16333,16343],{},[1342,16328,2466],{"fence":1174},[1346,16330,1348],{},[1342,16332,1344],{},[3018,16334,16335,16341],{},[1145,16336,16337,16339],{},[1151,16338,15537],{},[1151,16340,15151],{},[1151,16342,6632],{},[1342,16344,2475],{"fence":1174},[1342,16346,1344],{},[1151,16348,15537],{},[3018,16350,16351,16361],{},[1145,16352,16353,16355],{},[1151,16354,3024],{"mathvariant":2444},[1886,16356,16357,16359],{},[1151,16358,2450],{},[1346,16360,6526],{},[1145,16362,16363,16365],{},[1151,16364,3024],{"mathvariant":2444},[1151,16366,1153],{},[1166,16368,16369],{"encoding":1168},"w \\to w\\left(1 - \\frac{\\eta\\lambda}{n}\\right) - \\eta \\frac{\\partial C_0}{\\partial w}",[1129,16371,16373,16391,16510],{"className":16372,"ariaHidden":1174},[1173],[1129,16374,16376,16379,16382,16385,16388],{"className":16375},[1178],[1129,16377],{"className":16378,"style":3696},[1182],[1129,16380,1153],{"className":16381,"style":1192},[1187,1191],[1129,16383],{"className":16384,"style":1996},[1368],[1129,16386,15526],{"className":16387},[2000],[1129,16389],{"className":16390,"style":1996},[1368],[1129,16392,16394,16397,16400,16403,16501,16504,16507],{"className":16393},[1178],[1129,16395],{"className":16396,"style":8142},[1182],[1129,16398,1153],{"className":16399,"style":1192},[1187,1191],[1129,16401],{"className":16402,"style":2061},[1368],[1129,16404,16406,16412,16415,16418,16421,16424,16495],{"className":16405},[3793],[1129,16407,16409],{"className":16408,"style":6843},[2634,6842],[1129,16410,2466],{"className":16411},[8158,8159],[1129,16413,1348],{"className":16414},[1187],[1129,16416],{"className":16417,"style":1369},[1368],[1129,16419,1344],{"className":16420},[1373],[1129,16422],{"className":16423,"style":1369},[1368],[1129,16425,16427,16430,16492],{"className":16426},[1187],[1129,16428],{"className":16429},[2634,3068],[1129,16431,16433],{"className":16432},[3018],[1129,16434,16436,16484],{"className":16435},[1200,1201],[1129,16437,16439,16481],{"className":16438},[1205],[1129,16440,16442,16456,16464],{"className":16441,"style":15641},[1209],[1129,16443,16444,16447],{"style":6739},[1129,16445],{"className":16446,"style":3088},[1217],[1129,16448,16450],{"className":16449},[1222,1223,1224,1225],[1129,16451,16453],{"className":16452},[1187,1225],[1129,16454,6632],{"className":16455},[1187,1191,1225],[1129,16457,16458,16461],{"style":3159},[1129,16459],{"className":16460,"style":3088},[1217],[1129,16462],{"className":16463,"style":3167},[3166],[1129,16465,16466,16469],{"style":8212},[1129,16467],{"className":16468,"style":3088},[1217],[1129,16470,16472],{"className":16471},[1222,1223,1224,1225],[1129,16473,16475,16478],{"className":16474},[1187,1225],[1129,16476,15537],{"className":16477,"style":2603},[1187,1191,1225],[1129,16479,15151],{"className":16480},[1187,1191,1225],[1129,16482,1254],{"className":16483},[1253],[1129,16485,16487],{"className":16486},[1205],[1129,16488,16490],{"className":16489,"style":6783},[1209],[1129,16491],{},[1129,16493],{"className":16494},[2667,3068],[1129,16496,16498],{"className":16497,"style":6843},[2667,6842],[1129,16499,2475],{"className":16500},[8158,8159],[1129,16502],{"className":16503,"style":1369},[1368],[1129,16505,1344],{"className":16506},[1373],[1129,16508],{"className":16509,"style":1369},[1368],[1129,16511,16513,16516,16519],{"className":16512},[1178],[1129,16514],{"className":16515,"style":15725},[1182],[1129,16517,15537],{"className":16518,"style":2603},[1187,1191],[1129,16520,16522,16525,16627],{"className":16521},[1187],[1129,16523],{"className":16524},[2634,3068],[1129,16526,16528],{"className":16527},[3018],[1129,16529,16531,16619],{"className":16530},[1200,1201],[1129,16532,16534,16616],{"className":16533},[1205],[1129,16535,16537,16554,16562],{"className":16536,"style":15747},[1209],[1129,16538,16539,16542],{"style":6739},[1129,16540],{"className":16541,"style":3088},[1217],[1129,16543,16545],{"className":16544},[1222,1223,1224,1225],[1129,16546,16548,16551],{"className":16547},[1187,1225],[1129,16549,3024],{"className":16550,"style":3098},[1187,1225],[1129,16552,1153],{"className":16553,"style":1192},[1187,1191,1225],[1129,16555,16556,16559],{"style":3159},[1129,16557],{"className":16558,"style":3088},[1217],[1129,16560],{"className":16561,"style":3167},[3166],[1129,16563,16564,16567],{"style":15775},[1129,16565],{"className":16566,"style":3088},[1217],[1129,16568,16570],{"className":16569},[1222,1223,1224,1225],[1129,16571,16573,16576],{"className":16572},[1187,1225],[1129,16574,3024],{"className":16575,"style":3098},[1187,1225],[1129,16577,16579,16582],{"className":16578},[1187,1225],[1129,16580,2450],{"className":16581,"style":2580},[1187,1191,1225],[1129,16583,16585],{"className":16584},[1196],[1129,16586,16588,16608],{"className":16587},[1200,1201],[1129,16589,16591,16605],{"className":16590},[1205],[1129,16592,16594],{"className":16593,"style":15806},[1209],[1129,16595,16596,16599],{"style":15809},[1129,16597],{"className":16598,"style":3124},[1217],[1129,16600,16602],{"className":16601},[1222,3128,3129,1225],[1129,16603,6526],{"className":16604},[1187,1225],[1129,16606,1254],{"className":16607},[1253],[1129,16609,16611],{"className":16610},[1205],[1129,16612,16614],{"className":16613,"style":15828},[1209],[1129,16615],{},[1129,16617,1254],{"className":16618},[1253],[1129,16620,16622],{"className":16621},[1205],[1129,16623,16625],{"className":16624,"style":6783},[1209],[1129,16626],{},[1129,16628],{"className":16629},[2667,3068],[1111,16631,16632,16663],{},[1126,16633,16634,16635],{},"偏置 ",[1129,16636,16638,16651],{"className":16637},[1132],[1129,16639,16641],{"className":16640},[1136],[1138,16642,16643],{"xmlns":1140},[1142,16644,16645,16649],{},[1145,16646,16647],{},[1151,16648,1436],{},[1166,16650,1436],{"encoding":1168},[1129,16652,16654],{"className":16653,"ariaHidden":1174},[1173],[1129,16655,16657,16660],{"className":16656},[1178],[1129,16658],{"className":16659,"style":1292},[1182],[1129,16661,1436],{"className":16662},[1187,1191],[1126,16664,16665,16867],{},[1129,16666,16668,16708],{"className":16667},[1132],[1129,16669,16671],{"className":16670},[1136],[1138,16672,16673],{"xmlns":1140},[1142,16674,16675,16705],{},[1145,16676,16677,16679,16681,16683,16685,16687],{},[1151,16678,1436],{},[1342,16680,15526],{},[1151,16682,1436],{},[1342,16684,1344],{},[1151,16686,15537],{},[3018,16688,16689,16699],{},[1145,16690,16691,16693],{},[1151,16692,3024],{"mathvariant":2444},[1886,16694,16695,16697],{},[1151,16696,2450],{},[1346,16698,6526],{},[1145,16700,16701,16703],{},[1151,16702,3024],{"mathvariant":2444},[1151,16704,1436],{},[1166,16706,16707],{"encoding":1168},"b \\to b - \\eta \\frac{\\partial C_0}{\\partial b}",[1129,16709,16711,16729,16747],{"className":16710,"ariaHidden":1174},[1173],[1129,16712,16714,16717,16720,16723,16726],{"className":16713},[1178],[1129,16715],{"className":16716,"style":1292},[1182],[1129,16718,1436],{"className":16719},[1187,1191],[1129,16721],{"className":16722,"style":1996},[1368],[1129,16724,15526],{"className":16725},[2000],[1129,16727],{"className":16728,"style":1996},[1368],[1129,16730,16732,16735,16738,16741,16744],{"className":16731},[1178],[1129,16733],{"className":16734,"style":1361},[1182],[1129,16736,1436],{"className":16737},[1187,1191],[1129,16739],{"className":16740,"style":1369},[1368],[1129,16742,1344],{"className":16743},[1373],[1129,16745],{"className":16746,"style":1369},[1368],[1129,16748,16750,16753,16756],{"className":16749},[1178],[1129,16751],{"className":16752,"style":15725},[1182],[1129,16754,15537],{"className":16755,"style":2603},[1187,1191],[1129,16757,16759,16762,16864],{"className":16758},[1187],[1129,16760],{"className":16761},[2634,3068],[1129,16763,16765],{"className":16764},[3018],[1129,16766,16768,16856],{"className":16767},[1200,1201],[1129,16769,16771,16853],{"className":16770},[1205],[1129,16772,16774,16791,16799],{"className":16773,"style":15747},[1209],[1129,16775,16776,16779],{"style":6739},[1129,16777],{"className":16778,"style":3088},[1217],[1129,16780,16782],{"className":16781},[1222,1223,1224,1225],[1129,16783,16785,16788],{"className":16784},[1187,1225],[1129,16786,3024],{"className":16787,"style":3098},[1187,1225],[1129,16789,1436],{"className":16790},[1187,1191,1225],[1129,16792,16793,16796],{"style":3159},[1129,16794],{"className":16795,"style":3088},[1217],[1129,16797],{"className":16798,"style":3167},[3166],[1129,16800,16801,16804],{"style":15775},[1129,16802],{"className":16803,"style":3088},[1217],[1129,16805,16807],{"className":16806},[1222,1223,1224,1225],[1129,16808,16810,16813],{"className":16809},[1187,1225],[1129,16811,3024],{"className":16812,"style":3098},[1187,1225],[1129,16814,16816,16819],{"className":16815},[1187,1225],[1129,16817,2450],{"className":16818,"style":2580},[1187,1191,1225],[1129,16820,16822],{"className":16821},[1196],[1129,16823,16825,16845],{"className":16824},[1200,1201],[1129,16826,16828,16842],{"className":16827},[1205],[1129,16829,16831],{"className":16830,"style":15806},[1209],[1129,16832,16833,16836],{"style":15809},[1129,16834],{"className":16835,"style":3124},[1217],[1129,16837,16839],{"className":16838},[1222,3128,3129,1225],[1129,16840,6526],{"className":16841},[1187,1225],[1129,16843,1254],{"className":16844},[1253],[1129,16846,16848],{"className":16847},[1205],[1129,16849,16851],{"className":16850,"style":15828},[1209],[1129,16852],{},[1129,16854,1254],{"className":16855},[1253],[1129,16857,16859],{"className":16858},[1205],[1129,16860,16862],{"className":16861,"style":6783},[1209],[1129,16863],{},[1129,16865],{"className":16866},[2667,3068],"（偏置不正则化）",[1101,16869,16870],{},[16871,16872,16873],"em",{},"λ 越大，权重被压得越小，网络越简单。太小则正则化没效果（过拟合），太大则网络能力被压垮（欠拟合）。需要通过验证集调参找到最优的 λ。",[1105,16875,16876,16889],{},[1108,16877,16878],{},[1111,16879,16880,16883,16886],{},[1114,16881,16882],{},"特性",[1114,16884,16885],{},"L1 正则化",[1114,16887,16888],{},"L2 正则化",[1121,16890,16891,17172,17407,17418,17429],{},[1111,16892,16893,16896,17019],{},[1126,16894,16895],{},"惩罚项",[1126,16897,16898],{},[1129,16899,16901,16927],{"className":16900},[1132],[1129,16902,16904],{"className":16903},[1136],[1138,16905,16906],{"xmlns":1140},[1142,16907,16908,16924],{},[1145,16909,16910,16916,16918,16920,16922],{},[3018,16911,16912,16914],{},[1151,16913,15151],{},[1151,16915,6632],{},[1342,16917,1890],{},[1342,16919,15162],{"stretchy":2465},[1151,16921,1153],{},[1342,16923,15162],{"stretchy":2465},[1166,16925,16926],{"encoding":1168},"\\frac{\\lambda}{n}\\sum \\lvert w \\rvert",[1129,16928,16930],{"className":16929,"ariaHidden":1174},[1173],[1129,16931,16933,16936,17004,17007,17010,17013,17016],{"className":16932},[1178],[1129,16934],{"className":16935,"style":9888},[1182],[1129,16937,16939,16942,17001],{"className":16938},[1187],[1129,16940],{"className":16941},[2634,3068],[1129,16943,16945],{"className":16944},[3018],[1129,16946,16948,16993],{"className":16947},[1200,1201],[1129,16949,16951,16990],{"className":16950},[1205],[1129,16952,16954,16968,16976],{"className":16953,"style":3081},[1209],[1129,16955,16956,16959],{"style":6739},[1129,16957],{"className":16958,"style":3088},[1217],[1129,16960,16962],{"className":16961},[1222,1223,1224,1225],[1129,16963,16965],{"className":16964},[1187,1225],[1129,16966,6632],{"className":16967},[1187,1191,1225],[1129,16969,16970,16973],{"style":3159},[1129,16971],{"className":16972,"style":3088},[1217],[1129,16974],{"className":16975,"style":3167},[3166],[1129,16977,16978,16981],{"style":3170},[1129,16979],{"className":16980,"style":3088},[1217],[1129,16982,16984],{"className":16983},[1222,1223,1224,1225],[1129,16985,16987],{"className":16986},[1187,1225],[1129,16988,15151],{"className":16989},[1187,1191,1225],[1129,16991,1254],{"className":16992},[1253],[1129,16994,16996],{"className":16995},[1205],[1129,16997,16999],{"className":16998,"style":6783},[1209],[1129,17000],{},[1129,17002],{"className":17003},[2667,3068],[1129,17005],{"className":17006,"style":2061},[1368],[1129,17008,1890],{"className":17009,"style":2020},[2014,2018,2019],[1129,17011,15162],{"className":17012},[2634],[1129,17014,1153],{"className":17015,"style":1192},[1187,1191],[1129,17017,15162],{"className":17018},[2667],[1126,17020,17021],{},[1129,17022,17024,17054],{"className":17023},[1132],[1129,17025,17027],{"className":17026},[1136],[1138,17028,17029],{"xmlns":1140},[1142,17030,17031,17051],{},[1145,17032,17033,17043,17045],{},[3018,17034,17035,17037],{},[1151,17036,15151],{},[1145,17038,17039,17041],{},[1346,17040,3724],{},[1151,17042,6632],{},[1342,17044,1890],{},[2431,17046,17047,17049],{},[1151,17048,1153],{},[1346,17050,3724],{},[1166,17052,17053],{"encoding":1168},"\\frac{\\lambda}{2n}\\sum w^2",[1129,17055,17057],{"className":17056,"ariaHidden":1174},[1173],[1129,17058,17060,17063,17134,17137,17140,17143],{"className":17059},[1178],[1129,17061],{"className":17062,"style":9888},[1182],[1129,17064,17066,17069,17131],{"className":17065},[1187],[1129,17067],{"className":17068},[2634,3068],[1129,17070,17072],{"className":17071},[3018],[1129,17073,17075,17123],{"className":17074},[1200,1201],[1129,17076,17078,17120],{"className":17077},[1205],[1129,17079,17081,17098,17106],{"className":17080,"style":3081},[1209],[1129,17082,17083,17086],{"style":6739},[1129,17084],{"className":17085,"style":3088},[1217],[1129,17087,17089],{"className":17088},[1222,1223,1224,1225],[1129,17090,17092,17095],{"className":17091},[1187,1225],[1129,17093,3724],{"className":17094},[1187,1225],[1129,17096,6632],{"className":17097},[1187,1191,1225],[1129,17099,17100,17103],{"style":3159},[1129,17101],{"className":17102,"style":3088},[1217],[1129,17104],{"className":17105,"style":3167},[3166],[1129,17107,17108,17111],{"style":3170},[1129,17109],{"className":17110,"style":3088},[1217],[1129,17112,17114],{"className":17113},[1222,1223,1224,1225],[1129,17115,17117],{"className":17116},[1187,1225],[1129,17118,15151],{"className":17119},[1187,1191,1225],[1129,17121,1254],{"className":17122},[1253],[1129,17124,17126],{"className":17125},[1205],[1129,17127,17129],{"className":17128,"style":6783},[1209],[1129,17130],{},[1129,17132],{"className":17133},[2667,3068],[1129,17135],{"className":17136,"style":2061},[1368],[1129,17138,1890],{"className":17139,"style":2020},[2014,2018,2019],[1129,17141],{"className":17142,"style":2061},[1368],[1129,17144,17146,17149],{"className":17145},[1187],[1129,17147,1153],{"className":17148,"style":1192},[1187,1191],[1129,17150,17152],{"className":17151},[1196],[1129,17153,17155],{"className":17154},[1200],[1129,17156,17158],{"className":17157},[1205],[1129,17159,17161],{"className":17160,"style":3651},[1209],[1129,17162,17163,17166],{"style":1239},[1129,17164],{"className":17165,"style":1218},[1217],[1129,17167,17169],{"className":17168},[1222,1223,1224,1225],[1129,17170,3724],{"className":17171},[1187,1225],[1111,17173,17174,17177,17301],{},[1126,17175,17176],{},"梯度贡献",[1126,17178,17179,17300],{},[1129,17180,17182,17208],{"className":17181},[1132],[1129,17183,17185],{"className":17184},[1136],[1138,17186,17187],{"xmlns":1140},[1142,17188,17189,17205],{},[1145,17190,17191,17197,17199,17201,17203],{},[3018,17192,17193,17195],{},[1151,17194,15151],{},[1151,17196,6632],{},[5470,17198,15544],{},[1342,17200,2466],{"stretchy":2465},[1151,17202,1153],{},[1342,17204,2475],{"stretchy":2465},[1166,17206,17207],{"encoding":1168},"\\frac{\\lambda}{n}\\text{sgn}(w)",[1129,17209,17211],{"className":17210,"ariaHidden":1174},[1173],[1129,17212,17214,17217,17285,17291,17294,17297],{"className":17213},[1178],[1129,17215],{"className":17216,"style":9888},[1182],[1129,17218,17220,17223,17282],{"className":17219},[1187],[1129,17221],{"className":17222},[2634,3068],[1129,17224,17226],{"className":17225},[3018],[1129,17227,17229,17274],{"className":17228},[1200,1201],[1129,17230,17232,17271],{"className":17231},[1205],[1129,17233,17235,17249,17257],{"className":17234,"style":3081},[1209],[1129,17236,17237,17240],{"style":6739},[1129,17238],{"className":17239,"style":3088},[1217],[1129,17241,17243],{"className":17242},[1222,1223,1224,1225],[1129,17244,17246],{"className":17245},[1187,1225],[1129,17247,6632],{"className":17248},[1187,1191,1225],[1129,17250,17251,17254],{"style":3159},[1129,17252],{"className":17253,"style":3088},[1217],[1129,17255],{"className":17256,"style":3167},[3166],[1129,17258,17259,17262],{"style":3170},[1129,17260],{"className":17261,"style":3088},[1217],[1129,17263,17265],{"className":17264},[1222,1223,1224,1225],[1129,17266,17268],{"className":17267},[1187,1225],[1129,17269,15151],{"className":17270},[1187,1191,1225],[1129,17272,1254],{"className":17273},[1253],[1129,17275,17277],{"className":17276},[1205],[1129,17278,17280],{"className":17279,"style":6783},[1209],[1129,17281],{},[1129,17283],{"className":17284},[2667,3068],[1129,17286,17288],{"className":17287},[1187,5683],[1129,17289,15544],{"className":17290},[1187],[1129,17292,2466],{"className":17293},[2634],[1129,17295,1153],{"className":17296,"style":1192},[1187,1191],[1129,17298,2475],{"className":17299},[2667],"（常数大小）",[1126,17302,17303,17406],{},[1129,17304,17306,17326],{"className":17305},[1132],[1129,17307,17309],{"className":17308},[1136],[1138,17310,17311],{"xmlns":1140},[1142,17312,17313,17323],{},[1145,17314,17315,17321],{},[3018,17316,17317,17319],{},[1151,17318,15151],{},[1151,17320,6632],{},[1151,17322,1153],{},[1166,17324,17325],{"encoding":1168},"\\frac{\\lambda}{n}w",[1129,17327,17329],{"className":17328,"ariaHidden":1174},[1173],[1129,17330,17332,17335,17403],{"className":17331},[1178],[1129,17333],{"className":17334,"style":9888},[1182],[1129,17336,17338,17341,17400],{"className":17337},[1187],[1129,17339],{"className":17340},[2634,3068],[1129,17342,17344],{"className":17343},[3018],[1129,17345,17347,17392],{"className":17346},[1200,1201],[1129,17348,17350,17389],{"className":17349},[1205],[1129,17351,17353,17367,17375],{"className":17352,"style":3081},[1209],[1129,17354,17355,17358],{"style":6739},[1129,17356],{"className":17357,"style":3088},[1217],[1129,17359,17361],{"className":17360},[1222,1223,1224,1225],[1129,17362,17364],{"className":17363},[1187,1225],[1129,17365,6632],{"className":17366},[1187,1191,1225],[1129,17368,17369,17372],{"style":3159},[1129,17370],{"className":17371,"style":3088},[1217],[1129,17373],{"className":17374,"style":3167},[3166],[1129,17376,17377,17380],{"style":3170},[1129,17378],{"className":17379,"style":3088},[1217],[1129,17381,17383],{"className":17382},[1222,1223,1224,1225],[1129,17384,17386],{"className":17385},[1187,1225],[1129,17387,15151],{"className":17388},[1187,1191,1225],[1129,17390,1254],{"className":17391},[1253],[1129,17393,17395],{"className":17394},[1205],[1129,17396,17398],{"className":17397,"style":6783},[1209],[1129,17399],{},[1129,17401],{"className":17402},[2667,3068],[1129,17404,1153],{"className":17405,"style":1192},[1187,1191],"（与 w 成正比）",[1111,17408,17409,17412,17415],{},[1126,17410,17411],{},"权重缩减方式",[1126,17413,17414],{},"等量缩减（固定步长）",[1126,17416,17417],{},"等比缩减（按比例衰减）",[1111,17419,17420,17423,17426],{},[1126,17421,17422],{},"结果特征",[1126,17424,17425],{},"产生稀疏权重（许多权重为 0）",[1126,17427,17428],{},"权重普遍较小但不为 0",[1111,17430,17431,17434,17437],{},[1126,17432,17433],{},"适用场景",[1126,17435,17436],{},"特征选择",[1126,17438,17439],{},"防止过拟合（通用）",[1096,17441,17443],{"id":17442},"_53-dropout","5.3 Dropout",[1101,17445,17446],{},[16871,17447,17448],{},"训练时，每次前向传播随机 \"关掉\" 一部分隐藏层神经元，让它们的输出变为 0。被关掉的神经元这一轮不参与计算，也不更新权重。强迫网络中的每个神经元都独立学到有用的特征，而不是依赖特定的搭配。效果相当于同时训练了大量不同的子网络，最终取平均，显著减轻过拟合",[3608,17450,17451,17483,17486],{},[2412,17452,17453,17454,17482],{},"训练时，以概率 ",[1129,17455,17457,17470],{"className":17456},[1132],[1129,17458,17460],{"className":17459},[1136],[1138,17461,17462],{"xmlns":1140},[1142,17463,17464,17468],{},[1145,17465,17466],{},[1151,17467,1101],{},[1166,17469,1101],{"encoding":1168},[1129,17471,17473],{"className":17472,"ariaHidden":1174},[1173],[1129,17474,17476,17479],{"className":17475},[1178],[1129,17477],{"className":17478,"style":7005},[1182],[1129,17480,1101],{"className":17481},[1187,1191]," 随机将隐藏层神经元的输出置零",[2412,17484,17485],{},"输入层和输出层保持不变",[2412,17487,17488,17489,17550],{},"测试时，使用所有神经元但将权重乘以 ",[1129,17490,17492,17514],{"className":17491},[1132],[1129,17493,17495],{"className":17494},[1136],[1138,17496,17497],{"xmlns":1140},[1142,17498,17499,17511],{},[1145,17500,17501,17503,17505,17507,17509],{},[1342,17502,2466],{"stretchy":2465},[1346,17504,1348],{},[1342,17506,1344],{},[1151,17508,1101],{},[1342,17510,2475],{"stretchy":2465},[1166,17512,17513],{"encoding":1168},"(1-p)",[1129,17515,17517,17538],{"className":17516,"ariaHidden":1174},[1173],[1129,17518,17520,17523,17526,17529,17532,17535],{"className":17519},[1178],[1129,17521],{"className":17522,"style":6081},[1182],[1129,17524,2466],{"className":17525},[2634],[1129,17527,1348],{"className":17528},[1187],[1129,17530],{"className":17531,"style":1369},[1368],[1129,17533,1344],{"className":17534},[1373],[1129,17536],{"className":17537,"style":1369},[1368],[1129,17539,17541,17544,17547],{"className":17540},[1178],[1129,17542],{"className":17543,"style":6081},[1182],[1129,17545,1101],{"className":17546},[1187,1191],[1129,17548,2475],{"className":17549},[2667]," 进行缩放",[1101,17552,17553],{},[2405,17554,17555],{},"Dropout 的直觉理解",[2409,17557,17558,17561,17564],{},[2412,17559,17560],{},"相当于训练了指数级数量的\"瘦\"网络的集成（Ensemble）",[2412,17562,17563],{},"每个神经元不能依赖于特定其他神经元的存在，必须学习更鲁棒的特征",[2412,17565,17566],{},"减少神经元之间的\"共适应\"（co-adaptation）",[5907,17568],{},[1091,17570,17572],{"id":17571},"六数据增强","六、数据增强",[1101,17574,17575],{},"通过对已有训练数据进行变换来扩充数据集，是对抗过拟合的有效手段。",[1096,17577,17579],{"id":17578},"_61-常用增强方法","6.1 常用增强方法",[1105,17581,17582,17592],{},[1108,17583,17584],{},[1111,17585,17586,17589],{},[1114,17587,17588],{},"方法",[1114,17590,17591],{},"描述",[1121,17593,17594,17602,17650,17658],{},[1111,17595,17596,17599],{},[1126,17597,17598],{},"平移（Translation）",[1126,17600,17601],{},"将图像在水平或垂直方向偏移若干像素",[1111,17603,17604,17607],{},[1126,17605,17606],{},"旋转（Rotation）",[1126,17608,17609,17610,15088],{},"将图像按一定角度旋转（如 ",[1129,17611,17613,17634],{"className":17612},[1132],[1129,17614,17616],{"className":17615},[1136],[1138,17617,17618],{"xmlns":1140},[1142,17619,17620,17631],{},[1145,17621,17622,17625,17628],{},[1342,17623,17624],{},"±",[1346,17626,17627],{},"15",[1151,17629,17630],{"mathvariant":2444},"°",[1166,17632,17633],{"encoding":1168},"\\pm15°",[1129,17635,17637],{"className":17636,"ariaHidden":1174},[1173],[1129,17638,17640,17643,17646],{"className":17639},[1178],[1129,17641],{"className":17642,"style":1361},[1182],[1129,17644,17624],{"className":17645},[1187],[1129,17647,17649],{"className":17648},[1187],"15°",[1111,17651,17652,17655],{},[1126,17653,17654],{},"镜像翻转（Flip）",[1126,17656,17657],{},"水平或垂直翻转图像",[1111,17659,17660,17663],{},[1126,17661,17662],{},"弹性形变（Elastic Deformation）",[1126,17664,17665],{},"对图像施加随机弹性变换，模拟手写变体",[1096,17667,17669],{"id":17668},"_62-效果","6.2 效果",[1101,17671,17672],{},"数据增强能有效增加训练数据的多样性，提升模型的泛化能力。实验表明，使用弹性形变增强后的手写数字识别准确率显著提升。",[1101,17674,17675,17678],{},[2405,17676,17677],{},"关键原则","：增强变换应模拟真实世界中可能出现的数据变体，同时保持标签不变。",[5907,17680],{},[1091,17682,17684],{"id":17683},"七权重初始化","七、权重初始化",[1101,17686,17687],{},"创建网络后，在开始训练之前需要给权重和偏置设定初始值。初始化方式直接影响训练能否顺利开始以及收敛速度。",[1096,17689,17691],{"id":17690},"_71-标准初始化的问题","7.1 标准初始化的问题",[1101,17693,17694,17695,17756],{},"使用标准正态分布 ",[1129,17696,17698,17724],{"className":17697},[1132],[1129,17699,17701],{"className":17700},[1136],[1138,17702,17703],{"xmlns":1140},[1142,17704,17705,17721],{},[1145,17706,17707,17711,17713,17715,17717,17719],{},[1151,17708,17710],{"mathvariant":17709},"script","N",[1342,17712,2466],{"stretchy":2465},[1346,17714,6526],{},[1342,17716,3727],{"separator":1174},[1346,17718,1348],{},[1342,17720,2475],{"stretchy":2465},[1166,17722,17723],{"encoding":1168},"\\mathcal{N}(0, 1)",[1129,17725,17727],{"className":17726,"ariaHidden":1174},[1173],[1129,17728,17730,17733,17738,17741,17744,17747,17750,17753],{"className":17729},[1178],[1129,17731],{"className":17732,"style":6081},[1182],[1129,17734,17710],{"className":17735,"style":17737},[1187,17736],"mathcal","margin-right:0.1474em;",[1129,17739,2466],{"className":17740},[2634],[1129,17742,6526],{"className":17743},[1187],[1129,17745,3727],{"className":17746},[3777],[1129,17748],{"className":17749,"style":2061},[1368],[1129,17751,1348],{"className":17752},[1187],[1129,17754,2475],{"className":17755},[2667]," 初始化所有权重时：",[2409,17758,17759,18216,18295],{},[2412,17760,17761,17762,17973,17974,18136,18137,18215],{},"加权输入 ",[1129,17763,17765,17803],{"className":17764},[1132],[1129,17766,17768],{"className":17767},[1136],[1138,17769,17770],{"xmlns":1140},[1142,17771,17772,17800],{},[1145,17773,17774,17776,17778,17784,17790,17796,17798],{},[1151,17775,1733],{},[1342,17777,1884],{},[1886,17779,17780,17782],{},[1342,17781,1890],{},[1151,17783,1158],{},[1886,17785,17786,17788],{},[1151,17787,1153],{},[1151,17789,1158],{},[1886,17791,17792,17794],{},[1151,17793,3638],{},[1151,17795,1158],{},[1342,17797,1921],{},[1151,17799,1436],{},[1166,17801,17802],{"encoding":1168},"z = \\sum_j w_j x_j + b",[1129,17804,17806,17824,17964],{"className":17805,"ariaHidden":1174},[1173],[1129,17807,17809,17812,17815,17818,17821],{"className":17808},[1178],[1129,17810],{"className":17811,"style":3696},[1182],[1129,17813,1733],{"className":17814,"style":1756},[1187,1191],[1129,17816],{"className":17817,"style":1996},[1368],[1129,17819,1884],{"className":17820},[2000],[1129,17822],{"className":17823,"style":1996},[1368],[1129,17825,17827,17831,17871,17874,17915,17955,17958,17961],{"className":17826},[1178],[1129,17828],{"className":17829,"style":17830},[1182],"height:1.1858em;vertical-align:-0.4358em;",[1129,17832,17834,17837],{"className":17833},[2014],[1129,17835,1890],{"className":17836,"style":2020},[2014,2018,2019],[1129,17838,17840],{"className":17839},[1196],[1129,17841,17843,17863],{"className":17842},[1200,1201],[1129,17844,17846,17860],{"className":17845},[1205],[1129,17847,17849],{"className":17848,"style":11057},[1209],[1129,17850,17851,17854],{"style":2036},[1129,17852],{"className":17853,"style":1218},[1217],[1129,17855,17857],{"className":17856},[1222,1223,1224,1225],[1129,17858,1158],{"className":17859,"style":1232},[1187,1191,1225],[1129,17861,1254],{"className":17862},[1253],[1129,17864,17866],{"className":17865},[1205],[1129,17867,17869],{"className":17868,"style":5696},[1209],[1129,17870],{},[1129,17872],{"className":17873,"style":2061},[1368],[1129,17875,17877,17880],{"className":17876},[1187],[1129,17878,1153],{"className":17879,"style":1192},[1187,1191],[1129,17881,17883],{"className":17882},[1196],[1129,17884,17886,17907],{"className":17885},[1200,1201],[1129,17887,17889,17904],{"className":17888},[1205],[1129,17890,17892],{"className":17891,"style":7442},[1209],[1129,17893,17895,17898],{"style":17894},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[1129,17896],{"className":17897,"style":1218},[1217],[1129,17899,17901],{"className":17900},[1222,1223,1224,1225],[1129,17902,1158],{"className":17903,"style":1232},[1187,1191,1225],[1129,17905,1254],{"className":17906},[1253],[1129,17908,17910],{"className":17909},[1205],[1129,17911,17913],{"className":17912,"style":7463},[1209],[1129,17914],{},[1129,17916,17918,17921],{"className":17917},[1187],[1129,17919,3638],{"className":17920},[1187,1191],[1129,17922,17924],{"className":17923},[1196],[1129,17925,17927,17947],{"className":17926},[1200,1201],[1129,17928,17930,17944],{"className":17929},[1205],[1129,17931,17933],{"className":17932,"style":7442},[1209],[1129,17934,17935,17938],{"style":2555},[1129,17936],{"className":17937,"style":1218},[1217],[1129,17939,17941],{"className":17940},[1222,1223,1224,1225],[1129,17942,1158],{"className":17943,"style":1232},[1187,1191,1225],[1129,17945,1254],{"className":17946},[1253],[1129,17948,17950],{"className":17949},[1205],[1129,17951,17953],{"className":17952,"style":7463},[1209],[1129,17954],{},[1129,17956],{"className":17957,"style":1369},[1368],[1129,17959,1921],{"className":17960},[1373],[1129,17962],{"className":17963,"style":1369},[1368],[1129,17965,17967,17970],{"className":17966},[1178],[1129,17968],{"className":17969,"style":1292},[1182],[1129,17971,1436],{"className":17972},[1187,1191]," 的标准差为 ",[1129,17975,17977,18009],{"className":17976},[1132],[1129,17978,17980],{"className":17979},[1136],[1138,17981,17982],{"xmlns":1140},[1142,17983,17984,18006],{},[1145,17985,17986],{},[17987,17988,17989],"msqrt",{},[1145,17990,17991,18002,18004],{},[1886,17992,17993,17995],{},[1151,17994,6632],{},[1145,17996,17997,18000],{},[1151,17998,17999],{},"i",[1151,18001,6632],{},[1342,18003,1921],{},[1346,18005,1348],{},[1166,18007,18008],{"encoding":1168},"\\sqrt{n_{in} + 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为输入连接数）",[2412,18217,5932,18218,18294],{},[1129,18219,18221,18242],{"className":18220},[1132],[1129,18222,18224],{"className":18223},[1136],[1138,18225,18226],{"xmlns":1140},[1142,18227,18228,18240],{},[1145,18229,18230],{},[1886,18231,18232,18234],{},[1151,18233,6632],{},[1145,18235,18236,18238],{},[1151,18237,17999],{},[1151,18239,6632],{},[1166,18241,18161],{"encoding":1168},[1129,18243,18245],{"className":18244,"ariaHidden":1174},[1173],[1129,18246,18248,18251],{"className":18247},[1178],[1129,18249],{"className":18250,"style":18171},[1182],[1129,18252,18254,18257],{"className":18253},[1187],[1129,18255,6632],{"className":18256},[1187,1191],[1129,18258,18260],{"className":18259},[1196],[1129,18261,18263,18286],{"className":18262},[1200,1201],[1129,18264,18266,18283],{"className":18265},[1205],[1129,18267,18269],{"className":18268,"style":7442},[1209],[1129,18270,18271,18274],{"style":2555},[1129,18272],{"className":18273,"style":1218},[1217],[1129,18275,18277],{"className":18276},[1222,1223,1224,1225],[1129,18278,18280],{"className":18279},[1187,1225],[1129,18281,18077],{"className":18282},[1187,1191,1225],[1129,18284,1254],{"className":18285},[1253],[1129,18287,18289],{"className":18288},[1205],[1129,18290,18292],{"className":18291,"style":2574},[1209],[1129,18293],{}," 较大时，∣ z∣ 很大时，σ(z) 接近 0 或 1（饱和）",[2412,18296,18297,18298,18396],{},"饱和导致 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改进的初始化方法",[1101,18402,18403,18406,18407,18571],{},[2405,18404,18405],{},"改进方案","：使用 ",[1129,18408,18410,18449],{"className":18409},[1132],[1129,18411,18413],{"className":18412},[1136],[1138,18414,18415],{"xmlns":1140},[1142,18416,18417,18446],{},[1145,18418,18419,18421,18423,18425,18427,18429,18432,18444],{},[1151,18420,17710],{"mathvariant":17709},[1342,18422,2466],{"stretchy":2465},[1346,18424,6526],{},[1342,18426,3727],{"separator":1174},[1346,18428,1348],{},[1151,18430,18431],{"mathvariant":2444},"\u002F",[17987,18433,18434],{},[1886,18435,18436,18438],{},[1151,18437,6632],{},[1145,18439,18440,18442],{},[1151,18441,17999],{},[1151,18443,6632],{},[1342,18445,2475],{"stretchy":2465},[1166,18447,18448],{"encoding":1168},"\\mathcal{N}(0, 1\u002F\\sqrt{n_{in}})",[1129,18450,18452],{"className":18451,"ariaHidden":1174},[1173],[1129,18453,18455,18459,18462,18465,18468,18471,18474,18478,18568],{"className":18454},[1178],[1129,18456],{"className":18457,"style":18458},[1182],"height:1.0647em;vertical-align:-0.3147em;",[1129,18460,17710],{"className":18461,"style":17737},[1187,17736],[1129,18463,2466],{"className":18464},[2634],[1129,18466,6526],{"className":18467},[1187],[1129,18469,3727],{"className":18470},[3777],[1129,18472],{"className":18473,"style":2061},[1368],[1129,18475,18477],{"className":18476},[1187],"1\u002F",[1129,18479,18481],{"className":18480},[1187,18022],[1129,18482,18484,18559],{"className":18483},[1200,1201],[1129,18485,18487,18556],{"className":18486},[1205],[1129,18488,18491,18543],{"className":18489,"style":18490},[1209],"height:0.7253em;",[1129,18492,18494,18497],{"className":18493,"style":18037},[18036],[1129,18495],{"className":18496,"style":3088},[1217],[1129,18498,18500],{"className":18499,"style":18044},[1187],[1129,18501,18503,18506],{"className":18502},[1187],[1129,18504,6632],{"className":18505},[1187,1191],[1129,18507,18509],{"className":18508},[1196],[1129,18510,18512,18535],{"className":18511},[1200,1201],[1129,18513,18515,18532],{"className":18514},[1205],[1129,18516,18518],{"className":18517,"style":7442},[1209],[1129,18519,18520,18523],{"style":2555},[1129,18521],{"className":18522,"style":1218},[1217],[1129,18524,18526],{"className":18525},[1222,1223,1224,1225],[1129,18527,18529],{"className":18528},[1187,1225],[1129,18530,18077],{"className":18531},[1187,1191,1225],[1129,18533,1254],{"className":18534},[1253],[1129,18536,18538],{"className":18537},[1205],[1129,18539,18541],{"className":18540,"style":2574},[1209],[1129,18542],{},[1129,18544,18546,18549],{"style":18545},"top:-2.6853em;",[1129,18547],{"className":18548,"style":3088},[1217],[1129,18550,18552],{"className":18551,"style":18111},[18110],[18113,18553,18554],{"xmlns":18115,"width":18116,"height":18117,"viewBox":18118,"preserveAspectRatio":18119},[18121,18555],{"d":18123},[1129,18557,1254],{"className":18558},[1253],[1129,18560,18562],{"className":18561},[1205],[1129,18563,18566],{"className":18564,"style":18565},[1209],"height:0.3147em;",[1129,18567],{},[1129,18569,2475],{"className":18570},[2667]," 初始化权重",[1101,18573,18574,18575,18603,18604,18720,18721,18778],{},"此时 ",[1129,18576,18578,18591],{"className":18577},[1132],[1129,18579,18581],{"className":18580},[1136],[1138,18582,18583],{"xmlns":1140},[1142,18584,18585,18589],{},[1145,18586,18587],{},[1151,18588,1733],{},[1166,18590,1733],{"encoding":1168},[1129,18592,18594],{"className":18593,"ariaHidden":1174},[1173],[1129,18595,18597,18600],{"className":18596},[1178],[1129,18598],{"className":18599,"style":3696},[1182],[1129,18601,1733],{"className":18602,"style":1756},[1187,1191]," 的标准差约为 ",[1129,18605,18607,18634],{"className":18606},[1132],[1129,18608,18610],{"className":18609},[1136],[1138,18611,18612],{"xmlns":1140},[1142,18613,18614,18631],{},[1145,18615,18616,18626,18628],{},[17987,18617,18618],{},[1145,18619,18620,18622,18624],{},[1346,18621,3730],{},[1151,18623,18431],{"mathvariant":2444},[1346,18625,3724],{},[1342,18627,6065],{},[1346,18629,18630],{},"1.22",[1166,18632,18633],{"encoding":1168},"\\sqrt{3\u002F2} \\approx 1.22",[1129,18635,18637,18711],{"className":18636,"ariaHidden":1174},[1173],[1129,18638,18640,18644,18702,18705,18708],{"className":18639},[1178],[1129,18641],{"className":18642,"style":18643},[1182],"height:1.24em;vertical-align:-0.305em;",[1129,18645,18647],{"className":18646},[1187,18022],[1129,18648,18650,18693],{"className":18649},[1200,1201],[1129,18651,18653,18690],{"className":18652},[1205],[1129,18654,18657,18673],{"className":18655,"style":18656},[1209],"height:0.935em;",[1129,18658,18661,18665],{"className":18659,"style":18660},[18036],"top:-3.2em;",[1129,18662],{"className":18663,"style":18664},[1217],"height:3.2em;",[1129,18666,18669],{"className":18667,"style":18668},[1187],"padding-left:1em;",[1129,18670,18672],{"className":18671},[1187],"3\u002F2",[1129,18674,18676,18679],{"style":18675},"top:-2.895em;",[1129,18677],{"className":18678,"style":18664},[1217],[1129,18680,18683],{"className":18681,"style":18682},[18110],"min-width:1.02em;height:1.28em;",[18113,18684,18687],{"xmlns":18115,"width":18116,"height":18685,"viewBox":18686,"preserveAspectRatio":18119},"1.28em","0 0 400000 1296",[18121,18688],{"d":18689},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[1129,18691,1254],{"className":18692},[1253],[1129,18694,18696],{"className":18695},[1205],[1129,18697,18700],{"className":18698,"style":18699},[1209],"height:0.305em;",[1129,18701],{},[1129,18703],{"className":18704,"style":1996},[1368],[1129,18706,6065],{"className":18707},[2000],[1129,18709],{"className":18710,"style":1996},[1368],[1129,18712,18714,18717],{"className":18713},[1178],[1129,18715],{"className":18716,"style":1383},[1182],[1129,18718,18630],{"className":18719},[1187],"（假设偏置用 ",[1129,18722,18724,18748],{"className":18723},[1132],[1129,18725,18727],{"className":18726},[1136],[1138,18728,18729],{"xmlns":1140},[1142,18730,18731,18745],{},[1145,18732,18733,18735,18737,18739,18741,18743],{},[1151,18734,17710],{"mathvariant":17709},[1342,18736,2466],{"stretchy":2465},[1346,18738,6526],{},[1342,18740,3727],{"separator":1174},[1346,18742,1348],{},[1342,18744,2475],{"stretchy":2465},[1166,18746,18747],{"encoding":1168},"\\mathcal{N}(0,1)",[1129,18749,18751],{"className":18750,"ariaHidden":1174},[1173],[1129,18752,18754,18757,18760,18763,18766,18769,18772,18775],{"className":18753},[1178],[1129,18755],{"className":18756,"style":6081},[1182],[1129,18758,17710],{"className":18759,"style":17737},[1187,17736],[1129,18761,2466],{"className":18762},[2634],[1129,18764,6526],{"className":18765},[1187],[1129,18767,3727],{"className":18768},[3777],[1129,18770],{"className":18771,"style":2061},[1368],[1129,18773,1348],{"className":18774},[1187],[1129,18776,2475],{"className":18777},[2667],"），神经元不再轻易饱和。",[1101,18780,18781,7019,18784],{},[2405,18782,18783],{},"标准初始化",[1129,18785,18787,18810],{"className":18786},[1132],[1129,18788,18790],{"className":18789},[1136],[1138,18791,18792],{"xmlns":1140},[1142,18793,18794,18808],{},[1145,18795,18796,18798,18800,18802,18804,18806],{},[1151,18797,17710],{"mathvariant":17709},[1342,18799,2466],{"stretchy":2465},[1346,18801,6526],{},[1342,18803,3727],{"separator":1174},[1346,18805,1348],{},[1342,18807,2475],{"stretchy":2465},[1166,18809,18747],{"encoding":1168},[1129,18811,18813],{"className":18812,"ariaHidden":1174},[1173],[1129,18814,18816,18819,18822,18825,18828,18831,18834,18837],{"className":18815},[1178],[1129,18817],{"className":18818,"style":6081},[1182],[1129,18820,17710],{"className":18821,"style":17737},[1187,17736],[1129,18823,2466],{"className":18824},[2634],[1129,18826,6526],{"className":18827},[1187],[1129,18829,3727],{"className":18830},[3777],[1129,18832],{"className":18833,"style":2061},[1368],[1129,18835,1348],{"className":18836},[1187],[1129,18838,2475],{"className":18839},[2667],[2409,18841,18842,18845,18848],{},[2412,18843,18844],{},"初始时大量神经元饱和",[2412,18846,18847],{},"学习起步极慢",[2412,18849,18850],{},"需要更多 epoch 才能收敛",[1101,18852,18853,7019,18856],{},[2405,18854,18855],{},"改进初始化",[1129,18857,18859,18896],{"className":18858},[1132],[1129,18860,18862],{"className":18861},[1136],[1138,18863,18864],{"xmlns":1140},[1142,18865,18866,18894],{},[1145,18867,18868,18870,18872,18874,18876,18878,18880,18892],{},[1151,18869,17710],{"mathvariant":17709},[1342,18871,2466],{"stretchy":2465},[1346,18873,6526],{},[1342,18875,3727],{"separator":1174},[1346,18877,1348],{},[1151,18879,18431],{"mathvariant":2444},[17987,18881,18882],{},[1886,18883,18884,18886],{},[1151,18885,6632],{},[1145,18887,18888,18890],{},[1151,18889,17999],{},[1151,18891,6632],{},[1342,18893,2475],{"stretchy":2465},[1166,18895,18448],{"encoding":1168},[1129,18897,18899],{"className":18898,"ariaHidden":1174},[1173],[1129,18900,18902,18905,18908,18911,18914,18917,18920,18923,19010],{"className":18901},[1178],[1129,18903],{"className":18904,"style":18458},[1182],[1129,18906,17710],{"className":18907,"style":17737},[1187,17736],[1129,18909,2466],{"className":18910},[2634],[1129,18912,6526],{"className":18913},[1187],[1129,18915,3727],{"className":18916},[3777],[1129,18918],{"className":18919,"style":2061},[1368],[1129,18921,18477],{"className":18922},[1187],[1129,18924,18926],{"className":18925},[1187,18022],[1129,18927,18929,19002],{"className":18928},[1200,1201],[1129,18930,18932,18999],{"className":18931},[1205],[1129,18933,18935,18987],{"className":18934,"style":18490},[1209],[1129,18936,18938,18941],{"className":18937,"style":18037},[18036],[1129,18939],{"className":18940,"style":3088},[1217],[1129,18942,18944],{"className":18943,"style":18044},[1187],[1129,18945,18947,18950],{"className":18946},[1187],[1129,18948,6632],{"className":18949},[1187,1191],[1129,18951,18953],{"className":18952},[1196],[1129,18954,18956,18979],{"className":18955},[1200,1201],[1129,18957,18959,18976],{"className":18958},[1205],[1129,18960,18962],{"className":18961,"style":7442},[1209],[1129,18963,18964,18967],{"style":2555},[1129,18965],{"className":18966,"style":1218},[1217],[1129,18968,18970],{"className":18969},[1222,1223,1224,1225],[1129,18971,18973],{"className":18972},[1187,1225],[1129,18974,18077],{"className":18975},[1187,1191,1225],[1129,18977,1254],{"className":18978},[1253],[1129,18980,18982],{"className":18981},[1205],[1129,18983,18985],{"className":18984,"style":2574},[1209],[1129,18986],{},[1129,18988,18989,18992],{"style":18545},[1129,18990],{"className":18991,"style":3088},[1217],[1129,18993,18995],{"className":18994,"style":18111},[18110],[18113,18996,18997],{"xmlns":18115,"width":18116,"height":18117,"viewBox":18118,"preserveAspectRatio":18119},[18121,18998],{"d":18123},[1129,19000,1254],{"className":19001},[1253],[1129,19003,19005],{"className":19004},[1205],[1129,19006,19008],{"className":19007,"style":18565},[1209],[1129,19009],{},[1129,19011,2475],{"className":19012},[2667],[2409,19014,19015,19018,19021],{},[2412,19016,19017],{},"初始时神经元处于非饱和区",[2412,19019,19020],{},"学习从一开始就很快",[2412,19022,19023],{},"更快收敛到更好的结果",[5907,19025],{},[1091,19027,19029],{"id":19028},"八数据预处理","八、数据预处理",[1101,19031,19032],{},"良好的数据预处理可以显著加速训练并提升模型性能。",[1096,19034,19036],{"id":19035},"_81-均值减法mean-subtraction","8.1 均值减法（Mean Subtraction）",[1101,19038,19039],{},[1129,19040,19042,19075],{"className":19041},[1132],[1129,19043,19045],{"className":19044},[1136],[1138,19046,19047],{"xmlns":1140},[1142,19048,19049,19072],{},[1145,19050,19051,19059,19061,19063,19065],{},[19052,19053,19054,19056],"mover",{"accent":1174},[1151,19055,3638],{},[1342,19057,19058],{},"^",[1342,19060,1884],{},[1151,19062,3638],{},[1342,19064,1344],{},[19052,19066,19067,19069],{"accent":1174},[1151,19068,3638],{},[1342,19070,19071],{},"ˉ",[1166,19073,19074],{"encoding":1168},"\\hat{x} = x - \\bar{x}",[1129,19076,19078,19127,19145],{"className":19077,"ariaHidden":1174},[1173],[1129,19079,19081,19084,19118,19121,19124],{"className":19080},[1178],[1129,19082],{"className":19083,"style":1292},[1182],[1129,19085,19088],{"className":19086},[1187,19087],"accent",[1129,19089,19091],{"className":19090},[1200],[1129,19092,19094],{"className":19093},[1205],[1129,19095,19097,19105],{"className":19096,"style":1292},[1209],[1129,19098,19099,19102],{"style":18037},[1129,19100],{"className":19101,"style":3088},[1217],[1129,19103,3638],{"className":19104},[1187,1191],[1129,19106,19107,19110],{"style":18037},[1129,19108],{"className":19109,"style":3088},[1217],[1129,19111,19115],{"className":19112,"style":19114},[19113],"accent-body","left:-0.2222em;",[1129,19116,19058],{"className":19117},[1187],[1129,19119],{"className":19120,"style":1996},[1368],[1129,19122,1884],{"className":19123},[2000],[1129,19125],{"className":19126,"style":1996},[1368],[1129,19128,19130,19133,19136,19139,19142],{"className":19129},[1178],[1129,19131],{"className":19132,"style":15603},[1182],[1129,19134,3638],{"className":19135},[1187,1191],[1129,19137],{"className":19138,"style":1369},[1368],[1129,19140,1344],{"className":19141},[1373],[1129,19143],{"className":19144,"style":1369},[1368],[1129,19146,19148,19152],{"className":19147},[1178],[1129,19149],{"className":19150,"style":19151},[1182],"height:0.5678em;",[1129,19153,19155],{"className":19154},[1187,19087],[1129,19156,19158],{"className":19157},[1200],[1129,19159,19161],{"className":19160},[1205],[1129,19162,19164,19172],{"className":19163,"style":19151},[1209],[1129,19165,19166,19169],{"style":18037},[1129,19167],{"className":19168,"style":3088},[1217],[1129,19170,3638],{"className":19171},[1187,1191],[1129,19173,19174,19177],{"style":18037},[1129,19175],{"className":19176,"style":3088},[1217],[1129,19178,19180],{"className":19179,"style":19114},[19113],[1129,19181,19071],{"className":19182},[1187],[1101,19184,19185],{},"将每个特征减去其在训练集上的均值，使数据以零为中心。",[1096,19187,19189],{"id":19188},"_82-均一化normalization","8.2 均一化（Normalization）",[1101,19191,19192],{},[1129,19193,19195,19228],{"className":19194},[1132],[1129,19196,19198],{"className":19197},[1136],[1138,19199,19200],{"xmlns":1140},[1142,19201,19202,19225],{},[1145,19203,19204,19210,19212],{},[19052,19205,19206,19208],{"accent":1174},[1151,19207,3638],{},[1342,19209,19058],{},[1342,19211,1884],{},[3018,19213,19214,19223],{},[1145,19215,19216,19218,19220],{},[1151,19217,3638],{},[1342,19219,1344],{},[1151,19221,19222],{},"μ",[1151,19224,2458],{},[1166,19226,19227],{"encoding":1168},"\\hat{x} = \\frac{x - \\mu}{\\sigma}",[1129,19229,19231,19277],{"className":19230,"ariaHidden":1174},[1173],[1129,19232,19234,19237,19268,19271,19274],{"className":19233},[1178],[1129,19235],{"className":19236,"style":1292},[1182],[1129,19238,19240],{"className":19239},[1187,19087],[1129,19241,19243],{"className":19242},[1200],[1129,19244,19246],{"className":19245},[1205],[1129,19247,19249,19257],{"className":19248,"style":1292},[1209],[1129,19250,19251,19254],{"style":18037},[1129,19252],{"className":19253,"style":3088},[1217],[1129,19255,3638],{"className":19256},[1187,1191],[1129,19258,19259,19262],{"style":18037},[1129,19260],{"className":19261,"style":3088},[1217],[1129,19263,19265],{"className":19264,"style":19114},[19113],[1129,19266,19058],{"className":19267},[1187],[1129,19269],{"className":19270,"style":1996},[1368],[1129,19272,1884],{"className":19273},[2000],[1129,19275],{"className":19276,"style":1996},[1368],[1129,19278,19280,19284],{"className":19279},[1178],[1129,19281],{"className":19282,"style":19283},[1182],"height:1.1994em;vertical-align:-0.345em;",[1129,19285,19287,19290,19355],{"className":19286},[1187],[1129,19288],{"className":19289},[2634,3068],[1129,19291,19293],{"className":19292},[3018],[1129,19294,19296,19347],{"className":19295},[1200,1201],[1129,19297,19299,19344],{"className":19298},[1205],[1129,19300,19302,19316,19324],{"className":19301,"style":10480},[1209],[1129,19303,19304,19307],{"style":6739},[1129,19305],{"className":19306,"style":3088},[1217],[1129,19308,19310],{"className":19309},[1222,1223,1224,1225],[1129,19311,19313],{"className":19312},[1187,1225],[1129,19314,2458],{"className":19315,"style":2603},[1187,1191,1225],[1129,19317,19318,19321],{"style":3159},[1129,19319],{"className":19320,"style":3088},[1217],[1129,19322],{"className":19323,"style":3167},[3166],[1129,19325,19326,19329],{"style":8212},[1129,19327],{"className":19328,"style":3088},[1217],[1129,19330,19332],{"className":19331},[1222,1223,1224,1225],[1129,19333,19335,19338,19341],{"className":19334},[1187,1225],[1129,19336,3638],{"className":19337},[1187,1191,1225],[1129,19339,1344],{"className":19340},[1373,1225],[1129,19342,19222],{"className":19343},[1187,1191,1225],[1129,19345,1254],{"className":19346},[1253],[1129,19348,19350],{"className":19349},[1205],[1129,19351,19353],{"className":19352,"style":6783},[1209],[1129,19354],{},[1129,19356],{"className":19357},[2667,3068],[1101,19359,19360],{},"进一步除以标准差，使每个特征的方差为 1。预处理后数据满足：均值为 0，方差为 1。",[1096,19362,19364],{"id":19363},"_83-zca-白化whitening","8.3 ZCA 白化（Whitening）",[1101,19366,19367],{},"白化将数据去相关化，使协方差矩阵变为单位矩阵：",[1101,19369,19370],{},[1129,19371,19373,19394],{"className":19372},[1132],[1129,19374,19376],{"className":19375},[1136],[1138,19377,19378],{"xmlns":1140},[1142,19379,19380,19391],{},[1145,19381,19382,19384,19386,19389],{},[1151,19383,6646],{},[1342,19385,1884],{},[1151,19387,19388],{},"W",[1151,19390,3638],{},[1166,19392,19393],{"encoding":1168},"y = W x",[1129,19395,19397,19415],{"className":19396,"ariaHidden":1174},[1173],[1129,19398,19400,19403,19406,19409,19412],{"className":19399},[1178],[1129,19401],{"className":19402,"style":7005},[1182],[1129,19404,6646],{"className":19405,"style":2603},[1187,1191],[1129,19407],{"className":19408,"style":1996},[1368],[1129,19410,1884],{"className":19411},[2000],[1129,19413],{"className":19414,"style":1996},[1368],[1129,19416,19418,19421,19424],{"className":19417},[1178],[1129,19419],{"className":19420,"style":5901},[1182],[1129,19422,19388],{"className":19423,"style":2876},[1187,1191],[1129,19425,3638],{"className":19426},[1187,1191],[1101,19428,19429],{},"ZCA 白化的变换矩阵为：",[1101,19431,19432],{},[1129,19433,19435,19478],{"className":19434},[1132],[1129,19436,19438],{"className":19437},[1136],[1138,19439,19440],{"xmlns":1140},[1142,19441,19442,19475],{},[1145,19443,19444,19458,19460],{},[1886,19445,19446,19448],{},[1151,19447,19388],{},[1145,19449,19450,19453,19455],{},[1151,19451,19452],{},"Z",[1151,19454,2450],{},[1151,19456,19457],{},"A",[1342,19459,1884],{},[2431,19461,19462,19465],{},[1151,19463,19464],{"mathvariant":2444},"Σ",[1145,19466,19467,19469,19471,19473],{},[1342,19468,1344],{},[1346,19470,1348],{},[1151,19472,18431],{"mathvariant":2444},[1346,19474,3724],{},[1166,19476,19477],{"encoding":1168},"W_{ZCA} = \\Sigma^{-1\u002F2}",[1129,19479,19481,19547],{"className":19480,"ariaHidden":1174},[1173],[1129,19482,19484,19487,19538,19541,19544],{"className":19483},[1178],[1129,19485],{"className":19486,"style":2533},[1182],[1129,19488,19490,19493],{"className":19489},[1187],[1129,19491,19388],{"className":19492,"style":2876},[1187,1191],[1129,19494,19496],{"className":19495},[1196],[1129,19497,19499,19530],{"className":19498},[1200,1201],[1129,19500,19502,19527],{"className":19501},[1205],[1129,19503,19506],{"className":19504,"style":19505},[1209],"height:0.3283em;",[1129,19507,19509,19512],{"style":19508},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[1129,19510],{"className":19511,"style":1218},[1217],[1129,19513,19515],{"className":19514},[1222,1223,1224,1225],[1129,19516,19518,19521,19524],{"className":19517},[1187,1225],[1129,19519,19452],{"className":19520,"style":2580},[1187,1191,1225],[1129,19522,2450],{"className":19523,"style":2580},[1187,1191,1225],[1129,19525,19457],{"className":19526},[1187,1191,1225],[1129,19528,1254],{"className":19529},[1253],[1129,19531,19533],{"className":19532},[1205],[1129,19534,19536],{"className":19535,"style":2574},[1209],[1129,19537],{},[1129,19539],{"className":19540,"style":1996},[1368],[1129,19542,1884],{"className":19543},[2000],[1129,19545],{"className":19546,"style":1996},[1368],[1129,19548,19550,19554],{"className":19549},[1178],[1129,19551],{"className":19552,"style":19553},[1182],"height:0.888em;",[1129,19555,19557,19560],{"className":19556},[1187],[1129,19558,19464],{"className":19559},[1187],[1129,19561,19563],{"className":19562},[1196],[1129,19564,19566],{"className":19565},[1200],[1129,19567,19569],{"className":19568},[1205],[1129,19570,19572],{"className":19571,"style":19553},[1209],[1129,19573,19574,19577],{"style":1239},[1129,19575],{"className":19576,"style":1218},[1217],[1129,19578,19580],{"className":19579},[1222,1223,1224,1225],[1129,19581,19583,19586],{"className":19582},[1187,1225],[1129,19584,1344],{"className":19585},[1187,1225],[1129,19587,19589],{"className":19588},[1187,1225],"1\u002F2",[1101,19591,6921,19592,19621],{},[1129,19593,19595,19609],{"className":19594},[1132],[1129,19596,19598],{"className":19597},[1136],[1138,19599,19600],{"xmlns":1140},[1142,19601,19602,19606],{},[1145,19603,19604],{},[1151,19605,19464],{"mathvariant":2444},[1166,19607,19608],{"encoding":1168},"\\Sigma",[1129,19610,19612],{"className":19611,"ariaHidden":1174},[1173],[1129,19613,19615,19618],{"className":19614},[1178],[1129,19616],{"className":19617,"style":5901},[1182],[1129,19619,19464],{"className":19620},[1187]," 为数据的协方差矩阵。",[1105,19623,19624,19636],{},[1108,19625,19626],{},[1111,19627,19628,19631,19634],{},[1114,19629,19630],{},"预处理方法",[1114,19632,19633],{},"效果",[1114,19635,17433],{},[1121,19637,19638,19649,19660],{},[1111,19639,19640,19643,19646],{},[1126,19641,19642],{},"均值减法",[1126,19644,19645],{},"中心化（均值=0）",[1126,19647,19648],{},"几乎所有情况",[1111,19650,19651,19654,19657],{},[1126,19652,19653],{},"均一化",[1126,19655,19656],{},"中心化 + 等方差",[1126,19658,19659],{},"特征尺度差异大时",[1111,19661,19662,19665,19668],{},[1126,19663,19664],{},"ZCA 白化",[1126,19666,19667],{},"去相关 + 等方差",[1126,19669,19670],{},"特征间相关性强时",[5907,19672],{},[1091,19674,19676],{"id":19675},"九其他优化算法","九、其他优化算法",[1096,19678,19680],{"id":19679},"_91-hessian-方法二阶优化","9.1 Hessian 方法（二阶优化）",[1101,19682,19683],{},"利用代价函数的二阶泰勒展开来优化：",[1101,19685,19686],{},[1129,19687,19689,19761],{"className":19688},[1132],[1129,19690,19692],{"className":19691},[1136],[1138,19693,19694],{"xmlns":1140},[1142,19695,19696,19758],{},[1145,19697,19698,19700,19702,19704,19706,19709,19711,19713,19715,19717,19719,19721,19723,19725,19727,19729,19731,19733,19735,19737,19743,19745,19751,19754,19756],{},[1151,19699,2450],{},[1342,19701,2466],{"stretchy":2465},[1151,19703,1153],{},[1342,19705,1921],{},[1151,19707,19708],{"mathvariant":2444},"Δ",[1151,19710,1153],{},[1342,19712,2475],{"stretchy":2465},[1342,19714,6065],{},[1151,19716,2450],{},[1342,19718,2466],{"stretchy":2465},[1151,19720,1153],{},[1342,19722,2475],{"stretchy":2465},[1342,19724,1921],{},[1151,19726,2445],{"mathvariant":2444},[1151,19728,2450],{},[1342,19730,7983],{},[1151,19732,19708],{"mathvariant":2444},[1151,19734,1153],{},[1342,19736,1921],{},[3018,19738,19739,19741],{},[1346,19740,1348],{},[1346,19742,3724],{},[1151,19744,19708],{"mathvariant":2444},[2431,19746,19747,19749],{},[1151,19748,1153],{},[1151,19750,2715],{},[1151,19752,19753],{},"H",[1151,19755,19708],{"mathvariant":2444},[1151,19757,1153],{},[1166,19759,19760],{"encoding":1168},"C(w + \\Delta w) \\approx C(w) + \\nabla C \\cdot \\Delta w + \\frac{1}{2} \\Delta w^T H \\Delta w",[1129,19762,19764,19788,19812,19839,19860,19881],{"className":19763,"ariaHidden":1174},[1173],[1129,19765,19767,19770,19773,19776,19779,19782,19785],{"className":19766},[1178],[1129,19768],{"className":19769,"style":6081},[1182],[1129,19771,2450],{"className":19772,"style":2580},[1187,1191],[1129,19774,2466],{"className":19775},[2634],[1129,19777,1153],{"className":19778,"style":1192},[1187,1191],[1129,19780],{"className":19781,"style":1369},[1368],[1129,19783,1921],{"className":19784},[1373],[1129,19786],{"className":19787,"style":1369},[1368],[1129,19789,19791,19794,19797,19800,19803,19806,19809],{"className":19790},[1178],[1129,19792],{"className":19793,"style":6081},[1182],[1129,19795,19708],{"className":19796},[1187],[1129,19798,1153],{"className":19799,"style":1192},[1187,1191],[1129,19801,2475],{"className":19802},[2667],[1129,19804],{"className":19805,"style":1996},[1368],[1129,19807,6065],{"className":19808},[2000],[1129,19810],{"className":19811,"style":1996},[1368],[1129,19813,19815,19818,19821,19824,19827,19830,19833,19836],{"className":19814},[1178],[1129,19816],{"className":19817,"style":6081},[1182],[1129,19819,2450],{"className":19820,"style":2580},[1187,1191],[1129,19822,2466],{"className":19823},[2634],[1129,19825,1153],{"className":19826,"style":1192},[1187,1191],[1129,19828,2475],{"className":19829},[2667],[1129,19831],{"className":19832,"style":1369},[1368],[1129,19834,1921],{"className":19835},[1373],[1129,19837],{"className":19838,"style":1369},[1368],[1129,19840,19842,19845,19848,19851,19854,19857],{"className":19841},[1178],[1129,19843],{"className":19844,"style":5901},[1182],[1129,19846,2445],{"className":19847},[1187],[1129,19849,2450],{"className":19850,"style":2580},[1187,1191],[1129,19852],{"className":19853,"style":1369},[1368],[1129,19855,7983],{"className":19856},[1373],[1129,19858],{"className":19859,"style":1369},[1368],[1129,19861,19863,19866,19869,19872,19875,19878],{"className":19862},[1178],[1129,19864],{"className":19865,"style":4453},[1182],[1129,19867,19708],{"className":19868},[1187],[1129,19870,1153],{"className":19871,"style":1192},[1187,1191],[1129,19873],{"className":19874,"style":1369},[1368],[1129,19876,1921],{"className":19877},[1373],[1129,19879],{"className":19880,"style":1369},[1368],[1129,19882,19884,19887,19955,19958,19987,19991,19994],{"className":19883},[1178],[1129,19885],{"className":19886,"style":6714},[1182],[1129,19888,19890,19893,19952],{"className":19889},[1187],[1129,19891],{"className":19892},[2634,3068],[1129,19894,19896],{"className":19895},[3018],[1129,19897,19899,19944],{"className":19898},[1200,1201],[1129,19900,19902,19941],{"className":19901},[1205],[1129,19903,19905,19919,19927],{"className":19904,"style":6736},[1209],[1129,19906,19907,19910],{"style":6739},[1129,19908],{"className":19909,"style":3088},[1217],[1129,19911,19913],{"className":19912},[1222,1223,1224,1225],[1129,19914,19916],{"className":19915},[1187,1225],[1129,19917,3724],{"className":19918},[1187,1225],[1129,19920,19921,19924],{"style":3159},[1129,19922],{"className":19923,"style":3088},[1217],[1129,19925],{"className":19926,"style":3167},[3166],[1129,19928,19929,19932],{"style":3170},[1129,19930],{"className":19931,"style":3088},[1217],[1129,19933,19935],{"className":19934},[1222,1223,1224,1225],[1129,19936,19938],{"className":19937},[1187,1225],[1129,19939,1348],{"className":19940},[1187,1225],[1129,19942,1254],{"className":19943},[1253],[1129,19945,19947],{"className":19946},[1205],[1129,19948,19950],{"className":19949,"style":6783},[1209],[1129,19951],{},[1129,19953],{"className":19954},[2667,3068],[1129,19956,19708],{"className":19957},[1187],[1129,19959,19961,19964],{"className":19960},[1187],[1129,19962,1153],{"className":19963,"style":1192},[1187,1191],[1129,19965,19967],{"className":19966},[1196],[1129,19968,19970],{"className":19969},[1200],[1129,19971,19973],{"className":19972},[1205],[1129,19974,19976],{"className":19975,"style":2488},[1209],[1129,19977,19978,19981],{"style":1239},[1129,19979],{"className":19980,"style":1218},[1217],[1129,19982,19984],{"className":19983},[1222,1223,1224,1225],[1129,19985,2715],{"className":19986,"style":2876},[1187,1191,1225],[1129,19988,19753],{"className":19989,"style":19990},[1187,1191],"margin-right:0.0813em;",[1129,19992,19708],{"className":19993},[1187],[1129,19995,1153],{"className":19996,"style":1192},[1187,1191],[1101,19998,6921,19999,20027,20028],{},[1129,20000,20002,20015],{"className":20001},[1132],[1129,20003,20005],{"className":20004},[1136],[1138,20006,20007],{"xmlns":1140},[1142,20008,20009,20013],{},[1145,20010,20011],{},[1151,20012,19753],{},[1166,20014,19753],{"encoding":1168},[1129,20016,20018],{"className":20017,"ariaHidden":1174},[1173],[1129,20019,20021,20024],{"className":20020},[1178],[1129,20022],{"className":20023,"style":5901},[1182],[1129,20025,19753],{"className":20026,"style":19990},[1187,1191]," 为 Hessian 矩阵（二阶偏导矩阵），",[1129,20029,20031,20085],{"className":20030},[1132],[1129,20032,20034],{"className":20033},[1136],[1138,20035,20036],{"xmlns":1140},[1142,20037,20038,20082],{},[1145,20039,20040,20050,20052],{},[1886,20041,20042,20044],{},[1151,20043,19753],{},[1145,20045,20046,20048],{},[1151,20047,17999],{},[1151,20049,1158],{},[1342,20051,1884],{},[3018,20053,20054,20064],{},[1145,20055,20056,20062],{},[2431,20057,20058,20060],{},[1151,20059,3024],{"mathvariant":2444},[1346,20061,3724],{},[1151,20063,2450],{},[1145,20065,20066,20068,20074,20076],{},[1151,20067,3024],{"mathvariant":2444},[1886,20069,20070,20072],{},[1151,20071,1153],{},[1151,20073,17999],{},[1151,20075,3024],{"mathvariant":2444},[1886,20077,20078,20080],{},[1151,20079,1153],{},[1151,20081,1158],{},[1166,20083,20084],{"encoding":1168},"H_{ij} = \\frac{\\partial^2 C}{\\partial w_i \\partial w_j}",[1129,20086,20088,20149],{"className":20087,"ariaHidden":1174},[1173],[1129,20089,20091,20095,20140,20143,20146],{"className":20090},[1178],[1129,20092],{"className":20093,"style":20094},[1182],"height:0.9694em;vertical-align:-0.2861em;",[1129,20096,20098,20101],{"className":20097},[1187],[1129,20099,19753],{"className":20100,"style":19990},[1187,1191],[1129,20102,20104],{"className":20103},[1196],[1129,20105,20107,20132],{"className":20106},[1200,1201],[1129,20108,20110,20129],{"className":20109},[1205],[1129,20111,20113],{"className":20112,"style":7442},[1209],[1129,20114,20116,20119],{"style":20115},"top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;",[1129,20117],{"className":20118,"style":1218},[1217],[1129,20120,20122],{"className":20121},[1222,1223,1224,1225],[1129,20123,20125],{"className":20124},[1187,1225],[1129,20126,20128],{"className":20127,"style":1232},[1187,1191,1225],"ij",[1129,20130,1254],{"className":20131},[1253],[1129,20133,20135],{"className":20134},[1205],[1129,20136,20138],{"className":20137,"style":7463},[1209],[1129,20139],{},[1129,20141],{"className":20142,"style":1996},[1368],[1129,20144,1884],{"className":20145},[2000],[1129,20147],{"className":20148,"style":1996},[1368],[1129,20150,20152,20156],{"className":20151},[1178],[1129,20153],{"className":20154,"style":20155},[1182],"height:1.5602em;vertical-align:-0.5423em;",[1129,20157,20159,20162,20335],{"className":20158},[1187],[1129,20160],{"className":20161},[2634,3068],[1129,20163,20165],{"className":20164},[3018],[1129,20166,20168,20327],{"className":20167},[1200,1201],[1129,20169,20171,20324],{"className":20170},[1205],[1129,20172,20175,20272,20280],{"className":20173,"style":20174},[1209],"height:1.0179em;",[1129,20176,20177,20180],{"style":6739},[1129,20178],{"className":20179,"style":3088},[1217],[1129,20181,20183],{"className":20182},[1222,1223,1224,1225],[1129,20184,20186,20189,20229,20232],{"className":20185},[1187,1225],[1129,20187,3024],{"className":20188,"style":3098},[1187,1225],[1129,20190,20192,20195],{"className":20191},[1187,1225],[1129,20193,1153],{"className":20194,"style":1192},[1187,1191,1225],[1129,20196,20198],{"className":20197},[1196],[1129,20199,20201,20221],{"className":20200},[1200,1201],[1129,20202,20204,20218],{"className":20203},[1205],[1129,20205,20207],{"className":20206,"style":7230},[1209],[1129,20208,20209,20212],{"style":7233},[1129,20210],{"className":20211,"style":3124},[1217],[1129,20213,20215],{"className":20214},[1222,3128,3129,1225],[1129,20216,17999],{"className":20217},[1187,1191,1225],[1129,20219,1254],{"className":20220},[1253],[1129,20222,20224],{"className":20223},[1205],[1129,20225,20227],{"className":20226,"style":15828},[1209],[1129,20228],{},[1129,20230,3024],{"className":20231,"style":3098},[1187,1225],[1129,20233,20235,20238],{"className":20234},[1187,1225],[1129,20236,1153],{"className":20237,"style":1192},[1187,1191,1225],[1129,20239,20241],{"className":20240},[1196],[1129,20242,20244,20264],{"className":20243},[1200,1201],[1129,20245,20247,20261],{"className":20246},[1205],[1129,20248,20250],{"className":20249,"style":7230},[1209],[1129,20251,20252,20255],{"style":7233},[1129,20253],{"className":20254,"style":3124},[1217],[1129,20256,20258],{"className":20257},[1222,3128,3129,1225],[1129,20259,1158],{"className":20260,"style":1232},[1187,1191,1225],[1129,20262,1254],{"className":20263},[1253],[1129,20265,20267],{"className":20266},[1205],[1129,20268,20270],{"className":20269,"style":7252},[1209],[1129,20271],{},[1129,20273,20274,20277],{"style":3159},[1129,20275],{"className":20276,"style":3088},[1217],[1129,20278],{"className":20279,"style":3167},[3166],[1129,20281,20282,20285],{"style":3170},[1129,20283],{"className":20284,"style":3088},[1217],[1129,20286,20288],{"className":20287},[1222,1223,1224,1225],[1129,20289,20291,20321],{"className":20290},[1187,1225],[1129,20292,20294,20297],{"className":20293},[1187,1225],[1129,20295,3024],{"className":20296,"style":3098},[1187,1225],[1129,20298,20300],{"className":20299},[1196],[1129,20301,20303],{"className":20302},[1200],[1129,20304,20306],{"className":20305},[1205],[1129,20307,20310],{"className":20308,"style":20309},[1209],"height:0.8913em;",[1129,20311,20312,20315],{"style":12550},[1129,20313],{"className":20314,"style":3124},[1217],[1129,20316,20318],{"className":20317},[1222,3128,3129,1225],[1129,20319,3724],{"className":20320},[1187,1225],[1129,20322,2450],{"className":20323,"style":2580},[1187,1191,1225],[1129,20325,1254],{"className":20326},[1253],[1129,20328,20330],{"className":20329},[1205],[1129,20331,20333],{"className":20332,"style":7289},[1209],[1129,20334],{},[1129,20336],{"className":20337},[2667,3068],[1101,20339,20340],{},"令梯度为零，求得最优步长：",[1101,20342,20343],{},[1129,20344,20346,20380],{"className":20345},[1132],[1129,20347,20349],{"className":20348},[1136],[1138,20350,20351],{"xmlns":1140},[1142,20352,20353,20377],{},[1145,20354,20355,20357,20359,20361,20363,20373,20375],{},[1151,20356,19708],{"mathvariant":2444},[1151,20358,1153],{},[1342,20360,1884],{},[1342,20362,1344],{},[2431,20364,20365,20367],{},[1151,20366,19753],{},[1145,20368,20369,20371],{},[1342,20370,1344],{},[1346,20372,1348],{},[1151,20374,2445],{"mathvariant":2444},[1151,20376,2450],{},[1166,20378,20379],{"encoding":1168},"\\Delta w = -H^{-1} \\nabla C",[1129,20381,20383,20404],{"className":20382,"ariaHidden":1174},[1173],[1129,20384,20386,20389,20392,20395,20398,20401],{"className":20385},[1178],[1129,20387],{"className":20388,"style":5901},[1182],[1129,20390,19708],{"className":20391},[1187],[1129,20393,1153],{"className":20394,"style":1192},[1187,1191],[1129,20396],{"className":20397,"style":1996},[1368],[1129,20399,1884],{"className":20400},[2000],[1129,20402],{"className":20403,"style":1996},[1368],[1129,20405,20407,20410,20413,20448,20451],{"className":20406},[1178],[1129,20408],{"className":20409,"style":12587},[1182],[1129,20411,1344],{"className":20412},[1187],[1129,20414,20416,20419],{"className":20415},[1187],[1129,20417,19753],{"className":20418,"style":19990},[1187,1191],[1129,20420,20422],{"className":20421},[1196],[1129,20423,20425],{"className":20424},[1200],[1129,20426,20428],{"className":20427},[1205],[1129,20429,20431],{"className":20430,"style":3651},[1209],[1129,20432,20433,20436],{"style":1239},[1129,20434],{"className":20435,"style":1218},[1217],[1129,20437,20439],{"className":20438},[1222,1223,1224,1225],[1129,20440,20442,20445],{"className":20441},[1187,1225],[1129,20443,1344],{"className":20444},[1187,1225],[1129,20446,1348],{"className":20447},[1187,1225],[1129,20449,2445],{"className":20450},[1187],[1129,20452,2450],{"className":20453,"style":2580},[1187,1191],[1101,20455,20456],{},[2405,20457,20458],{},"Hessian 方法的优缺点",[2409,20460,20461,20467],{},[2412,20462,20463,20466],{},[2405,20464,20465],{},"优点","：收敛速度快，不需要手动调节学习率",[2412,20468,20469,20472,20473,20550,20551,20625],{},[2405,20470,20471],{},"缺点","：Hessian 矩阵计算和存储成本极高（",[1129,20474,20476,20501],{"className":20475},[1132],[1129,20477,20479],{"className":20478},[1136],[1138,20480,20481],{"xmlns":1140},[1142,20482,20483,20498],{},[1145,20484,20485,20488,20490,20496],{},[1151,20486,20487],{},"O",[1342,20489,2466],{"stretchy":2465},[2431,20491,20492,20494],{},[1151,20493,6632],{},[1346,20495,3724],{},[1342,20497,2475],{"stretchy":2465},[1166,20499,20500],{"encoding":1168},"O(n^2)",[1129,20502,20504],{"className":20503,"ariaHidden":1174},[1173],[1129,20505,20507,20511,20515,20518,20547],{"className":20506},[1178],[1129,20508],{"className":20509,"style":20510},[1182],"height:1.0641em;vertical-align:-0.25em;",[1129,20512,20487],{"className":20513,"style":20514},[1187,1191],"margin-right:0.0278em;",[1129,20516,2466],{"className":20517},[2634],[1129,20519,20521,20524],{"className":20520},[1187],[1129,20522,6632],{"className":20523},[1187,1191],[1129,20525,20527],{"className":20526},[1196],[1129,20528,20530],{"className":20529},[1200],[1129,20531,20533],{"className":20532},[1205],[1129,20534,20536],{"className":20535,"style":3651},[1209],[1129,20537,20538,20541],{"style":1239},[1129,20539],{"className":20540,"style":1218},[1217],[1129,20542,20544],{"className":20543},[1222,1223,1224,1225],[1129,20545,3724],{"className":20546},[1187,1225],[1129,20548,2475],{"className":20549},[2667]," 存储，",[1129,20552,20554,20578],{"className":20553},[1132],[1129,20555,20557],{"className":20556},[1136],[1138,20558,20559],{"xmlns":1140},[1142,20560,20561,20575],{},[1145,20562,20563,20565,20567,20573],{},[1151,20564,20487],{},[1342,20566,2466],{"stretchy":2465},[2431,20568,20569,20571],{},[1151,20570,6632],{},[1346,20572,3730],{},[1342,20574,2475],{"stretchy":2465},[1166,20576,20577],{"encoding":1168},"O(n^3)",[1129,20579,20581],{"className":20580,"ariaHidden":1174},[1173],[1129,20582,20584,20587,20590,20593,20622],{"className":20583},[1178],[1129,20585],{"className":20586,"style":20510},[1182],[1129,20588,20487],{"className":20589,"style":20514},[1187,1191],[1129,20591,2466],{"className":20592},[2634],[1129,20594,20596,20599],{"className":20595},[1187],[1129,20597,6632],{"className":20598},[1187,1191],[1129,20600,20602],{"className":20601},[1196],[1129,20603,20605],{"className":20604},[1200],[1129,20606,20608],{"className":20607},[1205],[1129,20609,20611],{"className":20610,"style":3651},[1209],[1129,20612,20613,20616],{"style":1239},[1129,20614],{"className":20615,"style":1218},[1217],[1129,20617,20619],{"className":20618},[1222,1223,1224,1225],[1129,20620,3730],{"className":20621},[1187,1225],[1129,20623,2475],{"className":20624},[2667]," 求逆），实际中常用近似方法",[1096,20627,20629],{"id":20628},"_92-动量梯度下降momentum","9.2 动量梯度下降（Momentum）",[1101,20631,20632,20633,20662],{},"引入\"速度\"变量 ",[1129,20634,20636,20650],{"className":20635},[1132],[1129,20637,20639],{"className":20638},[1136],[1138,20640,20641],{"xmlns":1140},[1142,20642,20643,20648],{},[1145,20644,20645],{},[1151,20646,20647],{},"v",[1166,20649,20647],{"encoding":1168},[1129,20651,20653],{"className":20652,"ariaHidden":1174},[1173],[1129,20654,20656,20659],{"className":20655},[1178],[1129,20657],{"className":20658,"style":3696},[1182],[1129,20660,20647],{"className":20661,"style":2603},[1187,1191],"，模拟物理中的动量效应：",[1101,20664,20665],{},[1129,20666,20668,20696],{"className":20667},[1132],[1129,20669,20671],{"className":20670},[1136],[1138,20672,20673],{"xmlns":1140},[1142,20674,20675,20693],{},[1145,20676,20677,20679,20681,20683,20685,20687,20689,20691],{},[1151,20678,20647],{},[1342,20680,15526],{},[1151,20682,19222],{},[1151,20684,20647],{},[1342,20686,1344],{},[1151,20688,15537],{},[1151,20690,2445],{"mathvariant":2444},[1151,20692,2450],{},[1166,20694,20695],{"encoding":1168},"v \\to \\mu v - \\eta \\nabla C",[1129,20697,20699,20717,20737],{"className":20698,"ariaHidden":1174},[1173],[1129,20700,20702,20705,20708,20711,20714],{"className":20701},[1178],[1129,20703],{"className":20704,"style":3696},[1182],[1129,20706,20647],{"className":20707,"style":2603},[1187,1191],[1129,20709],{"className":20710,"style":1996},[1368],[1129,20712,15526],{"className":20713},[2000],[1129,20715],{"className":20716,"style":1996},[1368],[1129,20718,20720,20724,20728,20731,20734],{"className":20719},[1178],[1129,20721],{"className":20722,"style":20723},[1182],"height:0.7778em;vertical-align:-0.1944em;",[1129,20725,20727],{"className":20726,"style":2603},[1187,1191],"μv",[1129,20729],{"className":20730,"style":1369},[1368],[1129,20732,1344],{"className":20733},[1373],[1129,20735],{"className":20736,"style":1369},[1368],[1129,20738,20740,20743,20746,20749],{"className":20739},[1178],[1129,20741],{"className":20742,"style":3770},[1182],[1129,20744,15537],{"className":20745,"style":2603},[1187,1191],[1129,20747,2445],{"className":20748},[1187],[1129,20750,2450],{"className":20751,"style":2580},[1187,1191],[1101,20753,20754],{},[1129,20755,20757,20779],{"className":20756},[1132],[1129,20758,20760],{"className":20759},[1136],[1138,20761,20762],{"xmlns":1140},[1142,20763,20764,20776],{},[1145,20765,20766,20768,20770,20772,20774],{},[1151,20767,1153],{},[1342,20769,15526],{},[1151,20771,1153],{},[1342,20773,1921],{},[1151,20775,20647],{},[1166,20777,20778],{"encoding":1168},"w \\to w + v",[1129,20780,20782,20800,20818],{"className":20781,"ariaHidden":1174},[1173],[1129,20783,20785,20788,20791,20794,20797],{"className":20784},[1178],[1129,20786],{"className":20787,"style":3696},[1182],[1129,20789,1153],{"className":20790,"style":1192},[1187,1191],[1129,20792],{"className":20793,"style":1996},[1368],[1129,20795,15526],{"className":20796},[2000],[1129,20798],{"className":20799,"style":1996},[1368],[1129,20801,20803,20806,20809,20812,20815],{"className":20802},[1178],[1129,20804],{"className":20805,"style":15603},[1182],[1129,20807,1153],{"className":20808,"style":1192},[1187,1191],[1129,20810],{"className":20811,"style":1369},[1368],[1129,20813,1921],{"className":20814},[1373],[1129,20816],{"className":20817,"style":1369},[1368],[1129,20819,20821,20824],{"className":20820},[1178],[1129,20822],{"className":20823,"style":3696},[1182],[1129,20825,20647],{"className":20826,"style":2603},[1187,1191],[1101,20828,6921,20829,20904,20905,20934],{},[1129,20830,20832,20858],{"className":20831},[1132],[1129,20833,20835],{"className":20834},[1136],[1138,20836,20837],{"xmlns":1140},[1142,20838,20839,20855],{},[1145,20840,20841,20843,20845,20847,20849,20851,20853],{},[1151,20842,19222],{},[1342,20844,11919],{},[1342,20846,6643],{"stretchy":2465},[1346,20848,6526],{},[1342,20850,3727],{"separator":1174},[1346,20852,1348],{},[1342,20854,2475],{"stretchy":2465},[1166,20856,20857],{"encoding":1168},"\\mu \\in [0, 1)",[1129,20859,20861,20880],{"className":20860,"ariaHidden":1174},[1173],[1129,20862,20864,20868,20871,20874,20877],{"className":20863},[1178],[1129,20865],{"className":20866,"style":20867},[1182],"height:0.7335em;vertical-align:-0.1944em;",[1129,20869,19222],{"className":20870},[1187,1191],[1129,20872],{"className":20873,"style":1996},[1368],[1129,20875,11919],{"className":20876},[2000],[1129,20878],{"className":20879,"style":1996},[1368],[1129,20881,20883,20886,20889,20892,20895,20898,20901],{"className":20882},[1178],[1129,20884],{"className":20885,"style":6081},[1182],[1129,20887,6643],{"className":20888},[2634],[1129,20890,6526],{"className":20891},[1187],[1129,20893,3727],{"className":20894},[3777],[1129,20896],{"className":20897,"style":2061},[1368],[1129,20899,1348],{"className":20900},[1187],[1129,20902,2475],{"className":20903},[2667]," 为动量系数（通常取 0.9），",[1129,20906,20908,20922],{"className":20907},[1132],[1129,20909,20911],{"className":20910},[1136],[1138,20912,20913],{"xmlns":1140},[1142,20914,20915,20919],{},[1145,20916,20917],{},[1151,20918,15537],{},[1166,20920,20921],{"encoding":1168},"\\eta",[1129,20923,20925],{"className":20924,"ariaHidden":1174},[1173],[1129,20926,20928,20931],{"className":20927},[1178],[1129,20929],{"className":20930,"style":7005},[1182],[1129,20932,15537],{"className":20933,"style":2603},[1187,1191]," 为学习率",[1105,20936,20937,20949],{},[1108,20938,20939],{},[1111,20940,20941,20943,20946],{},[1114,20942,16882],{},[1114,20944,20945],{},"标准梯度下降",[1114,20947,20948],{},"动量梯度下降",[1121,20950,20951,21200,21211,21222],{},[1111,20952,20953,20955,21040],{},[1126,20954,16269],{},[1126,20956,20957],{},[1129,20958,20960,20986],{"className":20959},[1132],[1129,20961,20963],{"className":20962},[1136],[1138,20964,20965],{"xmlns":1140},[1142,20966,20967,20983],{},[1145,20968,20969,20971,20973,20975,20977,20979,20981],{},[1151,20970,1153],{},[1342,20972,15526],{},[1151,20974,1153],{},[1342,20976,1344],{},[1151,20978,15537],{},[1151,20980,2445],{"mathvariant":2444},[1151,20982,2450],{},[1166,20984,20985],{"encoding":1168},"w \\to w - \\eta\\nabla C",[1129,20987,20989,21007,21025],{"className":20988,"ariaHidden":1174},[1173],[1129,20990,20992,20995,20998,21001,21004],{"className":20991},[1178],[1129,20993],{"className":20994,"style":3696},[1182],[1129,20996,1153],{"className":20997,"style":1192},[1187,1191],[1129,20999],{"className":21000,"style":1996},[1368],[1129,21002,15526],{"className":21003},[2000],[1129,21005],{"className":21006,"style":1996},[1368],[1129,21008,21010,21013,21016,21019,21022],{"className":21009},[1178],[1129,21011],{"className":21012,"style":15603},[1182],[1129,21014,1153],{"className":21015,"style":1192},[1187,1191],[1129,21017],{"className":21018,"style":1369},[1368],[1129,21020,1344],{"className":21021},[1373],[1129,21023],{"className":21024,"style":1369},[1368],[1129,21026,21028,21031,21034,21037],{"className":21027},[1178],[1129,21029],{"className":21030,"style":3770},[1182],[1129,21032,15537],{"className":21033,"style":2603},[1187,1191],[1129,21035,2445],{"className":21036},[1187],[1129,21038,2450],{"className":21039,"style":2580},[1187,1191],[1126,21041,21042,21127,21128],{},[1129,21043,21045,21073],{"className":21044},[1132],[1129,21046,21048],{"className":21047},[1136],[1138,21049,21050],{"xmlns":1140},[1142,21051,21052,21070],{},[1145,21053,21054,21056,21058,21060,21062,21064,21066,21068],{},[1151,21055,20647],{},[1342,21057,15526],{},[1151,21059,19222],{},[1151,21061,20647],{},[1342,21063,1344],{},[1151,21065,15537],{},[1151,21067,2445],{"mathvariant":2444},[1151,21069,2450],{},[1166,21071,21072],{"encoding":1168},"v \\to \\mu v - \\eta\\nabla C",[1129,21074,21076,21094,21112],{"className":21075,"ariaHidden":1174},[1173],[1129,21077,21079,21082,21085,21088,21091],{"className":21078},[1178],[1129,21080],{"className":21081,"style":3696},[1182],[1129,21083,20647],{"className":21084,"style":2603},[1187,1191],[1129,21086],{"className":21087,"style":1996},[1368],[1129,21089,15526],{"className":21090},[2000],[1129,21092],{"className":21093,"style":1996},[1368],[1129,21095,21097,21100,21103,21106,21109],{"className":21096},[1178],[1129,21098],{"className":21099,"style":20723},[1182],[1129,21101,20727],{"className":21102,"style":2603},[1187,1191],[1129,21104],{"className":21105,"style":1369},[1368],[1129,21107,1344],{"className":21108},[1373],[1129,21110],{"className":21111,"style":1369},[1368],[1129,21113,21115,21118,21121,21124],{"className":21114},[1178],[1129,21116],{"className":21117,"style":3770},[1182],[1129,21119,15537],{"className":21120,"style":2603},[1187,1191],[1129,21122,2445],{"className":21123},[1187],[1129,21125,2450],{"className":21126,"style":2580},[1187,1191],"，",[1129,21129,21131,21152],{"className":21130},[1132],[1129,21132,21134],{"className":21133},[1136],[1138,21135,21136],{"xmlns":1140},[1142,21137,21138,21150],{},[1145,21139,21140,21142,21144,21146,21148],{},[1151,21141,1153],{},[1342,21143,15526],{},[1151,21145,1153],{},[1342,21147,1921],{},[1151,21149,20647],{},[1166,21151,20778],{"encoding":1168},[1129,21153,21155,21173,21191],{"className":21154,"ariaHidden":1174},[1173],[1129,21156,21158,21161,21164,21167,21170],{"className":21157},[1178],[1129,21159],{"className":21160,"style":3696},[1182],[1129,21162,1153],{"className":21163,"style":1192},[1187,1191],[1129,21165],{"className":21166,"style":1996},[1368],[1129,21168,15526],{"className":21169},[2000],[1129,21171],{"className":21172,"style":1996},[1368],[1129,21174,21176,21179,21182,21185,21188],{"className":21175},[1178],[1129,21177],{"className":21178,"style":15603},[1182],[1129,21180,1153],{"className":21181,"style":1192},[1187,1191],[1129,21183],{"className":21184,"style":1369},[1368],[1129,21186,1921],{"className":21187},[1373],[1129,21189],{"className":21190,"style":1369},[1368],[1129,21192,21194,21197],{"className":21193},[1178],[1129,21195],{"className":21196,"style":3696},[1182],[1129,21198,20647],{"className":21199,"style":2603},[1187,1191],[1111,21201,21202,21205,21208],{},[1126,21203,21204],{},"梯度噪声",[1126,21206,21207],{},"容易震荡",[1126,21209,21210],{},"平滑梯度方向",[1111,21212,21213,21216,21219],{},[1126,21214,21215],{},"平坦区域",[1126,21217,21218],{},"缓慢通过",[1126,21220,21221],{},"积累速度快速通过",[1111,21223,21224,21227,21230],{},[1126,21225,21226],{},"收敛速度",[1126,21228,21229],{},"较慢",[1126,21231,21232],{},"更快",[5907,21234],{},[1091,21236,21238],{"id":21237},"十其他激活函数","十、其他激活函数",[1096,21240,21242],{"id":21241},"_101-tanh-激活函数","10.1 tanh 激活函数",[1101,21244,21245],{},"定义：",[1101,21247,21248],{},[1129,21249,21251,21318],{"className":21250},[1132],[1129,21252,21254],{"className":21253},[1136],[1138,21255,21256],{"xmlns":1140},[1142,21257,21258,21315],{},[1145,21259,21260,21263,21265,21267,21269,21271,21273],{},[1151,21261,21262],{},"tanh",[1342,21264,6652],{},[1342,21266,2466],{"stretchy":2465},[1151,21268,1733],{},[1342,21270,2475],{"stretchy":2465},[1342,21272,1884],{},[3018,21274,21275,21295],{},[1145,21276,21277,21283,21285],{},[2431,21278,21279,21281],{},[1151,21280,11507],{},[1151,21282,1733],{},[1342,21284,1344],{},[2431,21286,21287,21289],{},[1151,21288,11507],{},[1145,21290,21291,21293],{},[1342,21292,1344],{},[1151,21294,1733],{},[1145,21296,21297,21303,21305],{},[2431,21298,21299,21301],{},[1151,21300,11507],{},[1151,21302,1733],{},[1342,21304,1921],{},[2431,21306,21307,21309],{},[1151,21308,11507],{},[1145,21310,21311,21313],{},[1342,21312,1344],{},[1151,21314,1733],{},[1166,21316,21317],{"encoding":1168},"\\tanh(z) = \\frac{e^z - e^{-z}}{e^z + e^{-z}}",[1129,21319,21321,21348],{"className":21320,"ariaHidden":1174},[1173],[1129,21322,21324,21327,21330,21333,21336,21339,21342,21345],{"className":21323},[1178],[1129,21325],{"className":21326,"style":6081},[1182],[1129,21328,21262],{"className":21329},[2014],[1129,21331,2466],{"className":21332},[2634],[1129,21334,1733],{"className":21335,"style":1756},[1187,1191],[1129,21337,2475],{"className":21338},[2667],[1129,21340],{"className":21341,"style":1996},[1368],[1129,21343,1884],{"className":21344},[2000],[1129,21346],{"className":21347,"style":1996},[1368],[1129,21349,21351,21355],{"className":21350},[1178],[1129,21352],{"className":21353,"style":21354},[1182],"height:1.3907em;vertical-align:-0.4033em;",[1129,21356,21358,21361,21555],{"className":21357},[1187],[1129,21359],{"className":21360},[2634,3068],[1129,21362,21364],{"className":21363},[3018],[1129,21365,21367,21546],{"className":21366},[1200,1201],[1129,21368,21370,21543],{"className":21369},[1205],[1129,21371,21374,21455,21463],{"className":21372,"style":21373},[1209],"height:0.9874em;",[1129,21375,21376,21379],{"style":6739},[1129,21377],{"className":21378,"style":3088},[1217],[1129,21380,21382],{"className":21381},[1222,1223,1224,1225],[1129,21383,21385,21416,21419],{"className":21384},[1187,1225],[1129,21386,21388,21391],{"className":21387},[1187,1225],[1129,21389,11507],{"className":21390},[1187,1191,1225],[1129,21392,21394],{"className":21393},[1196],[1129,21395,21397],{"className":21396},[1200],[1129,21398,21400],{"className":21399},[1205],[1129,21401,21404],{"className":21402,"style":21403},[1209],"height:0.5935em;",[1129,21405,21407,21410],{"style":21406},"top:-2.786em;margin-right:0.0714em;",[1129,21408],{"className":21409,"style":3124},[1217],[1129,21411,21413],{"className":21412},[1222,3128,3129,1225],[1129,21414,1733],{"className":21415,"style":1756},[1187,1191,1225],[1129,21417,1921],{"className":21418},[1373,1225],[1129,21420,21422,21425],{"className":21421},[1187,1225],[1129,21423,11507],{"className":21424},[1187,1191,1225],[1129,21426,21428],{"className":21427},[1196],[1129,21429,21431],{"className":21430},[1200],[1129,21432,21434],{"className":21433},[1205],[1129,21435,21438],{"className":21436,"style":21437},[1209],"height:0.7027em;",[1129,21439,21440,21443],{"style":21406},[1129,21441],{"className":21442,"style":3124},[1217],[1129,21444,21446],{"className":21445},[1222,3128,3129,1225],[1129,21447,21449,21452],{"className":21448},[1187,1225],[1129,21450,1344],{"className":21451},[1187,1225],[1129,21453,1733],{"className":21454,"style":1756},[1187,1191,1225],[1129,21456,21457,21460],{"style":3159},[1129,21458],{"className":21459,"style":3088},[1217],[1129,21461],{"className":21462,"style":3167},[3166],[1129,21464,21465,21468],{"style":3170},[1129,21466],{"className":21467,"style":3088},[1217],[1129,21469,21471],{"className":21470},[1222,1223,1224,1225],[1129,21472,21474,21504,21507],{"className":21473},[1187,1225],[1129,21475,21477,21480],{"className":21476},[1187,1225],[1129,21478,11507],{"className":21479},[1187,1191,1225],[1129,21481,21483],{"className":21482},[1196],[1129,21484,21486],{"className":21485},[1200],[1129,21487,21489],{"className":21488},[1205],[1129,21490,21493],{"className":21491,"style":21492},[1209],"height:0.7385em;",[1129,21494,21495,21498],{"style":12550},[1129,21496],{"className":21497,"style":3124},[1217],[1129,21499,21501],{"className":21500},[1222,3128,3129,1225],[1129,21502,1733],{"className":21503,"style":1756},[1187,1191,1225],[1129,21505,1344],{"className":21506},[1373,1225],[1129,21508,21510,21513],{"className":21509},[1187,1225],[1129,21511,11507],{"className":21512},[1187,1191,1225],[1129,21514,21516],{"className":21515},[1196],[1129,21517,21519],{"className":21518},[1200],[1129,21520,21522],{"className":21521},[1205],[1129,21523,21526],{"className":21524,"style":21525},[1209],"height:0.8477em;",[1129,21527,21528,21531],{"style":12550},[1129,21529],{"className":21530,"style":3124},[1217],[1129,21532,21534],{"className":21533},[1222,3128,3129,1225],[1129,21535,21537,21540],{"className":21536},[1187,1225],[1129,21538,1344],{"className":21539},[1187,1225],[1129,21541,1733],{"className":21542,"style":1756},[1187,1191,1225],[1129,21544,1254],{"className":21545},[1253],[1129,21547,21549],{"className":21548},[1205],[1129,21550,21553],{"className":21551,"style":21552},[1209],"height:0.4033em;",[1129,21554],{},[1129,21556],{"className":21557},[2667,3068],[1101,21559,21560],{},"与 Sigmoid 的关系：",[1101,21562,21563],{},[1129,21564,21566,21612],{"className":21565},[1132],[1129,21567,21569],{"className":21568},[1136],[1138,21570,21571],{"xmlns":1140},[1142,21572,21573,21609],{},[1145,21574,21575,21577,21579,21581,21583,21585],{},[1151,21576,2458],{},[1342,21578,2466],{"stretchy":2465},[1151,21580,1733],{},[1342,21582,2475],{"stretchy":2465},[1342,21584,1884],{},[3018,21586,21587,21607],{},[1145,21588,21589,21591,21593,21595,21597,21599,21601,21603,21605],{},[1346,21590,1348],{},[1342,21592,1921],{},[1151,21594,21262],{},[1342,21596,6652],{},[1342,21598,2466],{"stretchy":2465},[1151,21600,1733],{},[1151,21602,18431],{"mathvariant":2444},[1346,21604,3724],{},[1342,21606,2475],{"stretchy":2465},[1346,21608,3724],{},[1166,21610,21611],{"encoding":1168},"\\sigma(z) = \\frac{1 + \\tanh(z\u002F2)}{2}",[1129,21613,21615,21642],{"className":21614,"ariaHidden":1174},[1173],[1129,21616,21618,21621,21624,21627,21630,21633,21636,21639],{"className":21617},[1178],[1129,21619],{"className":21620,"style":6081},[1182],[1129,21622,2458],{"className":21623,"style":2603},[1187,1191],[1129,21625,2466],{"className":21626},[2634],[1129,21628,1733],{"className":21629,"style":1756},[1187,1191],[1129,21631,2475],{"className":21632},[2667],[1129,21634],{"className":21635,"style":1996},[1368],[1129,21637,1884],{"className":21638},[2000],[1129,21640],{"className":21641,"style":1996},[1368],[1129,21643,21645,21649],{"className":21644},[1178],[1129,21646],{"className":21647,"style":21648},[1182],"height:1.355em;vertical-align:-0.345em;",[1129,21650,21652,21655,21749],{"className":21651},[1187],[1129,21653],{"className":21654},[2634,3068],[1129,21656,21658],{"className":21657},[3018],[1129,21659,21661,21741],{"className":21660},[1200,1201],[1129,21662,21664,21738],{"className":21663},[1205],[1129,21665,21668,21682,21690],{"className":21666,"style":21667},[1209],"height:1.01em;",[1129,21669,21670,21673],{"style":6739},[1129,21671],{"className":21672,"style":3088},[1217],[1129,21674,21676],{"className":21675},[1222,1223,1224,1225],[1129,21677,21679],{"className":21678},[1187,1225],[1129,21680,3724],{"className":21681},[1187,1225],[1129,21683,21684,21687],{"style":3159},[1129,21685],{"className":21686,"style":3088},[1217],[1129,21688],{"className":21689,"style":3167},[3166],[1129,21691,21693,21696],{"style":21692},"top:-3.485em;",[1129,21694],{"className":21695,"style":3088},[1217],[1129,21697,21699],{"className":21698},[1222,1223,1224,1225],[1129,21700,21702,21705,21708,21725,21728,21731,21735],{"className":21701},[1187,1225],[1129,21703,1348],{"className":21704},[1187,1225],[1129,21706,1921],{"className":21707},[1373,1225],[1129,21709,21711,21715,21718,21721],{"className":21710},[2014,1225],[1129,21712,21714],{"className":21713},[1225],"t",[1129,21716,1586],{"className":21717},[1225],[1129,21719,6632],{"className":21720},[1225],[1129,21722,21724],{"className":21723},[1225],"h",[1129,21726,2466],{"className":21727},[2634,1225],[1129,21729,1733],{"className":21730,"style":1756},[1187,1191,1225],[1129,21732,21734],{"className":21733},[1187,1225],"\u002F2",[1129,21736,2475],{"className":21737},[2667,1225],[1129,21739,1254],{"className":21740},[1253],[1129,21742,21744],{"className":21743},[1205],[1129,21745,21747],{"className":21746,"style":6783},[1209],[1129,21748],{},[1129,21750],{"className":21751},[2667,3068],[1105,21753,21754,21810],{},[1108,21755,21756],{},[1111,21757,21758,21760,21807],{},[1114,21759,16882],{},[1114,21761,21762,21763],{},"Sigmoid ",[1129,21764,21766,21786],{"className":21765},[1132],[1129,21767,21769],{"className":21768},[1136],[1138,21770,21771],{"xmlns":1140},[1142,21772,21773,21783],{},[1145,21774,21775,21777,21779,21781],{},[1151,21776,2458],{},[1342,21778,2466],{"stretchy":2465},[1151,21780,1733],{},[1342,21782,2475],{"stretchy":2465},[1166,21784,21785],{"encoding":1168},"\\sigma(z)",[1129,21787,21789],{"className":21788,"ariaHidden":1174},[1173],[1129,21790,21792,21795,21798,21801,21804],{"className":21791},[1178],[1129,21793],{"className":21794,"style":6081},[1182],[1129,21796,2458],{"className":21797,"style":2603},[1187,1191],[1129,21799,2466],{"className":21800},[2634],[1129,21802,1733],{"className":21803,"style":1756},[1187,1191],[1129,21805,2475],{"className":21806},[2667],[1114,21808,21809],{},"tanh(z)",[1121,21811,21812,21930,21941,21952],{},[1111,21813,21814,21817,21871],{},[1126,21815,21816],{},"输出范围",[1126,21818,21819],{},[1129,21820,21822,21844],{"className":21821},[1132],[1129,21823,21825],{"className":21824},[1136],[1138,21826,21827],{"xmlns":1140},[1142,21828,21829,21841],{},[1145,21830,21831,21833,21835,21837,21839],{},[1342,21832,2466],{"stretchy":2465},[1346,21834,6526],{},[1342,21836,3727],{"separator":1174},[1346,21838,1348],{},[1342,21840,2475],{"stretchy":2465},[1166,21842,21843],{"encoding":1168},"(0, 1)",[1129,21845,21847],{"className":21846,"ariaHidden":1174},[1173],[1129,21848,21850,21853,21856,21859,21862,21865,21868],{"className":21849},[1178],[1129,21851],{"className":21852,"style":6081},[1182],[1129,21854,2466],{"className":21855},[2634],[1129,21857,6526],{"className":21858},[1187],[1129,21860,3727],{"className":21861},[3777],[1129,21863],{"className":21864,"style":2061},[1368],[1129,21866,1348],{"className":21867},[1187],[1129,21869,2475],{"className":21870},[2667],[1126,21872,21873],{},[1129,21874,21876,21900],{"className":21875},[1132],[1129,21877,21879],{"className":21878},[1136],[1138,21880,21881],{"xmlns":1140},[1142,21882,21883,21897],{},[1145,21884,21885,21887,21889,21891,21893,21895],{},[1342,21886,2466],{"stretchy":2465},[1342,21888,1344],{},[1346,21890,1348],{},[1342,21892,3727],{"separator":1174},[1346,21894,1348],{},[1342,21896,2475],{"stretchy":2465},[1166,21898,21899],{"encoding":1168},"(-1, 1)",[1129,21901,21903],{"className":21902,"ariaHidden":1174},[1173],[1129,21904,21906,21909,21912,21915,21918,21921,21924,21927],{"className":21905},[1178],[1129,21907],{"className":21908,"style":6081},[1182],[1129,21910,2466],{"className":21911},[2634],[1129,21913,1344],{"className":21914},[1187],[1129,21916,1348],{"className":21917},[1187],[1129,21919,3727],{"className":21920},[3777],[1129,21922],{"className":21923,"style":2061},[1368],[1129,21925,1348],{"className":21926},[1187],[1129,21928,2475],{"className":21929},[2667],[1111,21931,21932,21935,21938],{},[1126,21933,21934],{},"零中心",[1126,21936,21937],{},"否（输出总为正）",[1126,21939,21940],{},"是（零中心输出）",[1111,21942,21943,21946,21949],{},[1126,21944,21945],{},"饱和问题",[1126,21947,21948],{},"存在",[1126,21950,21951],{},"存在（但零中心有助于训练）",[1111,21953,21954,21957,21960],{},[1126,21955,21956],{},"典型应用",[1126,21958,21959],{},"输出层（二分类概率）",[1126,21961,21962],{},"隐藏层",[1096,21964,21966],{"id":21965},"_102-relu-激活函数","10.2 ReLU 激活函数",[1101,21968,21245],{},[1101,21970,21971],{},[1129,21972,21974,22012],{"className":21973},[1132],[1129,21975,21977],{"className":21976},[1136],[1138,21978,21979],{"xmlns":1140},[1142,21980,21981,22009],{},[1145,21982,21983,21986,21988,21990,21992,21994,21997,21999,22001,22003,22005,22007],{},[5470,21984,21985],{},"ReLU",[1342,21987,2466],{"stretchy":2465},[1151,21989,1733],{},[1342,21991,2475],{"stretchy":2465},[1342,21993,1884],{},[1151,21995,21996],{},"max",[1342,21998,6652],{},[1342,22000,2466],{"stretchy":2465},[1346,22002,6526],{},[1342,22004,3727],{"separator":1174},[1151,22006,1733],{},[1342,22008,2475],{"stretchy":2465},[1166,22010,22011],{"encoding":1168},"\\text{ReLU}(z) = \\max(0, z)",[1129,22013,22015,22045],{"className":22014,"ariaHidden":1174},[1173],[1129,22016,22018,22021,22027,22030,22033,22036,22039,22042],{"className":22017},[1178],[1129,22019],{"className":22020,"style":6081},[1182],[1129,22022,22024],{"className":22023},[1187,5683],[1129,22025,21985],{"className":22026},[1187],[1129,22028,2466],{"className":22029},[2634],[1129,22031,1733],{"className":22032,"style":1756},[1187,1191],[1129,22034,2475],{"className":22035},[2667],[1129,22037],{"className":22038,"style":1996},[1368],[1129,22040,1884],{"className":22041},[2000],[1129,22043],{"className":22044,"style":1996},[1368],[1129,22046,22048,22051,22054,22057,22060,22063,22066,22069],{"className":22047},[1178],[1129,22049],{"className":22050,"style":6081},[1182],[1129,22052,21996],{"className":22053},[2014],[1129,22055,2466],{"className":22056},[2634],[1129,22058,6526],{"className":22059},[1187],[1129,22061,3727],{"className":22062},[3777],[1129,22064],{"className":22065,"style":2061},[1368],[1129,22067,1733],{"className":22068,"style":1756},[1187,1191],[1129,22070,2475],{"className":22071},[2667],[1101,22073,22074],{},[2405,22075,22076],{},"ReLU 的优势",[2409,22078,22079,22085,22091,22097],{},[2412,22080,22081,22084],{},[2405,22082,22083],{},"无饱和问题","（正区间梯度恒为 1）",[2412,22086,22087,22090],{},[2405,22088,22089],{},"计算高效","（仅需比较和取零操作）",[2412,22092,22093,22096],{},[2405,22094,22095],{},"稀疏激活","（负输入直接输出零，天然正则化效果）",[2412,22098,22099],{},"收敛速度通常比 Sigmoid\u002Ftanh 快 6 倍",[1101,22101,22102],{},[2405,22103,22104],{},"ReLU 的潜在问题：Dead ReLU",[1101,22106,22107,22108,22173],{},"当某个神经元的输入始终为负时，该神经元永远输出 0，梯度也为 0，永远无法恢复。解决方案：使用 Leaky ReLU ",[1129,22109,22111,22140],{"className":22110},[1132],[1129,22112,22114],{"className":22113},[1136],[1138,22115,22116],{"xmlns":1140},[1142,22117,22118,22137],{},[1145,22119,22120,22122,22124,22126,22129,22131,22133,22135],{},[1151,22121,21996],{},[1342,22123,6652],{},[1342,22125,2466],{"stretchy":2465},[1346,22127,22128],{},"0.01",[1151,22130,1733],{},[1342,22132,3727],{"separator":1174},[1151,22134,1733],{},[1342,22136,2475],{"stretchy":2465},[1166,22138,22139],{"encoding":1168},"\\max(0.01z, z)",[1129,22141,22143],{"className":22142,"ariaHidden":1174},[1173],[1129,22144,22146,22149,22152,22155,22158,22161,22164,22167,22170],{"className":22145},[1178],[1129,22147],{"className":22148,"style":6081},[1182],[1129,22150,21996],{"className":22151},[2014],[1129,22153,2466],{"className":22154},[2634],[1129,22156,22128],{"className":22157},[1187],[1129,22159,1733],{"className":22160,"style":1756},[1187,1191],[1129,22162,3727],{"className":22163},[3777],[1129,22165],{"className":22166,"style":2061},[1368],[1129,22168,1733],{"className":22169,"style":1756},[1187,1191],[1129,22171,2475],{"className":22172},[2667]," 或适当的学习率。",[1096,22175,22177],{"id":22176},"_103-激活函数总览","10.3 激活函数总览",[1105,22179,22180,22198],{},[1108,22181,22182],{},[1111,22183,22184,22187,22190,22193,22195],{},[1114,22185,22186],{},"函数",[1114,22188,22189],{},"公式",[1114,22191,22192],{},"范围",[1114,22194,21934],{},[1114,22196,22197],{},"主要问题",[1121,22199,22200,22367,22644],{},[1111,22201,22202,22205,22358,22361,22364],{},[1126,22203,22204],{},"Sigmoid",[1126,22206,22207],{},[1129,22208,22210,22242],{"className":22209},[1132],[1129,22211,22213],{"className":22212},[1136],[1138,22214,22215],{"xmlns":1140},[1142,22216,22217,22239],{},[1145,22218,22219],{},[3018,22220,22221,22223],{},[1346,22222,1348],{},[1145,22224,22225,22227,22229],{},[1346,22226,1348],{},[1342,22228,1921],{},[2431,22230,22231,22233],{},[1151,22232,11507],{},[1145,22234,22235,22237],{},[1342,22236,1344],{},[1151,22238,1733],{},[1166,22240,22241],{"encoding":1168},"\\frac{1}{1+e^{-z}}",[1129,22243,22245],{"className":22244,"ariaHidden":1174},[1173],[1129,22246,22248,22252],{"className":22247},[1178],[1129,22249],{"className":22250,"style":22251},[1182],"height:1.2484em;vertical-align:-0.4033em;",[1129,22253,22255,22258,22355],{"className":22254},[1187],[1129,22256],{"className":22257},[2634,3068],[1129,22259,22261],{"className":22260},[3018],[1129,22262,22264,22347],{"className":22263},[1200,1201],[1129,22265,22267,22344],{"className":22266},[1205],[1129,22268,22270,22322,22330],{"className":22269,"style":6736},[1209],[1129,22271,22272,22275],{"style":6739},[1129,22273],{"className":22274,"style":3088},[1217],[1129,22276,22278],{"className":22277},[1222,1223,1224,1225],[1129,22279,22281,22284,22287],{"className":22280},[1187,1225],[1129,22282,1348],{"className":22283},[1187,1225],[1129,22285,1921],{"className":22286},[1373,1225],[1129,22288,22290,22293],{"className":22289},[1187,1225],[1129,22291,11507],{"className":22292},[1187,1191,1225],[1129,22294,22296],{"className":22295},[1196],[1129,22297,22299],{"className":22298},[1200],[1129,22300,22302],{"className":22301},[1205],[1129,22303,22305],{"className":22304,"style":21437},[1209],[1129,22306,22307,22310],{"style":21406},[1129,22308],{"className":22309,"style":3124},[1217],[1129,22311,22313],{"className":22312},[1222,3128,3129,1225],[1129,22314,22316,22319],{"className":22315},[1187,1225],[1129,22317,1344],{"className":22318},[1187,1225],[1129,22320,1733],{"className":22321,"style":1756},[1187,1191,1225],[1129,22323,22324,22327],{"style":3159},[1129,22325],{"className":22326,"style":3088},[1217],[1129,22328],{"className":22329,"style":3167},[3166],[1129,22331,22332,22335],{"style":3170},[1129,22333],{"className":22334,"style":3088},[1217],[1129,22336,22338],{"className":22337},[1222,1223,1224,1225],[1129,22339,22341],{"className":22340},[1187,1225],[1129,22342,1348],{"className":22343},[1187,1225],[1129,22345,1254],{"className":22346},[1253],[1129,22348,22350],{"className":22349},[1205],[1129,22351,22353],{"className":22352,"style":21552},[1209],[1129,22354],{},[1129,22356],{"className":22357},[2667,3068],[1126,22359,22360],{},"(0,1)",[1126,22362,22363],{},"否",[1126,22365,22366],{},"饱和、非零中心",[1111,22368,22369,22371,22635,22638,22641],{},[1126,22370,21262],{},[1126,22372,22373],{},[1129,22374,22376,22430],{"className":22375},[1132],[1129,22377,22379],{"className":22378},[1136],[1138,22380,22381],{"xmlns":1140},[1142,22382,22383,22427],{},[1145,22384,22385],{},[3018,22386,22387,22407],{},[1145,22388,22389,22395,22397],{},[2431,22390,22391,22393],{},[1151,22392,11507],{},[1151,22394,1733],{},[1342,22396,1344],{},[2431,22398,22399,22401],{},[1151,22400,11507],{},[1145,22402,22403,22405],{},[1342,22404,1344],{},[1151,22406,1733],{},[1145,22408,22409,22415,22417],{},[2431,22410,22411,22413],{},[1151,22412,11507],{},[1151,22414,1733],{},[1342,22416,1921],{},[2431,22418,22419,22421],{},[1151,22420,11507],{},[1145,22422,22423,22425],{},[1342,22424,1344],{},[1151,22426,1733],{},[1166,22428,22429],{"encoding":1168},"\\frac{e^z-e^{-z}}{e^z+e^{-z}}",[1129,22431,22433],{"className":22432,"ariaHidden":1174},[1173],[1129,22434,22436,22439],{"className":22435},[1178],[1129,22437],{"className":22438,"style":21354},[1182],[1129,22440,22442,22445,22632],{"className":22441},[1187],[1129,22443],{"className":22444},[2634,3068],[1129,22446,22448],{"className":22447},[3018],[1129,22449,22451,22624],{"className":22450},[1200,1201],[1129,22452,22454,22621],{"className":22453},[1205],[1129,22455,22457,22535,22543],{"className":22456,"style":21373},[1209],[1129,22458,22459,22462],{"style":6739},[1129,22460],{"className":22461,"style":3088},[1217],[1129,22463,22465],{"className":22464},[1222,1223,1224,1225],[1129,22466,22468,22497,22500],{"className":22467},[1187,1225],[1129,22469,22471,22474],{"className":22470},[1187,1225],[1129,22472,11507],{"className":22473},[1187,1191,1225],[1129,22475,22477],{"className":22476},[1196],[1129,22478,22480],{"className":22479},[1200],[1129,22481,22483],{"className":22482},[1205],[1129,22484,22486],{"className":22485,"style":21403},[1209],[1129,22487,22488,22491],{"style":21406},[1129,22489],{"className":22490,"style":3124},[1217],[1129,22492,22494],{"className":22493},[1222,3128,3129,1225],[1129,22495,1733],{"className":22496,"style":1756},[1187,1191,1225],[1129,22498,1921],{"className":22499},[1373,1225],[1129,22501,22503,22506],{"className":22502},[1187,1225],[1129,22504,11507],{"className":22505},[1187,1191,1225],[1129,22507,22509],{"className":22508},[1196],[1129,22510,22512],{"className":22511},[1200],[1129,22513,22515],{"className":22514},[1205],[1129,22516,22518],{"className":22517,"style":21437},[1209],[1129,22519,22520,22523],{"style":21406},[1129,22521],{"className":22522,"style":3124},[1217],[1129,22524,22526],{"className":22525},[1222,3128,3129,1225],[1129,22527,22529,22532],{"className":22528},[1187,1225],[1129,22530,1344],{"className":22531},[1187,1225],[1129,22533,1733],{"className":22534,"style":1756},[1187,1191,1225],[1129,22536,22537,22540],{"style":3159},[1129,22538],{"className":22539,"style":3088},[1217],[1129,22541],{"className":22542,"style":3167},[3166],[1129,22544,22545,22548],{"style":3170},[1129,22546],{"className":22547,"style":3088},[1217],[1129,22549,22551],{"className":22550},[1222,1223,1224,1225],[1129,22552,22554,22583,22586],{"className":22553},[1187,1225],[1129,22555,22557,22560],{"className":22556},[1187,1225],[1129,22558,11507],{"className":22559},[1187,1191,1225],[1129,22561,22563],{"className":22562},[1196],[1129,22564,22566],{"className":22565},[1200],[1129,22567,22569],{"className":22568},[1205],[1129,22570,22572],{"className":22571,"style":21492},[1209],[1129,22573,22574,22577],{"style":12550},[1129,22575],{"className":22576,"style":3124},[1217],[1129,22578,22580],{"className":22579},[1222,3128,3129,1225],[1129,22581,1733],{"className":22582,"style":1756},[1187,1191,1225],[1129,22584,1344],{"className":22585},[1373,1225],[1129,22587,22589,22592],{"className":22588},[1187,1225],[1129,22590,11507],{"className":22591},[1187,1191,1225],[1129,22593,22595],{"className":22594},[1196],[1129,22596,22598],{"className":22597},[1200],[1129,22599,22601],{"className":22600},[1205],[1129,22602,22604],{"className":22603,"style":21525},[1209],[1129,22605,22606,22609],{"style":12550},[1129,22607],{"className":22608,"style":3124},[1217],[1129,22610,22612],{"className":22611},[1222,3128,3129,1225],[1129,22613,22615,22618],{"className":22614},[1187,1225],[1129,22616,1344],{"className":22617},[1187,1225],[1129,22619,1733],{"className":22620,"style":1756},[1187,1191,1225],[1129,22622,1254],{"className":22623},[1253],[1129,22625,22627],{"className":22626},[1205],[1129,22628,22630],{"className":22629,"style":21552},[1209],[1129,22631],{},[1129,22633],{"className":22634},[2667,3068],[1126,22636,22637],{},"(-1,1)",[1126,22639,22640],{},"是",[1126,22642,22643],{},"饱和",[1111,22645,22646,22648,22709,22712,22714],{},[1126,22647,21985],{},[1126,22649,22650],{},[1129,22651,22653,22679],{"className":22652},[1132],[1129,22654,22656],{"className":22655},[1136],[1138,22657,22658],{"xmlns":1140},[1142,22659,22660,22676],{},[1145,22661,22662,22664,22666,22668,22670,22672,22674],{},[1151,22663,21996],{},[1342,22665,6652],{},[1342,22667,2466],{"stretchy":2465},[1346,22669,6526],{},[1342,22671,3727],{"separator":1174},[1151,22673,1733],{},[1342,22675,2475],{"stretchy":2465},[1166,22677,22678],{"encoding":1168},"\\max(0,z)",[1129,22680,22682],{"className":22681,"ariaHidden":1174},[1173],[1129,22683,22685,22688,22691,22694,22697,22700,22703,22706],{"className":22684},[1178],[1129,22686],{"className":22687,"style":6081},[1182],[1129,22689,21996],{"className":22690},[2014],[1129,22692,2466],{"className":22693},[2634],[1129,22695,6526],{"className":22696},[1187],[1129,22698,3727],{"className":22699},[3777],[1129,22701],{"className":22702,"style":2061},[1368],[1129,22704,1733],{"className":22705,"style":1756},[1187,1191],[1129,22707,2475],{"className":22708},[2667],[1126,22710,22711],{},"[0,+∞)",[1126,22713,22363],{},[1126,22715,22716],{},"Dead ReLU",[5907,22718],{},[2409,22720,22721,23343,23814,24370,24906,25091],{},[2412,22722,22723,2417,22726,22989,22990],{},[2405,22724,22725],{},"交叉熵",[1129,22727,22729,22792],{"className":22728},[1132],[1129,22730,22732],{"className":22731},[1136],[1138,22733,22734],{"xmlns":1140},[1142,22735,22736,22790],{},[1145,22737,22738,22740,22742,22744,22750,22752,22754,22756,22758,22760,22762,22764,22766,22768,22770,22772,22774,22776,22778,22780,22782,22784,22786,22788],{},[1151,22739,2450],{},[1342,22741,1884],{},[1342,22743,1344],{},[3018,22745,22746,22748],{},[1346,22747,1348],{},[1151,22749,6632],{},[1342,22751,1890],{},[1342,22753,6643],{"stretchy":2465},[1151,22755,6646],{},[1151,22757,6649],{},[1342,22759,6652],{},[1151,22761,1586],{},[1342,22763,1921],{},[1342,22765,2466],{"stretchy":2465},[1346,22767,1348],{},[1342,22769,1344],{},[1151,22771,6646],{},[1342,22773,2475],{"stretchy":2465},[1151,22775,6649],{},[1342,22777,6652],{},[1342,22779,2466],{"stretchy":2465},[1346,22781,1348],{},[1342,22783,1344],{},[1151,22785,1586],{},[1342,22787,2475],{"stretchy":2465},[1342,22789,6683],{"stretchy":2465},[1166,22791,14696],{"encoding":1168},[1129,22793,22795,22813,22923,22944,22977],{"className":22794,"ariaHidden":1174},[1173],[1129,22796,22798,22801,22804,22807,22810],{"className":22797},[1178],[1129,22799],{"className":22800,"style":5901},[1182],[1129,22802,2450],{"className":22803,"style":2580},[1187,1191],[1129,22805],{"className":22806,"style":1996},[1368],[1129,22808,1884],{"className":22809},[2000],[1129,22811],{"className":22812,"style":1996},[1368],[1129,22814,22816,22819,22822,22890,22893,22896,22899,22902,22905,22908,22911,22914,22917,22920],{"className":22815},[1178],[1129,22817],{"className":22818,"style":6714},[1182],[1129,22820,1344],{"className":22821},[1187],[1129,22823,22825,22828,22887],{"className":22824},[1187],[1129,22826],{"className":22827},[2634,3068],[1129,22829,22831],{"className":22830},[3018],[1129,22832,22834,22879],{"className":22833},[1200,1201],[1129,22835,22837,22876],{"className":22836},[1205],[1129,22838,22840,22854,22862],{"className":22839,"style":6736},[1209],[1129,22841,22842,22845],{"style":6739},[1129,22843],{"className":22844,"style":3088},[1217],[1129,22846,22848],{"className":22847},[1222,1223,1224,1225],[1129,22849,22851],{"className":22850},[1187,1225],[1129,22852,6632],{"className":22853},[1187,1191,1225],[1129,22855,22856,22859],{"style":3159},[1129,22857],{"className":22858,"style":3088},[1217],[1129,22860],{"className":22861,"style":3167},[3166],[1129,22863,22864,22867],{"style":3170},[1129,22865],{"className":22866,"style":3088},[1217],[1129,22868,22870],{"className":22869},[1222,1223,1224,1225],[1129,22871,22873],{"className":22872},[1187,1225],[1129,22874,1348],{"className":22875},[1187,1225],[1129,22877,1254],{"className":22878},[1253],[1129,22880,22882],{"className":22881},[1205],[1129,22883,22885],{"className":22884,"style":6783},[1209],[1129,22886],{},[1129,22888],{"className":22889},[2667,3068],[1129,22891],{"className":22892,"style":2061},[1368],[1129,22894,1890],{"className":22895,"style":2020},[2014,2018,2019],[1129,22897,6643],{"className":22898},[2634],[1129,22900,6646],{"className":22901,"style":2603},[1187,1191],[1129,22903],{"className":22904,"style":2061},[1368],[1129,22906,6649],{"className":22907},[2014],[1129,22909],{"className":22910,"style":2061},[1368],[1129,22912,1586],{"className":22913},[1187,1191],[1129,22915],{"className":22916,"style":1369},[1368],[1129,22918,1921],{"className":22919},[1373],[1129,22921],{"className":22922,"style":1369},[1368],[1129,22924,22926,22929,22932,22935,22938,22941],{"className":22925},[1178],[1129,22927],{"className":22928,"style":6081},[1182],[1129,22930,2466],{"className":22931},[2634],[1129,22933,1348],{"className":22934},[1187],[1129,22936],{"className":22937,"style":1369},[1368],[1129,22939,1344],{"className":22940},[1373],[1129,22942],{"className":22943,"style":1369},[1368],[1129,22945,22947,22950,22953,22956,22959,22962,22965,22968,22971,22974],{"className":22946},[1178],[1129,22948],{"className":22949,"style":6081},[1182],[1129,22951,6646],{"className":22952,"style":2603},[1187,1191],[1129,22954,2475],{"className":22955},[2667],[1129,22957],{"className":22958,"style":2061},[1368],[1129,22960,6649],{"className":22961},[2014],[1129,22963,2466],{"className":22964},[2634],[1129,22966,1348],{"className":22967},[1187],[1129,22969],{"className":22970,"style":1369},[1368],[1129,22972,1344],{"className":22973},[1373],[1129,22975],{"className":22976,"style":1369},[1368],[1129,22978,22980,22983,22986],{"className":22979},[1178],[1129,22981],{"className":22982,"style":6081},[1182],[1129,22984,1586],{"className":22985},[1187,1191],[1129,22987,14894],{"className":22988},[2667],"，梯度：",[1129,22991,22993,23055],{"className":22992},[1132],[1129,22994,22996],{"className":22995},[1136],[1138,22997,22998],{"xmlns":1140},[1142,22999,23000,23052],{},[1145,23001,23002,23020,23022,23028,23030,23036,23038,23040,23042,23044,23046,23048,23050],{},[3018,23003,23004,23010],{},[1145,23005,23006,23008],{},[1151,23007,3024],{"mathvariant":2444},[1151,23009,2450],{},[1145,23011,23012,23014],{},[1151,23013,3024],{"mathvariant":2444},[1886,23015,23016,23018],{},[1151,23017,1153],{},[1151,23019,1158],{},[1342,23021,1884],{},[3018,23023,23024,23026],{},[1346,23025,1348],{},[1151,23027,6632],{},[1342,23029,1890],{},[1886,23031,23032,23034],{},[1151,23033,3638],{},[1151,23035,1158],{},[1342,23037,2466],{"stretchy":2465},[1151,23039,2458],{},[1342,23041,2466],{"stretchy":2465},[1151,23043,1733],{},[1342,23045,2475],{"stretchy":2465},[1342,23047,1344],{},[1151,23049,6646],{},[1342,23051,2475],{"stretchy":2465},[1166,23053,23054],{"encoding":1168},"\\frac{\\partial C}{\\partial w_j} = \\frac{1}{n}\\sum x_j(\\sigma(z)-y)",[1129,23056,23058,23184,23331],{"className":23057,"ariaHidden":1174},[1173],[1129,23059,23061,23064,23175,23178,23181],{"className":23060},[1178],[1129,23062],{"className":23063,"style":7179},[1182],[1129,23065,23067,23070,23172],{"className":23066},[1187],[1129,23068],{"className":23069},[2634,3068],[1129,23071,23073],{"className":23072},[3018],[1129,23074,23076,23164],{"className":23075},[1200,1201],[1129,23077,23079,23161],{"className":23078},[1205],[1129,23080,23082,23136,23144],{"className":23081,"style":3081},[1209],[1129,23083,23084,23087],{"style":6739},[1129,23085],{"className":23086,"style":3088},[1217],[1129,23088,23090],{"className":23089},[1222,1223,1224,1225],[1129,23091,23093,23096],{"className":23092},[1187,1225],[1129,23094,3024],{"className":23095,"style":3098},[1187,1225],[1129,23097,23099,23102],{"className":23098},[1187,1225],[1129,23100,1153],{"className":23101,"style":1192},[1187,1191,1225],[1129,23103,23105],{"className":23104},[1196],[1129,23106,23108,23128],{"className":23107},[1200,1201],[1129,23109,23111,23125],{"className":23110},[1205],[1129,23112,23114],{"className":23113,"style":7230},[1209],[1129,23115,23116,23119],{"style":7233},[1129,23117],{"className":23118,"style":3124},[1217],[1129,23120,23122],{"className":23121},[1222,3128,3129,1225],[1129,23123,1158],{"className":23124,"style":1232},[1187,1191,1225],[1129,23126,1254],{"className":23127},[1253],[1129,23129,23131],{"className":23130},[1205],[1129,23132,23134],{"className":23133,"style":7252},[1209],[1129,23135],{},[1129,23137,23138,23141],{"style":3159},[1129,23139],{"className":23140,"style":3088},[1217],[1129,23142],{"className":23143,"style":3167},[3166],[1129,23145,23146,23149],{"style":3170},[1129,23147],{"className":23148,"style":3088},[1217],[1129,23150,23152],{"className":23151},[1222,1223,1224,1225],[1129,23153,23155,23158],{"className":23154},[1187,1225],[1129,23156,3024],{"className":23157,"style":3098},[1187,1225],[1129,23159,2450],{"className":23160,"style":2580},[1187,1191,1225],[1129,23162,1254],{"className":23163},[1253],[1129,23165,23167],{"className":23166},[1205],[1129,23168,23170],{"className":23169,"style":7289},[1209],[1129,23171],{},[1129,23173],{"className":23174},[2667,3068],[1129,23176],{"className":23177,"style":1996},[1368],[1129,23179,1884],{"className":23180},[2000],[1129,23182],{"className":23183,"style":1996},[1368],[1129,23185,23187,23190,23258,23261,23264,23267,23307,23310,23313,23316,23319,23322,23325,23328],{"className":23186},[1178],[1129,23188],{"className":23189,"style":6714},[1182],[1129,23191,23193,23196,23255],{"className":23192},[1187],[1129,23194],{"className":23195},[2634,3068],[1129,23197,23199],{"className":23198},[3018],[1129,23200,23202,23247],{"className":23201},[1200,1201],[1129,23203,23205,23244],{"className":23204},[1205],[1129,23206,23208,23222,23230],{"className":23207,"style":6736},[1209],[1129,23209,23210,23213],{"style":6739},[1129,23211],{"className":23212,"style":3088},[1217],[1129,23214,23216],{"className":23215},[1222,1223,1224,1225],[1129,23217,23219],{"className":23218},[1187,1225],[1129,23220,6632],{"className":23221},[1187,1191,1225],[1129,23223,23224,23227],{"style":3159},[1129,23225],{"className":23226,"style":3088},[1217],[1129,23228],{"className":23229,"style":3167},[3166],[1129,23231,23232,23235],{"style":3170},[1129,23233],{"className":23234,"style":3088},[1217],[1129,23236,23238],{"className":23237},[1222,1223,1224,1225],[1129,23239,23241],{"className":23240},[1187,1225],[1129,23242,1348],{"className":23243},[1187,1225],[1129,23245,1254],{"className":23246},[1253],[1129,23248,23250],{"className":23249},[1205],[1129,23251,23253],{"className":23252,"style":6783},[1209],[1129,23254],{},[1129,23256],{"className":23257},[2667,3068],[1129,23259],{"className":23260,"style":2061},[1368],[1129,23262,1890],{"className":23263,"style":2020},[2014,2018,2019],[1129,23265],{"className":23266,"style":2061},[1368],[1129,23268,23270,23273],{"className":23269},[1187],[1129,23271,3638],{"className":23272},[1187,1191],[1129,23274,23276],{"className":23275},[1196],[1129,23277,23279,23299],{"className":23278},[1200,1201],[1129,23280,23282,23296],{"className":23281},[1205],[1129,23283,23285],{"className":23284,"style":7442},[1209],[1129,23286,23287,23290],{"style":2555},[1129,23288],{"className":23289,"style":1218},[1217],[1129,23291,23293],{"className":23292},[1222,1223,1224,1225],[1129,23294,1158],{"className":23295,"style":1232},[1187,1191,1225],[1129,23297,1254],{"className":23298},[1253],[1129,23300,23302],{"className":23301},[1205],[1129,23303,23305],{"className":23304,"style":7463},[1209],[1129,23306],{},[1129,23308,2466],{"className":23309},[2634],[1129,23311,2458],{"className":23312,"style":2603},[1187,1191],[1129,23314,2466],{"className":23315},[2634],[1129,23317,1733],{"className":23318,"style":1756},[1187,1191],[1129,23320,2475],{"className":23321},[2667],[1129,23323],{"className":23324,"style":1369},[1368],[1129,23326,1344],{"className":23327},[1373],[1129,23329],{"className":23330,"style":1369},[1368],[1129,23332,23334,23337,23340],{"className":23333},[1178],[1129,23335],{"className":23336,"style":6081},[1182],[1129,23338,6646],{"className":23339,"style":2603},[1187,1191],[1129,23341,2475],{"className":23342},[2667],[2412,23344,23345,2417,23348,23690,23691],{},[2405,23346,23347],{},"Softmax",[1129,23349,23351,23405],{"className":23350},[1132],[1129,23352,23354],{"className":23353},[1136],[1138,23355,23356],{"xmlns":1140},[1142,23357,23358,23402],{},[1145,23359,23360,23368,23370,23382,23384,23390],{},[1148,23361,23362,23364,23366],{},[1151,23363,1586],{},[1151,23365,1158],{},[1151,23367,2437],{},[1342,23369,1884],{},[2431,23371,23372,23374],{},[1151,23373,11507],{},[1148,23375,23376,23378,23380],{},[1151,23377,1733],{},[1151,23379,1158],{},[1151,23381,2437],{},[1151,23383,18431],{"mathvariant":2444},[1886,23385,23386,23388],{},[1342,23387,1890],{},[1151,23389,1161],{},[2431,23391,23392,23394],{},[1151,23393,11507],{},[1148,23395,23396,23398,23400],{},[1151,23397,1733],{},[1151,23399,1161],{},[1151,23401,2437],{},[1166,23403,23404],{"encoding":1168},"a^L_j = e^{z^L_j}\u002F\\sum_k e^{z^L_k}",[1129,23406,23408,23474],{"className":23407,"ariaHidden":1174},[1173],[1129,23409,23411,23414,23465,23468,23471],{"className":23410},[1178],[1129,23412],{"className":23413,"style":11421},[1182],[1129,23415,23417,23420],{"className":23416},[1187],[1129,23418,1586],{"className":23419},[1187,1191],[1129,23421,23423],{"className":23422},[1196],[1129,23424,23426,23457],{"className":23425},[1200,1201],[1129,23427,23429,23454],{"className":23428},[1205],[1129,23430,23432,23443],{"className":23431,"style":2488},[1209],[1129,23433,23434,23437],{"style":1474},[1129,23435],{"className":23436,"style":1218},[1217],[1129,23438,23440],{"className":23439},[1222,1223,1224,1225],[1129,23441,1158],{"className":23442,"style":1232},[1187,1191,1225],[1129,23444,23445,23448],{"style":1239},[1129,23446],{"className":23447,"style":1218},[1217],[1129,23449,23451],{"className":23450},[1222,1223,1224,1225],[1129,23452,2437],{"className":23453},[1187,1191,1225],[1129,23455,1254],{"className":23456},[1253],[1129,23458,23460],{"className":23459},[1205],[1129,23461,23463],{"className":23462,"style":1504},[1209],[1129,23464],{},[1129,23466],{"className":23467,"style":1996},[1368],[1129,23469,1884],{"className":23470},[2000],[1129,23472],{"className":23473,"style":1996},[1368],[1129,23475,23477,23481,23561,23564,23567,23607,23610],{"className":23476},[1178],[1129,23478],{"className":23479,"style":23480},[1182],"height:1.3482em;vertical-align:-0.2997em;",[1129,23482,23484,23487],{"className":23483},[1187],[1129,23485,11507],{"className":23486},[1187,1191],[1129,23488,23490],{"className":23489},[1196],[1129,23491,23493],{"className":23492},[1200],[1129,23494,23496],{"className":23495},[1205],[1129,23497,23499],{"className":23498,"style":12917},[1209],[1129,23500,23501,23504],{"style":12938},[1129,23502],{"className":23503,"style":1218},[1217],[1129,23505,23507],{"className":23506},[1222,1223,1224,1225],[1129,23508,23510],{"className":23509},[1187,1225],[1129,23511,23513,23516],{"className":23512},[1187,1225],[1129,23514,1733],{"className":23515,"style":1756},[1187,1191,1225],[1129,23517,23519],{"className":23518},[1196],[1129,23520,23522,23553],{"className":23521},[1200,1201],[1129,23523,23525,23550],{"className":23524},[1205],[1129,23526,23528,23539],{"className":23527,"style":12535},[1209],[1129,23529,23530,23533],{"style":12538},[1129,23531],{"className":23532,"style":3124},[1217],[1129,23534,23536],{"className":23535},[1222,3128,3129,1225],[1129,23537,1158],{"className":23538,"style":1232},[1187,1191,1225],[1129,23540,23541,23544],{"style":12550},[1129,23542],{"className":23543,"style":3124},[1217],[1129,23545,23547],{"className":23546},[1222,3128,3129,1225],[1129,23548,2437],{"className":23549},[1187,1191,1225],[1129,23551,1254],{"className":23552},[1253],[1129,23554,23556],{"className":23555},[1205],[1129,23557,23559],{"className":23558,"style":12997},[1209],[1129,23560],{},[1129,23562,18431],{"className":23563},[1187],[1129,23565],{"className":23566,"style":2061},[1368],[1129,23568,23570,23573],{"className":23569},[2014],[1129,23571,1890],{"className":23572,"style":2020},[2014,2018,2019],[1129,23574,23576],{"className":23575},[1196],[1129,23577,23579,23599],{"className":23578},[1200,1201],[1129,23580,23582,23596],{"className":23581},[1205],[1129,23583,23585],{"className":23584,"style":2033},[1209],[1129,23586,23587,23590],{"style":2036},[1129,23588],{"className":23589,"style":1218},[1217],[1129,23591,23593],{"className":23592},[1222,1223,1224,1225],[1129,23594,1161],{"className":23595,"style":1236},[1187,1191,1225],[1129,23597,1254],{"className":23598},[1253],[1129,23600,23602],{"className":23601},[1205],[1129,23603,23605],{"className":23604,"style":2055},[1209],[1129,23606],{},[1129,23608],{"className":23609,"style":2061},[1368],[1129,23611,23613,23616],{"className":23612},[1187],[1129,23614,11507],{"className":23615},[1187,1191],[1129,23617,23619],{"className":23618},[1196],[1129,23620,23622],{"className":23621},[1200],[1129,23623,23625],{"className":23624},[1205],[1129,23626,23628],{"className":23627,"style":12505},[1209],[1129,23629,23630,23633],{"style":1239},[1129,23631],{"className":23632,"style":1218},[1217],[1129,23634,23636],{"className":23635},[1222,1223,1224,1225],[1129,23637,23639],{"className":23638},[1187,1225],[1129,23640,23642,23645],{"className":23641},[1187,1225],[1129,23643,1733],{"className":23644,"style":1756},[1187,1191,1225],[1129,23646,23648],{"className":23647},[1196],[1129,23649,23651,23682],{"className":23650},[1200,1201],[1129,23652,23654,23679],{"className":23653},[1205],[1129,23655,23657,23668],{"className":23656,"style":12535},[1209],[1129,23658,23659,23662],{"style":12538},[1129,23660],{"className":23661,"style":3124},[1217],[1129,23663,23665],{"className":23664},[1222,3128,3129,1225],[1129,23666,1161],{"className":23667,"style":1236},[1187,1191,1225],[1129,23669,23670,23673],{"style":12550},[1129,23671],{"className":23672,"style":3124},[1217],[1129,23674,23676],{"className":23675},[1222,3128,3129,1225],[1129,23677,2437],{"className":23678},[1187,1191,1225],[1129,23680,1254],{"className":23681},[1253],[1129,23683,23685],{"className":23684},[1205],[1129,23686,23688],{"className":23687,"style":12569},[1209],[1129,23689],{},"，对数似然：",[1129,23692,23694,23724],{"className":23693},[1132],[1129,23695,23697],{"className":23696},[1136],[1138,23698,23699],{"xmlns":1140},[1142,23700,23701,23721],{},[1145,23702,23703,23705,23707,23709,23711,23713],{},[1151,23704,2450],{},[1342,23706,1884],{},[1342,23708,1344],{},[1151,23710,6649],{},[1342,23712,6652],{},[1148,23714,23715,23717,23719],{},[1151,23716,1586],{},[1151,23718,6646],{},[1151,23720,2437],{},[1166,23722,23723],{"encoding":1168},"C=-\\ln a^L_y",[1129,23725,23727,23745],{"className":23726,"ariaHidden":1174},[1173],[1129,23728,23730,23733,23736,23739,23742],{"className":23729},[1178],[1129,23731],{"className":23732,"style":5901},[1182],[1129,23734,2450],{"className":23735,"style":2580},[1187,1191],[1129,23737],{"className":23738,"style":1996},[1368],[1129,23740,1884],{"className":23741},[2000],[1129,23743],{"className":23744,"style":1996},[1368],[1129,23746,23748,23751,23754,23757,23760,23763],{"className":23747},[1178],[1129,23749],{"className":23750,"style":13287},[1182],[1129,23752,1344],{"className":23753},[1187],[1129,23755],{"className":23756,"style":2061},[1368],[1129,23758,6649],{"className":23759},[2014],[1129,23761],{"className":23762,"style":2061},[1368],[1129,23764,23766,23769],{"className":23765},[1187],[1129,23767,1586],{"className":23768},[1187,1191],[1129,23770,23772],{"className":23771},[1196],[1129,23773,23775,23806],{"className":23774},[1200,1201],[1129,23776,23778,23803],{"className":23777},[1205],[1129,23779,23781,23792],{"className":23780,"style":2488},[1209],[1129,23782,23783,23786],{"style":13320},[1129,23784],{"className":23785,"style":1218},[1217],[1129,23787,23789],{"className":23788},[1222,1223,1224,1225],[1129,23790,6646],{"className":23791,"style":2603},[1187,1191,1225],[1129,23793,23794,23797],{"style":1239},[1129,23795],{"className":23796,"style":1218},[1217],[1129,23798,23800],{"className":23799},[1222,1223,1224,1225],[1129,23801,2437],{"className":23802},[1187,1191,1225],[1129,23804,1254],{"className":23805},[1253],[1129,23807,23809],{"className":23808},[1205],[1129,23810,23812],{"className":23811,"style":13350},[1209],[1129,23813],{},[2412,23815,23816,2417,23818,24054,24055],{},[2405,23817,16888],{},[1129,23819,23821,23863],{"className":23820},[1132],[1129,23822,23824],{"className":23823},[1136],[1138,23825,23826],{"xmlns":1140},[1142,23827,23828,23860],{},[1145,23829,23830,23832,23834,23840,23842,23852,23854],{},[1151,23831,2450],{},[1342,23833,1884],{},[1886,23835,23836,23838],{},[1151,23837,2450],{},[1346,23839,6526],{},[1342,23841,1921],{},[3018,23843,23844,23846],{},[1151,23845,15151],{},[1145,23847,23848,23850],{},[1346,23849,3724],{},[1151,23851,6632],{},[1342,23853,1890],{},[2431,23855,23856,23858],{},[1151,23857,1153],{},[1346,23859,3724],{},[1166,23861,23862],{"encoding":1168},"C = C_0 + \\frac{\\lambda}{2n}\\sum w^2",[1129,23864,23866,23884,23939],{"className":23865,"ariaHidden":1174},[1173],[1129,23867,23869,23872,23875,23878,23881],{"className":23868},[1178],[1129,23870],{"className":23871,"style":5901},[1182],[1129,23873,2450],{"className":23874,"style":2580},[1187,1191],[1129,23876],{"className":23877,"style":1996},[1368],[1129,23879,1884],{"className":23880},[2000],[1129,23882],{"className":23883,"style":1996},[1368],[1129,23885,23887,23890,23930,23933,23936],{"className":23886},[1178],[1129,23888],{"className":23889,"style":2533},[1182],[1129,23891,23893,23896],{"className":23892},[1187],[1129,23894,2450],{"className":23895,"style":2580},[1187,1191],[1129,23897,23899],{"className":23898},[1196],[1129,23900,23902,23922],{"className":23901},[1200,1201],[1129,23903,23905,23919],{"className":23904},[1205],[1129,23906,23908],{"className":23907,"style":15215},[1209],[1129,23909,23910,23913],{"style":15218},[1129,23911],{"className":23912,"style":1218},[1217],[1129,23914,23916],{"className":23915},[1222,1223,1224,1225],[1129,23917,6526],{"className":23918},[1187,1225],[1129,23920,1254],{"className":23921},[1253],[1129,23923,23925],{"className":23924},[1205],[1129,23926,23928],{"className":23927,"style":2574},[1209],[1129,23929],{},[1129,23931],{"className":23932,"style":1369},[1368],[1129,23934,1921],{"className":23935},[1373],[1129,23937],{"className":23938,"style":1369},[1368],[1129,23940,23942,23945,24016,24019,24022,24025],{"className":23941},[1178],[1129,23943],{"className":23944,"style":9888},[1182],[1129,23946,23948,23951,24013],{"className":23947},[1187],[1129,23949],{"className":23950},[2634,3068],[1129,23952,23954],{"className":23953},[3018],[1129,23955,23957,24005],{"className":23956},[1200,1201],[1129,23958,23960,24002],{"className":23959},[1205],[1129,23961,23963,23980,23988],{"className":23962,"style":3081},[1209],[1129,23964,23965,23968],{"style":6739},[1129,23966],{"className":23967,"style":3088},[1217],[1129,23969,23971],{"className":23970},[1222,1223,1224,1225],[1129,23972,23974,23977],{"className":23973},[1187,1225],[1129,23975,3724],{"className":23976},[1187,1225],[1129,23978,6632],{"className":23979},[1187,1191,1225],[1129,23981,23982,23985],{"style":3159},[1129,23983],{"className":23984,"style":3088},[1217],[1129,23986],{"className":23987,"style":3167},[3166],[1129,23989,23990,23993],{"style":3170},[1129,23991],{"className":23992,"style":3088},[1217],[1129,23994,23996],{"className":23995},[1222,1223,1224,1225],[1129,23997,23999],{"className":23998},[1187,1225],[1129,24000,15151],{"className":24001},[1187,1191,1225],[1129,24003,1254],{"className":24004},[1253],[1129,24006,24008],{"className":24007},[1205],[1129,24009,24011],{"className":24010,"style":6783},[1209],[1129,24012],{},[1129,24014],{"className":24015},[2667,3068],[1129,24017],{"className":24018,"style":2061},[1368],[1129,24020,1890],{"className":24021,"style":2020},[2014,2018,2019],[1129,24023],{"className":24024,"style":2061},[1368],[1129,24026,24028,24031],{"className":24027},[1187],[1129,24029,1153],{"className":24030,"style":1192},[1187,1191],[1129,24032,24034],{"className":24033},[1196],[1129,24035,24037],{"className":24036},[1200],[1129,24038,24040],{"className":24039},[1205],[1129,24041,24043],{"className":24042,"style":3651},[1209],[1129,24044,24045,24048],{"style":1239},[1129,24046],{"className":24047,"style":1218},[1217],[1129,24049,24051],{"className":24050},[1222,1223,1224,1225],[1129,24052,3724],{"className":24053},[1187,1225],"，更新：",[1129,24056,24058,24116],{"className":24057},[1132],[1129,24059,24061],{"className":24060},[1136],[1138,24062,24063],{"xmlns":1140},[1142,24064,24065,24113],{},[1145,24066,24067,24069,24071,24073,24075,24077,24079,24089,24091,24093,24095],{},[1151,24068,1153],{},[1342,24070,15526],{},[1151,24072,1153],{},[1342,24074,2466],{"stretchy":2465},[1346,24076,1348],{},[1342,24078,1344],{},[3018,24080,24081,24087],{},[1145,24082,24083,24085],{},[1151,24084,15537],{},[1151,24086,15151],{},[1151,24088,6632],{},[1342,24090,2475],{"stretchy":2465},[1342,24092,1344],{},[1151,24094,15537],{},[3018,24096,24097,24107],{},[1145,24098,24099,24101],{},[1151,24100,3024],{"mathvariant":2444},[1886,24102,24103,24105],{},[1151,24104,2450],{},[1346,24106,6526],{},[1145,24108,24109,24111],{},[1151,24110,3024],{"mathvariant":2444},[1151,24112,1153],{},[1166,24114,24115],{"encoding":1168},"w \\to w(1-\\frac{\\eta\\lambda}{n}) - \\eta\\frac{\\partial C_0}{\\partial w}",[1129,24117,24119,24137,24161,24250],{"className":24118,"ariaHidden":1174},[1173],[1129,24120,24122,24125,24128,24131,24134],{"className":24121},[1178],[1129,24123],{"className":24124,"style":3696},[1182],[1129,24126,1153],{"className":24127,"style":1192},[1187,1191],[1129,24129],{"className":24130,"style":1996},[1368],[1129,24132,15526],{"className":24133},[2000],[1129,24135],{"className":24136,"style":1996},[1368],[1129,24138,24140,24143,24146,24149,24152,24155,24158],{"className":24139},[1178],[1129,24141],{"className":24142,"style":6081},[1182],[1129,24144,1153],{"className":24145,"style":1192},[1187,1191],[1129,24147,2466],{"className":24148},[2634],[1129,24150,1348],{"className":24151},[1187],[1129,24153],{"className":24154,"style":1369},[1368],[1129,24156,1344],{"className":24157},[1373],[1129,24159],{"className":24160,"style":1369},[1368],[1129,24162,24164,24167,24238,24241,24244,24247],{"className":24163},[1178],[1129,24165],{"className":24166,"style":15622},[1182],[1129,24168,24170,24173,24235],{"className":24169},[1187],[1129,24171],{"className":24172},[2634,3068],[1129,24174,24176],{"className":24175},[3018],[1129,24177,24179,24227],{"className":24178},[1200,1201],[1129,24180,24182,24224],{"className":24181},[1205],[1129,24183,24185,24199,24207],{"className":24184,"style":15641},[1209],[1129,24186,24187,24190],{"style":6739},[1129,24188],{"className":24189,"style":3088},[1217],[1129,24191,24193],{"className":24192},[1222,1223,1224,1225],[1129,24194,24196],{"className":24195},[1187,1225],[1129,24197,6632],{"className":24198},[1187,1191,1225],[1129,24200,24201,24204],{"style":3159},[1129,24202],{"className":24203,"style":3088},[1217],[1129,24205],{"className":24206,"style":3167},[3166],[1129,24208,24209,24212],{"style":8212},[1129,24210],{"className":24211,"style":3088},[1217],[1129,24213,24215],{"className":24214},[1222,1223,1224,1225],[1129,24216,24218,24221],{"className":24217},[1187,1225],[1129,24219,15537],{"className":24220,"style":2603},[1187,1191,1225],[1129,24222,15151],{"className":24223},[1187,1191,1225],[1129,24225,1254],{"className":24226},[1253],[1129,24228,24230],{"className":24229},[1205],[1129,24231,24233],{"className":24232,"style":6783},[1209],[1129,24234],{},[1129,24236],{"className":24237},[2667,3068],[1129,24239,2475],{"className":24240},[2667],[1129,24242],{"className":24243,"style":1369},[1368],[1129,24245,1344],{"className":24246},[1373],[1129,24248],{"className":24249,"style":1369},[1368],[1129,24251,24253,24256,24259],{"className":24252},[1178],[1129,24254],{"className":24255,"style":15725},[1182],[1129,24257,15537],{"className":24258,"style":2603},[1187,1191],[1129,24260,24262,24265,24367],{"className":24261},[1187],[1129,24263],{"className":24264},[2634,3068],[1129,24266,24268],{"className":24267},[3018],[1129,24269,24271,24359],{"className":24270},[1200,1201],[1129,24272,24274,24356],{"className":24273},[1205],[1129,24275,24277,24294,24302],{"className":24276,"style":15747},[1209],[1129,24278,24279,24282],{"style":6739},[1129,24280],{"className":24281,"style":3088},[1217],[1129,24283,24285],{"className":24284},[1222,1223,1224,1225],[1129,24286,24288,24291],{"className":24287},[1187,1225],[1129,24289,3024],{"className":24290,"style":3098},[1187,1225],[1129,24292,1153],{"className":24293,"style":1192},[1187,1191,1225],[1129,24295,24296,24299],{"style":3159},[1129,24297],{"className":24298,"style":3088},[1217],[1129,24300],{"className":24301,"style":3167},[3166],[1129,24303,24304,24307],{"style":15775},[1129,24305],{"className":24306,"style":3088},[1217],[1129,24308,24310],{"className":24309},[1222,1223,1224,1225],[1129,24311,24313,24316],{"className":24312},[1187,1225],[1129,24314,3024],{"className":24315,"style":3098},[1187,1225],[1129,24317,24319,24322],{"className":24318},[1187,1225],[1129,24320,2450],{"className":24321,"style":2580},[1187,1191,1225],[1129,24323,24325],{"className":24324},[1196],[1129,24326,24328,24348],{"className":24327},[1200,1201],[1129,24329,24331,24345],{"className":24330},[1205],[1129,24332,24334],{"className":24333,"style":15806},[1209],[1129,24335,24336,24339],{"style":15809},[1129,24337],{"className":24338,"style":3124},[1217],[1129,24340,24342],{"className":24341},[1222,3128,3129,1225],[1129,24343,6526],{"className":24344},[1187,1225],[1129,24346,1254],{"className":24347},[1253],[1129,24349,24351],{"className":24350},[1205],[1129,24352,24354],{"className":24353,"style":15828},[1209],[1129,24355],{},[1129,24357,1254],{"className":24358},[1253],[1129,24360,24362],{"className":24361},[1205],[1129,24363,24365],{"className":24364,"style":6783},[1209],[1129,24366],{},[1129,24368],{"className":24369},[2667,3068],[2412,24371,24372,2417,24374,24054,24583],{},[2405,24373,16885],{},[1129,24375,24377,24415],{"className":24376},[1132],[1129,24378,24380],{"className":24379},[1136],[1138,24381,24382],{"xmlns":1140},[1142,24383,24384,24412],{},[1145,24385,24386,24388,24390,24396,24398,24404,24406,24408,24410],{},[1151,24387,2450],{},[1342,24389,1884],{},[1886,24391,24392,24394],{},[1151,24393,2450],{},[1346,24395,6526],{},[1342,24397,1921],{},[3018,24399,24400,24402],{},[1151,24401,15151],{},[1151,24403,6632],{},[1342,24405,1890],{},[1151,24407,15162],{"mathvariant":2444},[1151,24409,1153],{},[1151,24411,15162],{"mathvariant":2444},[1166,24413,24414],{"encoding":1168},"C = C_0 + \\frac{\\lambda}{n}\\sum|w|",[1129,24416,24418,24436,24491],{"className":24417,"ariaHidden":1174},[1173],[1129,24419,24421,24424,24427,24430,24433],{"className":24420},[1178],[1129,24422],{"className":24423,"style":5901},[1182],[1129,24425,2450],{"className":24426,"style":2580},[1187,1191],[1129,24428],{"className":24429,"style":1996},[1368],[1129,24431,1884],{"className":24432},[2000],[1129,24434],{"className":24435,"style":1996},[1368],[1129,24437,24439,24442,24482,24485,24488],{"className":24438},[1178],[1129,24440],{"className":24441,"style":2533},[1182],[1129,24443,24445,24448],{"className":24444},[1187],[1129,24446,2450],{"className":24447,"style":2580},[1187,1191],[1129,24449,24451],{"className":24450},[1196],[1129,24452,24454,24474],{"className":24453},[1200,1201],[1129,24455,24457,24471],{"className":24456},[1205],[1129,24458,24460],{"className":24459,"style":15215},[1209],[1129,24461,24462,24465],{"style":15218},[1129,24463],{"className":24464,"style":1218},[1217],[1129,24466,24468],{"className":24467},[1222,1223,1224,1225],[1129,24469,6526],{"className":24470},[1187,1225],[1129,24472,1254],{"className":24473},[1253],[1129,24475,24477],{"className":24476},[1205],[1129,24478,24480],{"className":24479,"style":2574},[1209],[1129,24481],{},[1129,24483],{"className":24484,"style":1369},[1368],[1129,24486,1921],{"className":24487},[1373],[1129,24489],{"className":24490,"style":1369},[1368],[1129,24492,24494,24497,24565,24568,24571,24574,24577,24580],{"className":24493},[1178],[1129,24495],{"className":24496,"style":9888},[1182],[1129,24498,24500,24503,24562],{"className":24499},[1187],[1129,24501],{"className":24502},[2634,3068],[1129,24504,24506],{"className":24505},[3018],[1129,24507,24509,24554],{"className":24508},[1200,1201],[1129,24510,24512,24551],{"className":24511},[1205],[1129,24513,24515,24529,24537],{"className":24514,"style":3081},[1209],[1129,24516,24517,24520],{"style":6739},[1129,24518],{"className":24519,"style":3088},[1217],[1129,24521,24523],{"className":24522},[1222,1223,1224,1225],[1129,24524,24526],{"className":24525},[1187,1225],[1129,24527,6632],{"className":24528},[1187,1191,1225],[1129,24530,24531,24534],{"style":3159},[1129,24532],{"className":24533,"style":3088},[1217],[1129,24535],{"className":24536,"style":3167},[3166],[1129,24538,24539,24542],{"style":3170},[1129,24540],{"className":24541,"style":3088},[1217],[1129,24543,24545],{"className":24544},[1222,1223,1224,1225],[1129,24546,24548],{"className":24547},[1187,1225],[1129,24549,15151],{"className":24550},[1187,1191,1225],[1129,24552,1254],{"className":24553},[1253],[1129,24555,24557],{"className":24556},[1205],[1129,24558,24560],{"className":24559,"style":6783},[1209],[1129,24561],{},[1129,24563],{"className":24564},[2667,3068],[1129,24566],{"className":24567,"style":2061},[1368],[1129,24569,1890],{"className":24570,"style":2020},[2014,2018,2019],[1129,24572],{"className":24573,"style":2061},[1368],[1129,24575,15162],{"className":24576},[1187],[1129,24578,1153],{"className":24579,"style":1192},[1187,1191],[1129,24581,15162],{"className":24582},[1187],[1129,24584,24586,24646],{"className":24585},[1132],[1129,24587,24589],{"className":24588},[1136],[1138,24590,24591],{"xmlns":1140},[1142,24592,24593,24643],{},[1145,24594,24595,24597,24599,24601,24603,24613,24615,24617,24619,24621,24623,24625],{},[1151,24596,1153],{},[1342,24598,15526],{},[1151,24600,1153],{},[1342,24602,1344],{},[3018,24604,24605,24611],{},[1145,24606,24607,24609],{},[1151,24608,15537],{},[1151,24610,15151],{},[1151,24612,6632],{},[5470,24614,15544],{},[1342,24616,2466],{"stretchy":2465},[1151,24618,1153],{},[1342,24620,2475],{"stretchy":2465},[1342,24622,1344],{},[1151,24624,15537],{},[3018,24626,24627,24637],{},[1145,24628,24629,24631],{},[1151,24630,3024],{"mathvariant":2444},[1886,24632,24633,24635],{},[1151,24634,2450],{},[1346,24636,6526],{},[1145,24638,24639,24641],{},[1151,24640,3024],{"mathvariant":2444},[1151,24642,1153],{},[1166,24644,24645],{"encoding":1168},"w \\to w - \\frac{\\eta\\lambda}{n}\\text{sgn}(w) - \\eta\\frac{\\partial C_0}{\\partial 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