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f_\\theta(x)",[1095,1877,1879,1898],{"className":1878,"ariaHidden":1137},[1136],[1095,1880,1882,1886,1889,1892,1895],{"className":1881},[1141],[1095,1883],{"className":1884,"style":1885},[1145],"height:0.4306em;",[1095,1887,1352],{"className":1888,"style":1388},[1150,1151],[1095,1890],{"className":1891,"style":1542},[1383],[1095,1893,1463],{"className":1894},[1546],[1095,1896],{"className":1897,"style":1542},[1383],[1095,1899,1901,1904,1948,1951,1954],{"className":1900},[1141],[1095,1902],{"className":1903,"style":1146},[1145],[1095,1905,1907,1911],{"className":1906},[1150],[1095,1908,1863],{"className":1909,"style":1910},[1150,1151],"margin-right:0.1076em;",[1095,1912,1914],{"className":1913},[1570],[1095,1915,1917,1940],{"className":1916},[1574,1575],[1095,1918,1920,1937],{"className":1919},[1579],[1095,1921,1924],{"className":1922,"style":1923},[1583],"height:0.3361em;",[1095,1925,1927,1930],{"style":1926},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[1095,1928],{"className":1929,"style":1592},[1591],[1095,1931,1933],{"className":1932},[1596,1597,1598,1599],[1095,1934,1866],{"className":1935,"style":1936},[1150,1151,1599],"margin-right:0.0278em;",[1095,1938,1607],{"className":1939},[1606],[1095,1941,1943],{"className":1942},[1579],[1095,1944,1946],{"className":1945,"style":1666},[1583],[1095,1947],{},[1095,1949,1121],{"className":1950},[1156],[1095,1952,1124],{"className":1953},[1150,1151],[1095,1955,1127],{"className":1956},[1163],"，再通过解码器重建 ",[1095,1959,1961,1997],{"className":1960},[1098],[1095,1962,1964],{"className":1963},[1102],[1104,1965,1966],{"xmlns":1106},[1108,1967,1968,1994],{},[1111,1969,1970,1978,1980,1988,1990,1992],{},[1971,1972,1973,1975],"mover",{"accent":1137},[1114,1974,1124],{},[1118,1976,1977],{},"^",[1118,1979,1463],{},[1465,1981,1982,1985],{},[1114,1983,1984],{},"g",[1114,1986,1987],{},"ϕ",[1118,1989,1121],{"stretchy":1120},[1114,1991,1352],{},[1118,1993,1127],{"stretchy":1120},[1129,1995,1996],{"encoding":1131},"\\hat{x} = g_\\phi(z)",[1095,1998,2000,2052],{"className":1999,"ariaHidden":1137},[1136],[1095,2001,2003,2007,2043,2046,2049],{"className":2002},[1141],[1095,2004],{"className":2005,"style":2006},[1145],"height:0.6944em;",[1095,2008,2011],{"className":2009},[1150,2010],"accent",[1095,2012,2014],{"className":2013},[1574],[1095,2015,2017],{"className":2016},[1579],[1095,2018,2020,2030],{"className":2019,"style":2006},[1583],[1095,2021,2023,2027],{"style":2022},"top:-3em;",[1095,2024],{"className":2025,"style":2026},[1591],"height:3em;",[1095,2028,1124],{"className":2029},[1150,1151],[1095,2031,2032,2035],{"style":2022},[1095,2033],{"className":2034,"style":2026},[1591],[1095,2036,2040],{"className":2037,"style":2039},[2038],"accent-body","left:-0.2222em;",[1095,2041,1977],{"className":2042},[1150],[1095,2044],{"className":2045,"style":1542},[1383],[1095,2047,1463],{"className":2048},[1546],[1095,2050],{"className":2051,"style":1542},[1383],[1095,2053,2055,2059,2101,2104,2107],{"className":2054},[1141],[1095,2056],{"className":2057,"style":2058},[1145],"height:1.0361em;vertical-align:-0.2861em;",[1095,2060,2062,2065],{"className":2061},[1150],[1095,2063,1984],{"className":2064,"style":1256},[1150,1151],[1095,2066,2068],{"className":2067},[1570],[1095,2069,2071,2092],{"className":2070},[1574,1575],[1095,2072,2074,2089],{"className":2073},[1579],[1095,2075,2077],{"className":2076,"style":1923},[1583],[1095,2078,2080,2083],{"style":2079},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1095,2081],{"className":2082,"style":1592},[1591],[1095,2084,2086],{"className":2085},[1596,1597,1598,1599],[1095,2087,1987],{"className":2088},[1150,1151,1599],[1095,2090,1607],{"className":2091},[1606],[1095,2093,2095],{"className":2094},[1579],[1095,2096,2099],{"className":2097,"style":2098},[1583],"height:0.2861em;",[1095,2100],{},[1095,2102,1121],{"className":2103},[1156],[1095,2105,1352],{"className":2106,"style":1388},[1150,1151],[1095,2108,1127],{"className":2109},[1163],"。训练目标是最小化重建误差：",[1091,2112,2113],{},[1095,2114,2116,2181],{"className":2115},[1098],[1095,2117,2119],{"className":2118},[1102],[1104,2120,2121],{"xmlns":1106},[1108,2122,2123,2178],{},[1111,2124,2125,2139,2141,2144,2146,2148,2154,2156,2162,2164,2166,2168,2170],{},[1465,2126,2127,2131],{},[1114,2128,2130],{"mathvariant":2129},"script","L",[1111,2132,2133,2136],{},[1114,2134,2135],{},"A",[1114,2137,2138],{},"E",[1118,2140,1463],{},[1114,2142,2143],{"mathvariant":1229},"∥",[1114,2145,1124],{},[1118,2147,1510],{},[1465,2149,2150,2152],{},[1114,2151,1984],{},[1114,2153,1987],{},[1118,2155,1121],{"stretchy":1120},[1465,2157,2158,2160],{},[1114,2159,1863],{},[1114,2161,1866],{},[1118,2163,1121],{"stretchy":1120},[1114,2165,1124],{},[1118,2167,1127],{"stretchy":1120},[1118,2169,1127],{"stretchy":1120},[2171,2172,2173,2175],"msup",{},[1114,2174,2143],{"mathvariant":1229},[1490,2176,2177],{},"2",[1129,2179,2180],{"encoding":1131},"\\mathcal{L}_{AE} = \\|x - g_\\phi(f_\\theta(x))\\|^2",[1095,2182,2184,2249,2271],{"className":2183,"ariaHidden":1137},[1136],[1095,2185,2187,2191,2240,2243,2246],{"className":2186},[1141],[1095,2188],{"className":2189,"style":2190},[1145],"height:0.8333em;vertical-align:-0.15em;",[1095,2192,2194,2198],{"className":2193},[1150],[1095,2195,2130],{"className":2196},[1150,2197],"mathcal",[1095,2199,2201],{"className":2200},[1570],[1095,2202,2204,2232],{"className":2203},[1574,1575],[1095,2205,2207,2229],{"className":2206},[1579],[1095,2208,2211],{"className":2209,"style":2210},[1583],"height:0.3283em;",[1095,2212,2213,2216],{"style":1647},[1095,2214],{"className":2215,"style":1592},[1591],[1095,2217,2219],{"className":2218},[1596,1597,1598,1599],[1095,2220,2222,2225],{"className":2221},[1150,1599],[1095,2223,2135],{"className":2224},[1150,1151,1599],[1095,2226,2138],{"className":2227,"style":2228},[1150,1151,1599],"margin-right:0.0576em;",[1095,2230,1607],{"className":2231},[1606],[1095,2233,2235],{"className":2234},[1579],[1095,2236,2238],{"className":2237,"style":1666},[1583],[1095,2239],{},[1095,2241],{"className":2242,"style":1542},[1383],[1095,2244,1463],{"className":2245},[1546],[1095,2247],{"className":2248,"style":1542},[1383],[1095,2250,2252,2255,2258,2261,2265,2268],{"className":2251},[1141],[1095,2253],{"className":2254,"style":1146},[1145],[1095,2256,2143],{"className":2257},[1150],[1095,2259,1124],{"className":2260},[1150,1151],[1095,2262],{"className":2263,"style":2264},[1383],"margin-right:0.2222em;",[1095,2266,1510],{"className":2267},[1779],[1095,2269],{"className":2270,"style":2264},[1383],[1095,2272,2274,2278,2318,2321,2361,2364,2367,2371],{"className":2273},[1141],[1095,2275],{"className":2276,"style":2277},[1145],"height:1.1002em;vertical-align:-0.2861em;",[1095,2279,2281,2284],{"className":2280},[1150],[1095,2282,1984],{"className":2283,"style":1256},[1150,1151],[1095,2285,2287],{"className":2286},[1570],[1095,2288,2290,2310],{"className":2289},[1574,1575],[1095,2291,2293,2307],{"className":2292},[1579],[1095,2294,2296],{"className":2295,"style":1923},[1583],[1095,2297,2298,2301],{"style":2079},[1095,2299],{"className":2300,"style":1592},[1591],[1095,2302,2304],{"className":2303},[1596,1597,1598,1599],[1095,2305,1987],{"className":2306},[1150,1151,1599],[1095,2308,1607],{"className":2309},[1606],[1095,2311,2313],{"className":2312},[1579],[1095,2314,2316],{"className":2315,"style":2098},[1583],[1095,2317],{},[1095,2319,1121],{"className":2320},[1156],[1095,2322,2324,2327],{"className":2323},[1150],[1095,2325,1863],{"className":2326,"style":1910},[1150,1151],[1095,2328,2330],{"className":2329},[1570],[1095,2331,2333,2353],{"className":2332},[1574,1575],[1095,2334,2336,2350],{"className":2335},[1579],[1095,2337,2339],{"className":2338,"style":1923},[1583],[1095,2340,2341,2344],{"style":1926},[1095,2342],{"className":2343,"style":1592},[1591],[1095,2345,2347],{"className":2346},[1596,1597,1598,1599],[1095,2348,1866],{"className":2349,"style":1936},[1150,1151,1599],[1095,2351,1607],{"className":2352},[1606],[1095,2354,2356],{"className":2355},[1579],[1095,2357,2359],{"className":2358,"style":1666},[1583],[1095,2360],{},[1095,2362,1121],{"className":2363},[1156],[1095,2365,1124],{"className":2366},[1150,1151],[1095,2368,2370],{"className":2369},[1163],"))",[1095,2372,2374,2377],{"className":2373},[1150],[1095,2375,2143],{"className":2376},[1150],[1095,2378,2380],{"className":2379},[1570],[1095,2381,2383],{"className":2382},[1574],[1095,2384,2386],{"className":2385},[1579],[1095,2387,2390],{"className":2388,"style":2389},[1583],"height:0.8141em;",[1095,2391,2393,2396],{"style":2392},"top:-3.063em;margin-right:0.05em;",[1095,2394],{"className":2395,"style":1592},[1591],[1095,2397,2399],{"className":2398},[1596,1597,1598,1599],[1095,2400,2177],{"className":2401},[1150,1599],[1091,2403,2404],{},[1172,2405,2406],{},"传统自编码器的问题",[1166,2408,2409,2412,2415],{},[1169,2410,2411],{},"隐空间缺乏结构：不同样本的编码可能不连续、不规整",[1169,2413,2414],{},"无法从隐空间随机采样生成有意义的新样本",[1169,2416,2417],{},"没有概率解释，不是真正的生成模型",[1194,2419,2421],{"id":2420},"_22-vae-的核心思想","2.2 VAE 的核心思想",[1091,2423,2424,2425,2428,2429,2460,2461,2521,2522,2550],{},"VAE 的关键创新：",[1172,2426,2427],{},"不再将输入编码为确定性的点，而是编码为一个概率分布","。编码器输出隐变量的均值 ",[1095,2430,2432,2447],{"className":2431},[1098],[1095,2433,2435],{"className":2434},[1102],[1104,2436,2437],{"xmlns":1106},[1108,2438,2439,2444],{},[1111,2440,2441],{},[1114,2442,2443],{},"μ",[1129,2445,2446],{"encoding":1131},"\\mu",[1095,2448,2450],{"className":2449,"ariaHidden":1137},[1136],[1095,2451,2453,2457],{"className":2452},[1141],[1095,2454],{"className":2455,"style":2456},[1145],"height:0.625em;vertical-align:-0.1944em;",[1095,2458,2443],{"className":2459},[1150,1151]," 和方差 ",[1095,2462,2464,2483],{"className":2463},[1098],[1095,2465,2467],{"className":2466},[1102],[1104,2468,2469],{"xmlns":1106},[1108,2470,2471,2480],{},[1111,2472,2473],{},[2171,2474,2475,2478],{},[1114,2476,2477],{},"σ",[1490,2479,2177],{},[1129,2481,2482],{"encoding":1131},"\\sigma^2",[1095,2484,2486],{"className":2485,"ariaHidden":1137},[1136],[1095,2487,2489,2492],{"className":2488},[1141],[1095,2490],{"className":2491,"style":2389},[1145],[1095,2493,2495,2498],{"className":2494},[1150],[1095,2496,2477],{"className":2497,"style":1256},[1150,1151],[1095,2499,2501],{"className":2500},[1570],[1095,2502,2504],{"className":2503},[1574],[1095,2505,2507],{"className":2506},[1579],[1095,2508,2510],{"className":2509,"style":2389},[1583],[1095,2511,2512,2515],{"style":2392},[1095,2513],{"className":2514,"style":1592},[1591],[1095,2516,2518],{"className":2517},[1596,1597,1598,1599],[1095,2519,2177],{"className":2520},[1150,1599],"，从该分布中采样得到 ",[1095,2523,2525,2538],{"className":2524},[1098],[1095,2526,2528],{"className":2527},[1102],[1104,2529,2530],{"xmlns":1106},[1108,2531,2532,2536],{},[1111,2533,2534],{},[1114,2535,1352],{},[1129,2537,1352],{"encoding":1131},[1095,2539,2541],{"className":2540,"ariaHidden":1137},[1136],[1095,2542,2544,2547],{"className":2543},[1141],[1095,2545],{"className":2546,"style":1885},[1145],[1095,2548,1352],{"className":2549,"style":1388},[1150,1151],"。",[1194,2552,2554],{"id":2553},"_23-数学框架","2.3 数学框架",[2556,2557,2559],"h3",{"id":2558},"_231-生成模型假设","2.3.1 生成模型假设",[1091,2561,2562],{},"假设数据由如下过程生成：",[2564,2565,2566,2691],"ol",{},[1169,2567,2568,2569],{},"从先验分布采样隐变量：",[1095,2570,2572,2614],{"className":2571},[1098],[1095,2573,2575],{"className":2574},[1102],[1104,2576,2577],{"xmlns":1106},[1108,2578,2579,2611],{},[1111,2580,2581,2583,2586,2588,2590,2592,2594,2596,2599,2601,2604,2606,2609],{},[1114,2582,1352],{},[1118,2584,2585],{},"∼",[1114,2587,1091],{},[1118,2589,1121],{"stretchy":1120},[1114,2591,1352],{},[1118,2593,1127],{"stretchy":1120},[1118,2595,1463],{},[1114,2597,2598],{"mathvariant":2129},"N",[1118,2600,1121],{"stretchy":1120},[1490,2602,2603],{},"0",[1118,2605,1349],{"separator":1137},[1114,2607,2608],{},"I",[1118,2610,1127],{"stretchy":1120},[1129,2612,2613],{"encoding":1131},"z \\sim p(z) = \\mathcal{N}(0, I)",[1095,2615,2617,2635,2662],{"className":2616,"ariaHidden":1137},[1136],[1095,2618,2620,2623,2626,2629,2632],{"className":2619},[1141],[1095,2621],{"className":2622,"style":1885},[1145],[1095,2624,1352],{"className":2625,"style":1388},[1150,1151],[1095,2627],{"className":2628,"style":1542},[1383],[1095,2630,2585],{"className":2631},[1546],[1095,2633],{"className":2634,"style":1542},[1383],[1095,2636,2638,2641,2644,2647,2650,2653,2656,2659],{"className":2637},[1141],[1095,2639],{"className":2640,"style":1146},[1145],[1095,2642,1091],{"className":2643},[1150,1151],[1095,2645,1121],{"className":2646},[1156],[1095,2648,1352],{"className":2649,"style":1388},[1150,1151],[1095,2651,1127],{"className":2652},[1163],[1095,2654],{"className":2655,"style":1542},[1383],[1095,2657,1463],{"className":2658},[1546],[1095,2660],{"className":2661,"style":1542},[1383],[1095,2663,2665,2668,2672,2675,2678,2681,2684,2688],{"className":2664},[1141],[1095,2666],{"className":2667,"style":1146},[1145],[1095,2669,2598],{"className":2670,"style":2671},[1150,2197],"margin-right:0.1474em;",[1095,2673,1121],{"className":2674},[1156],[1095,2676,2603],{"className":2677},[1150],[1095,2679,1349],{"className":2680},[1379],[1095,2682],{"className":2683,"style":1384},[1383],[1095,2685,2608],{"className":2686,"style":2687},[1150,1151],"margin-right:0.0785em;",[1095,2689,1127],{"className":2690},[1163],[1169,2692,2693,2694],{},"由隐变量生成观测数据：",[1095,2695,2697,2729],{"className":2696},[1098],[1095,2698,2700],{"className":2699},[1102],[1104,2701,2702],{"xmlns":1106},[1108,2703,2704,2726],{},[1111,2705,2706,2708,2710,2716,2718,2720,2722,2724],{},[1114,2707,1124],{},[1118,2709,2585],{},[1465,2711,2712,2714],{},[1114,2713,1091],{},[1114,2715,1866],{},[1118,2717,1121],{"stretchy":1120},[1114,2719,1124],{},[1114,2721,1230],{"mathvariant":1229},[1114,2723,1352],{},[1118,2725,1127],{"stretchy":1120},[1129,2727,2728],{"encoding":1131},"x \\sim p_\\theta(x|z)",[1095,2730,2732,2750],{"className":2731,"ariaHidden":1137},[1136],[1095,2733,2735,2738,2741,2744,2747],{"className":2734},[1141],[1095,2736],{"className":2737,"style":1885},[1145],[1095,2739,1124],{"className":2740},[1150,1151],[1095,2742],{"className":2743,"style":1542},[1383],[1095,2745,2585],{"className":2746},[1546],[1095,2748],{"className":2749,"style":1542},[1383],[1095,2751,2753,2756,2796,2799,2802,2805,2808],{"className":2752},[1141],[1095,2754],{"className":2755,"style":1146},[1145],[1095,2757,2759,2762],{"className":2758},[1150],[1095,2760,1091],{"className":2761},[1150,1151],[1095,2763,2765],{"className":2764},[1570],[1095,2766,2768,2788],{"className":2767},[1574,1575],[1095,2769,2771,2785],{"className":2770},[1579],[1095,2772,2774],{"className":2773,"style":1923},[1583],[1095,2775,2776,2779],{"style":1647},[1095,2777],{"className":2778,"style":1592},[1591],[1095,2780,2782],{"className":2781},[1596,1597,1598,1599],[1095,2783,1866],{"className":2784,"style":1936},[1150,1151,1599],[1095,2786,1607],{"className":2787},[1606],[1095,2789,2791],{"className":2790},[1579],[1095,2792,2794],{"className":2793,"style":1666},[1583],[1095,2795],{},[1095,2797,1121],{"className":2798},[1156],[1095,2800,1124],{"className":2801},[1150,1151],[1095,2803,1230],{"className":2804},[1150],[1095,2806,1352],{"className":2807,"style":1388},[1150,1151],[1095,2809,1127],{"className":2810},[1163],[1091,2812,2813],{},"数据的边际似然为：",[1091,2815,2816],{},[1095,2817,2819,2881],{"className":2818},[1098],[1095,2820,2822],{"className":2821},[1102],[1104,2823,2824],{"xmlns":1106},[1108,2825,2826,2878],{},[1111,2827,2828,2834,2836,2838,2840,2842,2845,2851,2853,2855,2857,2859,2861,2863,2865,2867,2869,2873,2876],{},[1465,2829,2830,2832],{},[1114,2831,1091],{},[1114,2833,1866],{},[1118,2835,1121],{"stretchy":1120},[1114,2837,1124],{},[1118,2839,1127],{"stretchy":1120},[1118,2841,1463],{},[1118,2843,2844],{},"∫",[1465,2846,2847,2849],{},[1114,2848,1091],{},[1114,2850,1866],{},[1118,2852,1121],{"stretchy":1120},[1114,2854,1124],{},[1114,2856,1230],{"mathvariant":1229},[1114,2858,1352],{},[1118,2860,1127],{"stretchy":1120},[1114,2862,1091],{},[1118,2864,1121],{"stretchy":1120},[1114,2866,1352],{},[1118,2868,1127],{"stretchy":1120},[2870,2871,2872],"mtext",{}," ",[1114,2874,2875],{},"d",[1114,2877,1352],{},[1129,2879,2880],{"encoding":1131},"p_\\theta(x) = \\int p_\\theta(x|z) p(z) \\, dz",[1095,2882,2884,2948],{"className":2883,"ariaHidden":1137},[1136],[1095,2885,2887,2890,2930,2933,2936,2939,2942,2945],{"className":2886},[1141],[1095,2888],{"className":2889,"style":1146},[1145],[1095,2891,2893,2896],{"className":2892},[1150],[1095,2894,1091],{"className":2895},[1150,1151],[1095,2897,2899],{"className":2898},[1570],[1095,2900,2902,2922],{"className":2901},[1574,1575],[1095,2903,2905,2919],{"className":2904},[1579],[1095,2906,2908],{"className":2907,"style":1923},[1583],[1095,2909,2910,2913],{"style":1647},[1095,2911],{"className":2912,"style":1592},[1591],[1095,2914,2916],{"className":2915},[1596,1597,1598,1599],[1095,2917,1866],{"className":2918,"style":1936},[1150,1151,1599],[1095,2920,1607],{"className":2921},[1606],[1095,2923,2925],{"className":2924},[1579],[1095,2926,2928],{"className":2927,"style":1666},[1583],[1095,2929],{},[1095,2931,1121],{"className":2932},[1156],[1095,2934,1124],{"className":2935},[1150,1151],[1095,2937,1127],{"className":2938},[1163],[1095,2940],{"className":2941,"style":1542},[1383],[1095,2943,1463],{"className":2944},[1546],[1095,2946],{"className":2947,"style":1542},[1383],[1095,2949,2951,2955,2959,2962,3002,3005,3008,3011,3014,3017,3020,3023,3026,3029,3032,3035],{"className":2950},[1141],[1095,2952],{"className":2953,"style":2954},[1145],"height:1.1111em;vertical-align:-0.3061em;",[1095,2956,2844],{"className":2957,"style":2958},[1560,1564,1565],"margin-right:0.1945em;position:relative;top:-0.0006em;",[1095,2960],{"className":2961,"style":1384},[1383],[1095,2963,2965,2968],{"className":2964},[1150],[1095,2966,1091],{"className":2967},[1150,1151],[1095,2969,2971],{"className":2970},[1570],[1095,2972,2974,2994],{"className":2973},[1574,1575],[1095,2975,2977,2991],{"className":2976},[1579],[1095,2978,2980],{"className":2979,"style":1923},[1583],[1095,2981,2982,2985],{"style":1647},[1095,2983],{"className":2984,"style":1592},[1591],[1095,2986,2988],{"className":2987},[1596,1597,1598,1599],[1095,2989,1866],{"className":2990,"style":1936},[1150,1151,1599],[1095,2992,1607],{"className":2993},[1606],[1095,2995,2997],{"className":2996},[1579],[1095,2998,3000],{"className":2999,"style":1666},[1583],[1095,3001],{},[1095,3003,1121],{"className":3004},[1156],[1095,3006,1124],{"className":3007},[1150,1151],[1095,3009,1230],{"className":3010},[1150],[1095,3012,1352],{"className":3013,"style":1388},[1150,1151],[1095,3015,1127],{"className":3016},[1163],[1095,3018,1091],{"className":3019},[1150,1151],[1095,3021,1121],{"className":3022},[1156],[1095,3024,1352],{"className":3025,"style":1388},[1150,1151],[1095,3027,1127],{"className":3028},[1163],[1095,3030],{"className":3031,"style":1384},[1383],[1095,3033,2875],{"className":3034},[1150,1151],[1095,3036,1352],{"className":3037,"style":1388},[1150,1151],[1091,3039,3040,3043,3044,3072,3073,3421],{},[1172,3041,3042],{},"关键困难","：该积分在高维空间中不可解析计算（intractable），因为需要对所有可能的 ",[1095,3045,3047,3060],{"className":3046},[1098],[1095,3048,3050],{"className":3049},[1102],[1104,3051,3052],{"xmlns":1106},[1108,3053,3054,3058],{},[1111,3055,3056],{},[1114,3057,1352],{},[1129,3059,1352],{"encoding":1131},[1095,3061,3063],{"className":3062,"ariaHidden":1137},[1136],[1095,3064,3066,3069],{"className":3065},[1141],[1095,3067],{"className":3068,"style":1885},[1145],[1095,3070,1352],{"className":3071,"style":1388},[1150,1151]," 求积分。同样，真实后验 ",[1095,3074,3076,3149],{"className":3075},[1098],[1095,3077,3079],{"className":3078},[1102],[1104,3080,3081],{"xmlns":1106},[1108,3082,3083,3146],{},[1111,3084,3085,3091,3093,3095,3097,3099,3101,3103],{},[1465,3086,3087,3089],{},[1114,3088,1091],{},[1114,3090,1866],{},[1118,3092,1121],{"stretchy":1120},[1114,3094,1352],{},[1114,3096,1230],{"mathvariant":1229},[1114,3098,1124],{},[1118,3100,1127],{"stretchy":1120},[1118,3102,1463],{},[3104,3105,3106,3132],"mfrac",{},[1111,3107,3108,3114,3116,3118,3120,3122,3124,3126,3128,3130],{},[1465,3109,3110,3112],{},[1114,3111,1091],{},[1114,3113,1866],{},[1118,3115,1121],{"stretchy":1120},[1114,3117,1124],{},[1114,3119,1230],{"mathvariant":1229},[1114,3121,1352],{},[1118,3123,1127],{"stretchy":1120},[1114,3125,1091],{},[1118,3127,1121],{"stretchy":1120},[1114,3129,1352],{},[1118,3131,1127],{"stretchy":1120},[1111,3133,3134,3140,3142,3144],{},[1465,3135,3136,3138],{},[1114,3137,1091],{},[1114,3139,1866],{},[1118,3141,1121],{"stretchy":1120},[1114,3143,1124],{},[1118,3145,1127],{"stretchy":1120},[1129,3147,3148],{"encoding":1131},"p_\\theta(z|x) = \\frac{p_\\theta(x|z)p(z)}{p_\\theta(x)}",[1095,3150,3152,3222],{"className":3151,"ariaHidden":1137},[1136],[1095,3153,3155,3158,3198,3201,3204,3207,3210,3213,3216,3219],{"className":3154},[1141],[1095,3156],{"className":3157,"style":1146},[1145],[1095,3159,3161,3164],{"className":3160},[1150],[1095,3162,1091],{"className":3163},[1150,1151],[1095,3165,3167],{"className":3166},[1570],[1095,3168,3170,3190],{"className":3169},[1574,1575],[1095,3171,3173,3187],{"className":3172},[1579],[1095,3174,3176],{"className":3175,"style":1923},[1583],[1095,3177,3178,3181],{"style":1647},[1095,3179],{"className":3180,"style":1592},[1591],[1095,3182,3184],{"className":3183},[1596,1597,1598,1599],[1095,3185,1866],{"className":3186,"style":1936},[1150,1151,1599],[1095,3188,1607],{"className":3189},[1606],[1095,3191,3193],{"className":3192},[1579],[1095,3194,3196],{"className":3195,"style":1666},[1583],[1095,3197],{},[1095,3199,1121],{"className":3200},[1156],[1095,3202,1352],{"className":3203,"style":1388},[1150,1151],[1095,3205,1230],{"className":3206},[1150],[1095,3208,1124],{"className":3209},[1150,1151],[1095,3211,1127],{"className":3212},[1163],[1095,3214],{"className":3215,"style":1542},[1383],[1095,3217,1463],{"className":3218},[1546],[1095,3220],{"className":3221,"style":1542},[1383],[1095,3223,3225,3229],{"className":3224},[1141],[1095,3226],{"className":3227,"style":3228},[1145],"height:1.53em;vertical-align:-0.52em;",[1095,3230,3232,3236,3418],{"className":3231},[1150],[1095,3233],{"className":3234},[1156,3235],"nulldelimiter",[1095,3237,3239],{"className":3238},[3104],[1095,3240,3242,3409],{"className":3241},[1574,1575],[1095,3243,3245,3406],{"className":3244},[1579],[1095,3246,3249,3316,3327],{"className":3247,"style":3248},[1583],"height:1.01em;",[1095,3250,3252,3255],{"style":3251},"top:-2.655em;",[1095,3253],{"className":3254,"style":2026},[1591],[1095,3256,3258],{"className":3257},[1596,1597,1598,1599],[1095,3259,3261,3307,3310,3313],{"className":3260},[1150,1599],[1095,3262,3264,3267],{"className":3263},[1150,1599],[1095,3265,1091],{"className":3266},[1150,1151,1599],[1095,3268,3270],{"className":3269},[1570],[1095,3271,3273,3298],{"className":3272},[1574,1575],[1095,3274,3276,3295],{"className":3275},[1579],[1095,3277,3280],{"className":3278,"style":3279},[1583],"height:0.3448em;",[1095,3281,3283,3287],{"style":3282},"top:-2.3488em;margin-left:0em;margin-right:0.0714em;",[1095,3284],{"className":3285,"style":3286},[1591],"height:2.5em;",[1095,3288,3292],{"className":3289},[1596,3290,3291,1599],"reset-size3","size1",[1095,3293,1866],{"className":3294,"style":1936},[1150,1151,1599],[1095,3296,1607],{"className":3297},[1606],[1095,3299,3301],{"className":3300},[1579],[1095,3302,3305],{"className":3303,"style":3304},[1583],"height:0.1512em;",[1095,3306],{},[1095,3308,1121],{"className":3309},[1156,1599],[1095,3311,1124],{"className":3312},[1150,1151,1599],[1095,3314,1127],{"className":3315},[1163,1599],[1095,3317,3319,3322],{"style":3318},"top:-3.23em;",[1095,3320],{"className":3321,"style":2026},[1591],[1095,3323],{"className":3324,"style":3326},[3325],"frac-line","border-bottom-width:0.04em;",[1095,3328,3330,3333],{"style":3329},"top:-3.485em;",[1095,3331],{"className":3332,"style":2026},[1591],[1095,3334,3336],{"className":3335},[1596,1597,1598,1599],[1095,3337,3339,3379,3382,3385,3388,3391,3394,3397,3400,3403],{"className":3338},[1150,1599],[1095,3340,3342,3345],{"className":3341},[1150,1599],[1095,3343,1091],{"className":3344},[1150,1151,1599],[1095,3346,3348],{"className":3347},[1570],[1095,3349,3351,3371],{"className":3350},[1574,1575],[1095,3352,3354,3368],{"className":3353},[1579],[1095,3355,3357],{"className":3356,"style":3279},[1583],[1095,3358,3359,3362],{"style":3282},[1095,3360],{"className":3361,"style":3286},[1591],[1095,3363,3365],{"className":3364},[1596,3290,3291,1599],[1095,3366,1866],{"className":3367,"style":1936},[1150,1151,1599],[1095,3369,1607],{"className":3370},[1606],[1095,3372,3374],{"className":3373},[1579],[1095,3375,3377],{"className":3376,"style":3304},[1583],[1095,3378],{},[1095,3380,1121],{"className":3381},[1156,1599],[1095,3383,1124],{"className":3384},[1150,1151,1599],[1095,3386,1230],{"className":3387},[1150,1599],[1095,3389,1352],{"className":3390,"style":1388},[1150,1151,1599],[1095,3392,1127],{"className":3393},[1163,1599],[1095,3395,1091],{"className":3396},[1150,1151,1599],[1095,3398,1121],{"className":3399},[1156,1599],[1095,3401,1352],{"className":3402,"style":1388},[1150,1151,1599],[1095,3404,1127],{"className":3405},[1163,1599],[1095,3407,1607],{"className":3408},[1606],[1095,3410,3412],{"className":3411},[1579],[1095,3413,3416],{"className":3414,"style":3415},[1583],"height:0.52em;",[1095,3417],{},[1095,3419],{"className":3420},[1163,3235]," 也不可解。",[2556,3423,3425],{"id":3424},"_232-变分推断","2.3.2 变分推断",[1091,3427,3428,3429,3525,3526,2550],{},"引入一个可学习的近似后验分布 ",[1095,3430,3432,3461],{"className":3431},[1098],[1095,3433,3435],{"className":3434},[1102],[1104,3436,3437],{"xmlns":1106},[1108,3438,3439,3458],{},[1111,3440,3441,3448,3450,3452,3454,3456],{},[1465,3442,3443,3446],{},[1114,3444,3445],{},"q",[1114,3447,1987],{},[1118,3449,1121],{"stretchy":1120},[1114,3451,1352],{},[1114,3453,1230],{"mathvariant":1229},[1114,3455,1124],{},[1118,3457,1127],{"stretchy":1120},[1129,3459,3460],{"encoding":1131},"q_\\phi(z|x)",[1095,3462,3464],{"className":3463,"ariaHidden":1137},[1136],[1095,3465,3467,3470,3510,3513,3516,3519,3522],{"className":3466},[1141],[1095,3468],{"className":3469,"style":2058},[1145],[1095,3471,3473,3476],{"className":3472},[1150],[1095,3474,3445],{"className":3475,"style":1256},[1150,1151],[1095,3477,3479],{"className":3478},[1570],[1095,3480,3482,3502],{"className":3481},[1574,1575],[1095,3483,3485,3499],{"className":3484},[1579],[1095,3486,3488],{"className":3487,"style":1923},[1583],[1095,3489,3490,3493],{"style":2079},[1095,3491],{"className":3492,"style":1592},[1591],[1095,3494,3496],{"className":3495},[1596,1597,1598,1599],[1095,3497,1987],{"className":3498},[1150,1151,1599],[1095,3500,1607],{"className":3501},[1606],[1095,3503,3505],{"className":3504},[1579],[1095,3506,3508],{"className":3507,"style":2098},[1583],[1095,3509],{},[1095,3511,1121],{"className":3512},[1156],[1095,3514,1352],{"className":3515,"style":1388},[1150,1151],[1095,3517,1230],{"className":3518},[1150],[1095,3520,1124],{"className":3521},[1150,1151],[1095,3523,1127],{"className":3524},[1163],"（由编码器参数化），来近似真实后验 ",[1095,3527,3529,3557],{"className":3528},[1098],[1095,3530,3532],{"className":3531},[1102],[1104,3533,3534],{"xmlns":1106},[1108,3535,3536,3554],{},[1111,3537,3538,3544,3546,3548,3550,3552],{},[1465,3539,3540,3542],{},[1114,3541,1091],{},[1114,3543,1866],{},[1118,3545,1121],{"stretchy":1120},[1114,3547,1352],{},[1114,3549,1230],{"mathvariant":1229},[1114,3551,1124],{},[1118,3553,1127],{"stretchy":1120},[1129,3555,3556],{"encoding":1131},"p_\\theta(z|x)",[1095,3558,3560],{"className":3559,"ariaHidden":1137},[1136],[1095,3561,3563,3566,3606,3609,3612,3615,3618],{"className":3562},[1141],[1095,3564],{"className":3565,"style":1146},[1145],[1095,3567,3569,3572],{"className":3568},[1150],[1095,3570,1091],{"className":3571},[1150,1151],[1095,3573,3575],{"className":3574},[1570],[1095,3576,3578,3598],{"className":3577},[1574,1575],[1095,3579,3581,3595],{"className":3580},[1579],[1095,3582,3584],{"className":3583,"style":1923},[1583],[1095,3585,3586,3589],{"style":1647},[1095,3587],{"className":3588,"style":1592},[1591],[1095,3590,3592],{"className":3591},[1596,1597,1598,1599],[1095,3593,1866],{"className":3594,"style":1936},[1150,1151,1599],[1095,3596,1607],{"className":3597},[1606],[1095,3599,3601],{"className":3600},[1579],[1095,3602,3604],{"className":3603,"style":1666},[1583],[1095,3605],{},[1095,3607,1121],{"className":3608},[1156],[1095,3610,1352],{"className":3611,"style":1388},[1150,1151],[1095,3613,1230],{"className":3614},[1150],[1095,3616,1124],{"className":3617},[1150,1151],[1095,3619,1127],{"className":3620},[1163],[1091,3622,3623],{},"对数据对数似然进行分解：",[1091,3625,3626],{},[1095,3627,3629,3787],{"className":3628},[1098],[1095,3630,3632],{"className":3631},[1102],[1104,3633,3634],{"xmlns":1106},[1108,3635,3636,3784],{},[1111,3637,3638,3641,3644,3650,3652,3654,3656,3658,3681,3731,3734,3746,3748,3754,3756,3758,3760,3762,3764,3766,3772,3774,3776,3778,3780,3782],{},[1114,3639,3640],{},"log",[1118,3642,3643],{},"⁡",[1465,3645,3646,3648],{},[1114,3647,1091],{},[1114,3649,1866],{},[1118,3651,1121],{"stretchy":1120},[1114,3653,1124],{},[1118,3655,1127],{"stretchy":1120},[1118,3657,1463],{},[1465,3659,3660,3663],{},[1114,3661,2138],{"mathvariant":3662},"double-struck",[1111,3664,3665,3671,3673,3675,3677,3679],{},[1465,3666,3667,3669],{},[1114,3668,3445],{},[1114,3670,1987],{},[1118,3672,1121],{"stretchy":1120},[1114,3674,1352],{},[1114,3676,1230],{"mathvariant":1229},[1114,3678,1124],{},[1118,3680,1127],{"stretchy":1120},[1111,3682,3683,3686,3688,3690,3728],{},[1118,3684,3685],{"fence":1137},"[",[1114,3687,3640],{},[1118,3689,3643],{},[3104,3691,3692,3710],{},[1111,3693,3694,3700,3702,3704,3706,3708],{},[1465,3695,3696,3698],{},[1114,3697,1091],{},[1114,3699,1866],{},[1118,3701,1121],{"stretchy":1120},[1114,3703,1124],{},[1118,3705,1349],{"separator":1137},[1114,3707,1352],{},[1118,3709,1127],{"stretchy":1120},[1111,3711,3712,3718,3720,3722,3724,3726],{},[1465,3713,3714,3716],{},[1114,3715,3445],{},[1114,3717,1987],{},[1118,3719,1121],{"stretchy":1120},[1114,3721,1352],{},[1114,3723,1230],{"mathvariant":1229},[1114,3725,1124],{},[1118,3727,1127],{"stretchy":1120},[1118,3729,3730],{"fence":1137},"]",[1118,3732,3733],{},"+",[1465,3735,3736,3739],{},[1114,3737,3738],{},"D",[1111,3740,3741,3744],{},[1114,3742,3743],{},"K",[1114,3745,2130],{},[1118,3747,1121],{"stretchy":1120},[1465,3749,3750,3752],{},[1114,3751,3445],{},[1114,3753,1987],{},[1118,3755,1121],{"stretchy":1120},[1114,3757,1352],{},[1114,3759,1230],{"mathvariant":1229},[1114,3761,1124],{},[1118,3763,1127],{"stretchy":1120},[1114,3765,2143],{"mathvariant":1229},[1465,3767,3768,3770],{},[1114,3769,1091],{},[1114,3771,1866],{},[1118,3773,1121],{"stretchy":1120},[1114,3775,1352],{},[1114,3777,1230],{"mathvariant":1229},[1114,3779,1124],{},[1118,3781,1127],{"stretchy":1120},[1118,3783,1127],{"stretchy":1120},[1129,3785,3786],{"encoding":1131},"\\log p_\\theta(x) = \\mathbb{E}_{q_\\phi(z|x)}\\left[\\log \\frac{p_\\theta(x, z)}{q_\\phi(z|x)}\\right] + D_{KL}(q_\\phi(z|x) \\| p_\\theta(z|x))",[1095,3788,3790,3864,4183],{"className":3789,"ariaHidden":1137},[1136],[1095,3791,3793,3796,3803,3806,3846,3849,3852,3855,3858,3861],{"className":3792},[1141],[1095,3794],{"className":3795,"style":1146},[1145],[1095,3797,3799,3800],{"className":3798},[1560],"lo",[1095,3801,1984],{"style":3802},"margin-right:0.0139em;",[1095,3804],{"className":3805,"style":1384},[1383],[1095,3807,3809,3812],{"className":3808},[1150],[1095,3810,1091],{"className":3811},[1150,1151],[1095,3813,3815],{"className":3814},[1570],[1095,3816,3818,3838],{"className":3817},[1574,1575],[1095,3819,3821,3835],{"className":3820},[1579],[1095,3822,3824],{"className":3823,"style":1923},[1583],[1095,3825,3826,3829],{"style":1647},[1095,3827],{"className":3828,"style":1592},[1591],[1095,3830,3832],{"className":3831},[1596,1597,1598,1599],[1095,3833,1866],{"className":3834,"style":1936},[1150,1151,1599],[1095,3836,1607],{"className":3837},[1606],[1095,3839,3841],{"className":3840},[1579],[1095,3842,3844],{"className":3843,"style":1666},[1583],[1095,3845],{},[1095,3847,1121],{"className":3848},[1156],[1095,3850,1124],{"className":3851},[1150,1151],[1095,3853,1127],{"className":3854},[1163],[1095,3856],{"className":3857,"style":1542},[1383],[1095,3859,1463],{"className":3860},[1546],[1095,3862],{"className":3863,"style":1542},[1383],[1095,3865,3867,3871,3971,3974,4174,4177,4180],{"className":3866},[1141],[1095,3868],{"className":3869,"style":3870},[1145],"height:1.8em;vertical-align:-0.65em;",[1095,3872,3874,3878],{"className":3873},[1150],[1095,3875,2138],{"className":3876},[1150,3877],"mathbb",[1095,3879,3881],{"className":3880},[1570],[1095,3882,3884,3962],{"className":3883},[1574,1575],[1095,3885,3887,3959],{"className":3886},[1579],[1095,3888,3890],{"className":3889,"style":3279},[1583],[1095,3891,3893,3896],{"style":3892},"top:-2.5198em;margin-left:0em;margin-right:0.05em;",[1095,3894],{"className":3895,"style":1592},[1591],[1095,3897,3899],{"className":3898},[1596,1597,1598,1599],[1095,3900,3902,3944,3947,3950,3953,3956],{"className":3901},[1150,1599],[1095,3903,3905,3908],{"className":3904},[1150,1599],[1095,3906,3445],{"className":3907,"style":1256},[1150,1151,1599],[1095,3909,3911],{"className":3910},[1570],[1095,3912,3914,3935],{"className":3913},[1574,1575],[1095,3915,3917,3932],{"className":3916},[1579],[1095,3918,3920],{"className":3919,"style":3279},[1583],[1095,3921,3923,3926],{"style":3922},"top:-2.3488em;margin-left:-0.0359em;margin-right:0.0714em;",[1095,3924],{"className":3925,"style":3286},[1591],[1095,3927,3929],{"className":3928},[1596,3290,3291,1599],[1095,3930,1987],{"className":3931},[1150,1151,1599],[1095,3933,1607],{"className":3934},[1606],[1095,3936,3938],{"className":3937},[1579],[1095,3939,3942],{"className":3940,"style":3941},[1583],"height:0.2901em;",[1095,3943],{},[1095,3945,1121],{"className":3946},[1156,1599],[1095,3948,1352],{"className":3949,"style":1388},[1150,1151,1599],[1095,3951,1230],{"className":3952},[1150,1599],[1095,3954,1124],{"className":3955},[1150,1151,1599],[1095,3957,1127],{"className":3958},[1163,1599],[1095,3960,1607],{"className":3961},[1606],[1095,3963,3965],{"className":3964},[1579],[1095,3966,3969],{"className":3967,"style":3968},[1583],"height:0.3833em;",[1095,3970],{},[1095,3972],{"className":3973,"style":1384},[1383],[1095,3975,3977,3987,3992,3995,4168],{"className":3976},[1734],[1095,3978,3982],{"className":3979,"style":3981},[1156,3980],"delimcenter","top:0em;",[1095,3983,3685],{"className":3984},[3985,3986],"delimsizing","size2",[1095,3988,3799,3990],{"className":3989},[1560],[1095,3991,1984],{"style":3802},[1095,3993],{"className":3994,"style":1384},[1383],[1095,3996,3998,4001,4165],{"className":3997},[1150],[1095,3999],{"className":4000},[1156,3235],[1095,4002,4004],{"className":4003},[3104],[1095,4005,4007,4156],{"className":4006},[1574,1575],[1095,4008,4010,4153],{"className":4009},[1579],[1095,4011,4013,4079,4087],{"className":4012,"style":3248},[1583],[1095,4014,4015,4018],{"style":3251},[1095,4016],{"className":4017,"style":2026},[1591],[1095,4019,4021],{"className":4020},[1596,1597,1598,1599],[1095,4022,4024,4064,4067,4070,4073,4076],{"className":4023},[1150,1599],[1095,4025,4027,4030],{"className":4026},[1150,1599],[1095,4028,3445],{"className":4029,"style":1256},[1150,1151,1599],[1095,4031,4033],{"className":4032},[1570],[1095,4034,4036,4056],{"className":4035},[1574,1575],[1095,4037,4039,4053],{"className":4038},[1579],[1095,4040,4042],{"className":4041,"style":3279},[1583],[1095,4043,4044,4047],{"style":3922},[1095,4045],{"className":4046,"style":3286},[1591],[1095,4048,4050],{"className":4049},[1596,3290,3291,1599],[1095,4051,1987],{"className":4052},[1150,1151,1599],[1095,4054,1607],{"className":4055},[1606],[1095,4057,4059],{"className":4058},[1579],[1095,4060,4062],{"className":4061,"style":3941},[1583],[1095,4063],{},[1095,4065,1121],{"className":4066},[1156,1599],[1095,4068,1352],{"className":4069,"style":1388},[1150,1151,1599],[1095,4071,1230],{"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KL 散度非负，我们得到",[1172,4357,4358],{},"证据下界（ELBO）","：",[1091,4361,4362],{},[1172,4363,4364],{},"ELBO（Evidence Lower 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z 准确重建 x",[1169,5169,5170,5173,5174,5231],{},[1172,5171,5172],{},"KL 散度项","：迫使近似后验接近先验 ",[1095,5175,5177,5201],{"className":5176},[1098],[1095,5178,5180],{"className":5179},[1102],[1104,5181,5182],{"xmlns":1106},[1108,5183,5184,5198],{},[1111,5185,5186,5188,5190,5192,5194,5196],{},[1114,5187,2598],{"mathvariant":2129},[1118,5189,1121],{"stretchy":1120},[1490,5191,2603],{},[1118,5193,1349],{"separator":1137},[1114,5195,2608],{},[1118,5197,1127],{"stretchy":1120},[1129,5199,5200],{"encoding":1131},"\\mathcal{N}(0, I)",[1095,5202,5204],{"className":5203,"ariaHidden":1137},[1136],[1095,5205,5207,5210,5213,5216,5219,5222,5225,5228],{"className":5206},[1141],[1095,5208],{"className":5209,"style":1146},[1145],[1095,5211,2598],{"className":5212,"style":2671},[1150,2197],[1095,5214,1121],{"className":5215},[1156],[1095,5217,2603],{"className":5218},[1150],[1095,5220,1349],{"className":5221},[1379],[1095,5223],{"className":5224,"style":1384},[1383],[1095,5226,2608],{"className":5227,"style":2687},[1150,1151],[1095,5229,1127],{"className":5230},[1163],"，保证隐空间的规整性",[2556,5233,5235],{"id":5234},"_233-kl-散度解析解","2.3.3 KL 散度解析解",[1091,5237,5238,5239,5431,5432,5526],{},"当 ",[1095,5240,5242,5295],{"className":5241},[1098],[1095,5243,5245],{"className":5244},[1102],[1104,5246,5247],{"xmlns":1106},[1108,5248,5249,5292],{},[1111,5250,5251,5257,5259,5261,5263,5265,5267,5269,5271,5273,5275,5277,5280,5282,5288,5290],{},[1465,5252,5253,5255],{},[1114,5254,3445],{},[1114,5256,1987],{},[1118,5258,1121],{"stretchy":1120},[1114,5260,1352],{},[1114,5262,1230],{"mathvariant":1229},[1114,5264,1124],{},[1118,5266,1127],{"stretchy":1120},[1118,5268,1463],{},[1114,5270,2598],{"mathvariant":2129},[1118,5272,1121],{"stretchy":1120},[1114,5274,2443],{},[1118,5276,1349],{"separator":1137},[2870,5278,5279],{},"diag",[1118,5281,1121],{"stretchy":1120},[2171,5283,5284,5286],{},[1114,5285,2477],{},[1490,5287,2177],{},[1118,5289,1127],{"stretchy":1120},[1118,5291,1127],{"stretchy":1120},[1129,5293,5294],{"encoding":1131},"q_\\phi(z|x) = \\mathcal{N}(\\mu, \\text{diag}(\\sigma^2))",[1095,5296,5298,5368],{"className":5297,"ariaHidden":1137},[1136],[1095,5299,5301,5304,5344,5347,5350,5353,5356,5359,5362,5365],{"className":5300},[1141],[1095,5302],{"className":5303,"style":2058},[1145],[1095,5305,5307,5310],{"className":5306},[1150],[1095,5308,3445],{"className":5309,"style":1256},[1150,1151],[1095,5311,5313],{"className":5312},[1570],[1095,5314,5316,5336],{"className":5315},[1574,1575],[1095,5317,5319,5333],{"className":5318},[1579],[1095,5320,5322],{"className":5321,"style":1923},[1583],[1095,5323,5324,5327],{"style":2079},[1095,5325],{"className":5326,"style":1592},[1591],[1095,5328,5330],{"className":5329},[1596,1597,1598,1599],[1095,5331,1987],{"className":5332},[1150,1151,1599],[1095,5334,1607],{"className":5335},[1606],[1095,5337,5339],{"className":5338},[1579],[1095,5340,5342],{"className":5341,"style":2098},[1583],[1095,5343],{},[1095,5345,1121],{"className":5346},[1156],[1095,5348,1352],{"className":5349,"style":1388},[1150,1151],[1095,5351,1230],{"className":5352},[1150],[1095,5354,1124],{"className":5355},[1150,1151],[1095,5357,1127],{"className":5358},[1163],[1095,5360],{"className":5361,"style":1542},[1383],[1095,5363,1463],{"className":5364},[1546],[1095,5366],{"className":5367,"style":1542},[1383],[1095,5369,5371,5375,5378,5381,5384,5387,5390,5396,5399,5428],{"className":5370},[1141],[1095,5372],{"className":5373,"style":5374},[1145],"height:1.0641em;vertical-align:-0.25em;",[1095,5376,2598],{"className":5377,"style":2671},[1150,2197],[1095,5379,1121],{"className":5380},[1156],[1095,5382,2443],{"className":5383},[1150,1151],[1095,5385,1349],{"className":5386},[1379],[1095,5388],{"className":5389,"style":1384},[1383],[1095,5391,5393],{"className":5392},[1150,4628],[1095,5394,5279],{"className":5395},[1150],[1095,5397,1121],{"className":5398},[1156],[1095,5400,5402,5405],{"className":5401},[1150],[1095,5403,2477],{"className":5404,"style":1256},[1150,1151],[1095,5406,5408],{"className":5407},[1570],[1095,5409,5411],{"className":5410},[1574],[1095,5412,5414],{"className":5413},[1579],[1095,5415,5417],{"className":5416,"style":2389},[1583],[1095,5418,5419,5422],{"style":2392},[1095,5420],{"className":5421,"style":1592},[1591],[1095,5423,5425],{"className":5424},[1596,1597,1598,1599],[1095,5426,2177],{"className":5427},[1150,1599],[1095,5429,2370],{"className":5430},[1163]," 且 ",[1095,5433,5435,5469],{"className":5434},[1098],[1095,5436,5438],{"className":5437},[1102],[1104,5439,5440],{"xmlns":1106},[1108,5441,5442,5466],{},[1111,5443,5444,5446,5448,5450,5452,5454,5456,5458,5460,5462,5464],{},[1114,5445,1091],{},[1118,5447,1121],{"stretchy":1120},[1114,5449,1352],{},[1118,5451,1127],{"stretchy":1120},[1118,5453,1463],{},[1114,5455,2598],{"mathvariant":2129},[1118,5457,1121],{"stretchy":1120},[1490,5459,2603],{},[1118,5461,1349],{"separator":1137},[1114,5463,2608],{},[1118,5465,1127],{"stretchy":1120},[1129,5467,5468],{"encoding":1131},"p(z) = \\mathcal{N}(0, I)",[1095,5470,5472,5499],{"className":5471,"ariaHidden":1137},[1136],[1095,5473,5475,5478,5481,5484,5487,5490,5493,5496],{"className":5474},[1141],[1095,5476],{"className":5477,"style":1146},[1145],[1095,5479,1091],{"className":5480},[1150,1151],[1095,5482,1121],{"className":5483},[1156],[1095,5485,1352],{"className":5486,"style":1388},[1150,1151],[1095,5488,1127],{"className":5489},[1163],[1095,5491],{"className":5492,"style":1542},[1383],[1095,5494,1463],{"className":5495},[1546],[1095,5497],{"className":5498,"style":1542},[1383],[1095,5500,5502,5505,5508,5511,5514,5517,5520,5523],{"className":5501},[1141],[1095,5503],{"className":5504,"style":1146},[1145],[1095,5506,2598],{"className":5507,"style":2671},[1150,2197],[1095,5509,1121],{"className":5510},[1156],[1095,5512,2603],{"className":5513},[1150],[1095,5515,1349],{"className":5516},[1379],[1095,5518],{"className":5519,"style":1384},[1383],[1095,5521,2608],{"className":5522,"style":2687},[1150,1151],[1095,5524,1127],{"className":5525},[1163]," 时，KL 散度有解析解：",[1091,5528,5529],{},[1095,5530,5532,5654],{"className":5531},[1098],[1095,5533,5535],{"className":5534},[1102],[1104,5536,5537],{"xmlns":1106},[1108,5538,5539,5651],{},[1111,5540,5541,5551,5553,5559,5561,5563,5565,5567,5569,5571,5573,5575,5577,5579,5581,5583,5585,5591,5609],{},[1465,5542,5543,5545],{},[1114,5544,3738],{},[1111,5546,5547,5549],{},[1114,5548,3743],{},[1114,5550,2130],{},[1118,5552,1121],{"stretchy":1120},[1465,5554,5555,5557],{},[1114,5556,3445],{},[1114,5558,1987],{},[1118,5560,1121],{"stretchy":1120},[1114,5562,1352],{},[1114,5564,1230],{"mathvariant":1229},[1114,5566,1124],{},[1118,5568,1127],{"stretchy":1120},[1114,5570,2143],{"mathvariant":1229},[1114,5572,1091],{},[1118,5574,1121],{"stretchy":1120},[1114,5576,1352],{},[1118,5578,1127],{"stretchy":1120},[1118,5580,1127],{"stretchy":1120},[1118,5582,1463],{},[1118,5584,1510],{},[3104,5586,5587,5589],{},[1490,5588,1492],{},[1490,5590,2177],{},[5592,5593,5594,5597,5606],"msubsup",{},[1118,5595,5596],{},"∑",[1111,5598,5599,5602,5604],{},[1114,5600,5601],{},"j",[1118,5603,1463],{},[1490,5605,1492],{},[1114,5607,5608],{},"J",[1111,5610,5611,5613,5615,5617,5619,5621,5629,5631,5639,5641,5649],{},[1118,5612,1121],{"fence":1137},[1490,5614,1492],{},[1118,5616,3733],{},[1114,5618,3640],{},[1118,5620,3643],{},[5592,5622,5623,5625,5627],{},[1114,5624,2477],{},[1114,5626,5601],{},[1490,5628,2177],{},[1118,5630,1510],{},[5592,5632,5633,5635,5637],{},[1114,5634,2443],{},[1114,5636,5601],{},[1490,5638,2177],{},[1118,5640,1510],{},[5592,5642,5643,5645,5647],{},[1114,5644,2477],{},[1114,5646,5601],{},[1490,5648,2177],{},[1118,5650,1127],{"fence":1137},[1129,5652,5653],{"encoding":1131},"D_{KL}(q_\\phi(z|x) \\| p(z)) = -\\frac{1}{2} \\sum_{j=1}^{J} \\left(1 + \\log \\sigma_j^2 - \\mu_j^2 - \\sigma_j^2\\right)",[1095,5655,5657,5791],{"className":5656,"ariaHidden":1137},[1136],[1095,5658,5660,5663,5709,5712,5752,5755,5758,5761,5764,5767,5770,5773,5776,5779,5782,5785,5788],{"className":5659},[1141],[1095,5661],{"className":5662,"style":2058},[1145],[1095,5664,5666,5669],{"className":5665},[1150],[1095,5667,3738],{"className":5668,"style":1936},[1150,1151],[1095,5670,5672],{"className":5671},[1570],[1095,5673,5675,5701],{"className":5674},[1574,1575],[1095,5676,5678,5698],{"className":5677},[1579],[1095,5679,5681],{"className":5680,"style":2210},[1583],[1095,5682,5683,5686],{"style":4209},[1095,5684],{"className":5685,"style":1592},[1591],[1095,5687,5689],{"className":5688},[1596,1597,1598,1599],[1095,5690,5692,5695],{"className":5691},[1150,1599],[1095,5693,3743],{"className":5694,"style":4222},[1150,1151,1599],[1095,5696,2130],{"className":5697},[1150,1151,1599],[1095,5699,1607],{"className":5700},[1606],[1095,5702,5704],{"className":5703},[1579],[1095,5705,5707],{"className":5706,"style":1666},[1583],[1095,5708],{},[1095,5710,1121],{"className":5711},[1156],[1095,5713,5715,5718],{"className":5714},[1150],[1095,5716,3445],{"className":5717,"style":1256},[1150,1151],[1095,5719,5721],{"className":5720},[1570],[1095,5722,5724,5744],{"className":5723},[1574,1575],[1095,5725,5727,5741],{"className":5726},[1579],[1095,5728,5730],{"className":5729,"style":1923},[1583],[1095,5731,5732,5735],{"style":2079},[1095,5733],{"className":5734,"style":1592},[1591],[1095,5736,5738],{"className":5737},[1596,1597,1598,1599],[1095,5739,1987],{"className":5740},[1150,1151,1599],[1095,5742,1607],{"className":5743},[1606],[1095,5745,5747],{"className":5746},[1579],[1095,5748,5750],{"className":5749,"style":2098},[1583],[1095,5751],{},[1095,5753,1121],{"className":5754},[1156],[1095,5756,1352],{"className":5757,"style":1388},[1150,1151],[1095,5759,1230],{"className":5760},[1150],[1095,5762,1124],{"className":5763},[1150,1151],[1095,5765,1127],{"className":5766},[1163],[1095,5768,2143],{"className":5769},[1150],[1095,5771,1091],{"className":5772},[1150,1151],[1095,5774,1121],{"className":5775},[1156],[1095,5777,1352],{"className":5778,"style":1388},[1150,1151],[1095,5780,2370],{"className":5781},[1163],[1095,5783],{"className":5784,"style":1542},[1383],[1095,5786,1463],{"className":5787},[1546],[1095,5789],{"className":5790,"style":1542},[1383],[1095,5792,5794,5798,5801,5872,5875,5943,5946],{"className":5793},[1141],[1095,5795],{"className":5796,"style":5797},[1145],"height:1.417em;vertical-align:-0.4358em;",[1095,5799,1510],{"className":5800},[1150],[1095,5802,5804,5807,5869],{"className":5803},[1150],[1095,5805],{"className":5806},[1156,3235],[1095,5808,5810],{"className":5809},[3104],[1095,5811,5813,5860],{"className":5812},[1574,1575],[1095,5814,5816,5857],{"className":5815},[1579],[1095,5817,5820,5834,5842],{"className":5818,"style":5819},[1583],"height:0.8451em;",[1095,5821,5822,5825],{"style":3251},[1095,5823],{"className":5824,"style":2026},[1591],[1095,5826,5828],{"className":5827},[1596,1597,1598,1599],[1095,5829,5831],{"className":5830},[1150,1599],[1095,5832,2177],{"className":5833},[1150,1599],[1095,5835,5836,5839],{"style":3318},[1095,5837],{"className":5838,"style":2026},[1591],[1095,5840],{"className":5841,"style":3326},[3325],[1095,5843,5845,5848],{"style":5844},"top:-3.394em;",[1095,5846],{"className":5847,"style":2026},[1591],[1095,5849,5851],{"className":5850},[1596,1597,1598,1599],[1095,5852,5854],{"className":5853},[1150,1599],[1095,5855,1492],{"className":5856},[1150,1599],[1095,5858,1607],{"className":5859},[1606],[1095,5861,5863],{"className":5862},[1579],[1095,5864,5867],{"className":5865,"style":5866},[1583],"height:0.345em;",[1095,5868],{},[1095,5870],{"className":5871},[1163,3235],[1095,5873],{"className":5874,"style":1384},[1383],[1095,5876,5878,5881],{"className":5877},[1560],[1095,5879,5596],{"className":5880,"style":1566},[1560,1564,1565],[1095,5882,5884],{"className":5883},[1570],[1095,5885,5887,5934],{"className":5886},[1574,1575],[1095,5888,5890,5931],{"className":5889},[1579],[1095,5891,5894,5915],{"className":5892,"style":5893},[1583],"height:0.9812em;",[1095,5895,5896,5899],{"style":1587},[1095,5897],{"className":5898,"style":1592},[1591],[1095,5900,5902],{"className":5901},[1596,1597,1598,1599],[1095,5903,5905,5909,5912],{"className":5904},[1150,1599],[1095,5906,5601],{"className":5907,"style":5908},[1150,1151,1599],"margin-right:0.0572em;",[1095,5910,1463],{"className":5911},[1546,1599],[1095,5913,1492],{"className":5914},[1150,1599],[1095,5916,5918,5921],{"style":5917},"top:-3.2029em;margin-right:0.05em;",[1095,5919],{"className":5920,"style":1592},[1591],[1095,5922,5924],{"className":5923},[1596,1597,1598,1599],[1095,5925,5927],{"className":5926},[1150,1599],[1095,5928,5608],{"className":5929,"style":5930},[1150,1151,1599],"margin-right:0.0962em;",[1095,5932,1607],{"className":5933},[1606],[1095,5935,5937],{"className":5936},[1579],[1095,5938,5941],{"className":5939,"style":5940},[1583],"height:0.4358em;",[1095,5942],{},[1095,5944],{"className":5945,"style":1384},[1383],[1095,5947,5949,5955,5958,5961,5964,5967,5972,5975,6028,6031,6034,6037,6089,6092,6095,6098,6149],{"className":5948},[1734],[1095,5950,5952],{"className":5951,"style":3981},[1156,3980],[1095,5953,1121],{"className":5954},[3985,3291],[1095,5956,1492],{"className":5957},[1150],[1095,5959],{"className":5960,"style":2264},[1383],[1095,5962,3733],{"className":5963},[1779],[1095,5965],{"className":5966,"style":2264},[1383],[1095,5968,3799,5970],{"className":5969},[1560],[1095,5971,1984],{"style":3802},[1095,5973],{"className":5974,"style":1384},[1383],[1095,5976,5978,5981],{"className":5977},[1150],[1095,5979,2477],{"className":5980,"style":1256},[1150,1151],[1095,5982,5984],{"className":5983},[1570],[1095,5985,5987,6019],{"className":5986},[1574,1575],[1095,5988,5990,6016],{"className":5989},[1579],[1095,5991,5993,6005],{"className":5992,"style":2389},[1583],[1095,5994,5996,5999],{"style":5995},"top:-2.4413em;margin-left:-0.0359em;margin-right:0.05em;",[1095,5997],{"className":5998,"style":1592},[1591],[1095,6000,6002],{"className":6001},[1596,1597,1598,1599],[1095,6003,5601],{"className":6004,"style":5908},[1150,1151,1599],[1095,6006,6007,6010],{"style":2392},[1095,6008],{"className":6009,"style":1592},[1591],[1095,6011,6013],{"className":6012},[1596,1597,1598,1599],[1095,6014,2177],{"className":6015},[1150,1599],[1095,6017,1607],{"className":6018},[1606],[1095,6020,6022],{"className":6021},[1579],[1095,6023,6026],{"className":6024,"style":6025},[1583],"height:0.3948em;",[1095,6027],{},[1095,6029],{"className":6030,"style":2264},[1383],[1095,6032,1510],{"className":6033},[1779],[1095,6035],{"className":6036,"style":2264},[1383],[1095,6038,6040,6043],{"className":6039},[1150],[1095,6041,2443],{"className":6042},[1150,1151],[1095,6044,6046],{"className":6045},[1570],[1095,6047,6049,6081],{"className":6048},[1574,1575],[1095,6050,6052,6078],{"className":6051},[1579],[1095,6053,6055,6067],{"className":6054,"style":2389},[1583],[1095,6056,6058,6061],{"style":6057},"top:-2.4413em;margin-left:0em;margin-right:0.05em;",[1095,6059],{"className":6060,"style":1592},[1591],[1095,6062,6064],{"className":6063},[1596,1597,1598,1599],[1095,6065,5601],{"className":6066,"style":5908},[1150,1151,1599],[1095,6068,6069,6072],{"style":2392},[1095,6070],{"className":6071,"style":1592},[1591],[1095,6073,6075],{"className":6074},[1596,1597,1598,1599],[1095,6076,2177],{"className":6077},[1150,1599],[1095,6079,1607],{"className":6080},[1606],[1095,6082,6084],{"className":6083},[1579],[1095,6085,6087],{"className":6086,"style":6025},[1583],[1095,6088],{},[1095,6090],{"className":6091,"style":2264},[1383],[1095,6093,1510],{"className":6094},[1779],[1095,6096],{"className":6097,"style":2264},[1383],[1095,6099,6101,6104],{"className":6100},[1150],[1095,6102,2477],{"className":6103,"style":1256},[1150,1151],[1095,6105,6107],{"className":6106},[1570],[1095,6108,6110,6141],{"className":6109},[1574,1575],[1095,6111,6113,6138],{"className":6112},[1579],[1095,6114,6116,6127],{"className":6115,"style":2389},[1583],[1095,6117,6118,6121],{"style":5995},[1095,6119],{"className":6120,"style":1592},[1591],[1095,6122,6124],{"className":6123},[1596,1597,1598,1599],[1095,6125,5601],{"className":6126,"style":5908},[1150,1151,1599],[1095,6128,6129,6132],{"style":2392},[1095,6130],{"className":6131,"style":1592},[1591],[1095,6133,6135],{"className":6134},[1596,1597,1598,1599],[1095,6136,2177],{"className":6137},[1150,1599],[1095,6139,1607],{"className":6140},[1606],[1095,6142,6144],{"className":6143},[1579],[1095,6145,6147],{"className":6146,"style":6025},[1583],[1095,6148],{},[1095,6150,6152],{"className":6151,"style":3981},[1163,3980],[1095,6153,1127],{"className":6154},[3985,3291],[1091,6156,6157,6158,6186],{},"其中 ",[1095,6159,6161,6174],{"className":6160},[1098],[1095,6162,6164],{"className":6163},[1102],[1104,6165,6166],{"xmlns":1106},[1108,6167,6168,6172],{},[1111,6169,6170],{},[1114,6171,5608],{},[1129,6173,5608],{"encoding":1131},[1095,6175,6177],{"className":6176,"ariaHidden":1137},[1136],[1095,6178,6180,6183],{"className":6179},[1141],[1095,6181],{"className":6182,"style":5154},[1145],[1095,6184,5608],{"className":6185,"style":5930},[1150,1151]," 是隐变量维度。",[1194,6188,6190],{"id":6189},"_24-重参数化技巧reparameterization-trick","2.4 重参数化技巧（Reparameterization Trick）",[1091,6192,6193,6196,6197,6314],{},[1172,6194,6195],{},"问题","：训练中需要对 ELBO 求梯度，但采样操作 ",[1095,6198,6200,6232],{"className":6199},[1098],[1095,6201,6203],{"className":6202},[1102],[1104,6204,6205],{"xmlns":1106},[1108,6206,6207,6229],{},[1111,6208,6209,6211,6213,6219,6221,6223,6225,6227],{},[1114,6210,1352],{},[1118,6212,2585],{},[1465,6214,6215,6217],{},[1114,6216,3445],{},[1114,6218,1987],{},[1118,6220,1121],{"stretchy":1120},[1114,6222,1352],{},[1114,6224,1230],{"mathvariant":1229},[1114,6226,1124],{},[1118,6228,1127],{"stretchy":1120},[1129,6230,6231],{"encoding":1131},"z \\sim q_\\phi(z|x)",[1095,6233,6235,6253],{"className":6234,"ariaHidden":1137},[1136],[1095,6236,6238,6241,6244,6247,6250],{"className":6237},[1141],[1095,6239],{"className":6240,"style":1885},[1145],[1095,6242,1352],{"className":6243,"style":1388},[1150,1151],[1095,6245],{"className":6246,"style":1542},[1383],[1095,6248,2585],{"className":6249},[1546],[1095,6251],{"className":6252,"style":1542},[1383],[1095,6254,6256,6259,6299,6302,6305,6308,6311],{"className":6255},[1141],[1095,6257],{"className":6258,"style":2058},[1145],[1095,6260,6262,6265],{"className":6261},[1150],[1095,6263,3445],{"className":6264,"style":1256},[1150,1151],[1095,6266,6268],{"className":6267},[1570],[1095,6269,6271,6291],{"className":6270},[1574,1575],[1095,6272,6274,6288],{"className":6273},[1579],[1095,6275,6277],{"className":6276,"style":1923},[1583],[1095,6278,6279,6282],{"style":2079},[1095,6280],{"className":6281,"style":1592},[1591],[1095,6283,6285],{"className":6284},[1596,1597,1598,1599],[1095,6286,1987],{"className":6287},[1150,1151,1599],[1095,6289,1607],{"className":6290},[1606],[1095,6292,6294],{"className":6293},[1579],[1095,6295,6297],{"className":6296,"style":2098},[1583],[1095,6298],{},[1095,6300,1121],{"className":6301},[1156],[1095,6303,1352],{"className":6304,"style":1388},[1150,1151],[1095,6306,1230],{"className":6307},[1150],[1095,6309,1124],{"className":6310},[1150,1151],[1095,6312,1127],{"className":6313},[1163]," 是随机的，梯度无法通过随机采样节点反向传播。",[1091,6316,6317,6320],{},[1172,6318,6319],{},"解决方案","：将随机性从计算图中分离出来：",[1091,6322,6323],{},[1095,6324,6326,6375],{"className":6325},[1098],[1095,6327,6329],{"className":6328},[1102],[1104,6330,6331],{"xmlns":1106},[1108,6332,6333,6372],{},[1111,6334,6335,6337,6339,6341,6343,6345,6348,6351,6353,6356,6358,6360,6362,6364,6366,6368,6370],{},[1114,6336,1352],{},[1118,6338,1463],{},[1114,6340,2443],{},[1118,6342,3733],{},[1114,6344,2477],{},[1118,6346,6347],{},"⊙",[1114,6349,6350],{},"ϵ",[1118,6352,1349],{"separator":1137},[1383,6354],{"width":6355},"1em",[1114,6357,6350],{},[1118,6359,2585],{},[1114,6361,2598],{"mathvariant":2129},[1118,6363,1121],{"stretchy":1120},[1490,6365,2603],{},[1118,6367,1349],{"separator":1137},[1114,6369,2608],{},[1118,6371,1127],{"stretchy":1120},[1129,6373,6374],{"encoding":1131},"z = \\mu + \\sigma \\odot \\epsilon, \\quad \\epsilon \\sim \\mathcal{N}(0, I)",[1095,6376,6378,6396,6415,6434,6465],{"className":6377,"ariaHidden":1137},[1136],[1095,6379,6381,6384,6387,6390,6393],{"className":6380},[1141],[1095,6382],{"className":6383,"style":1885},[1145],[1095,6385,1352],{"className":6386,"style":1388},[1150,1151],[1095,6388],{"className":6389,"style":1542},[1383],[1095,6391,1463],{"className":6392},[1546],[1095,6394],{"className":6395,"style":1542},[1383],[1095,6397,6399,6403,6406,6409,6412],{"className":6398},[1141],[1095,6400],{"className":6401,"style":6402},[1145],"height:0.7778em;vertical-align:-0.1944em;",[1095,6404,2443],{"className":6405},[1150,1151],[1095,6407],{"className":6408,"style":2264},[1383],[1095,6410,3733],{"className":6411},[1779],[1095,6413],{"className":6414,"style":2264},[1383],[1095,6416,6418,6422,6425,6428,6431],{"className":6417},[1141],[1095,6419],{"className":6420,"style":6421},[1145],"height:0.6667em;vertical-align:-0.0833em;",[1095,6423,2477],{"className":6424,"style":1256},[1150,1151],[1095,6426],{"className":6427,"style":2264},[1383],[1095,6429,6347],{"className":6430},[1779],[1095,6432],{"className":6433,"style":2264},[1383],[1095,6435,6437,6440,6443,6446,6450,6453,6456,6459,6462],{"className":6436},[1141],[1095,6438],{"className":6439,"style":2456},[1145],[1095,6441,6350],{"className":6442},[1150,1151],[1095,6444,1349],{"className":6445},[1379],[1095,6447],{"className":6448,"style":6449},[1383],"margin-right:1em;",[1095,6451],{"className":6452,"style":1384},[1383],[1095,6454,6350],{"className":6455},[1150,1151],[1095,6457],{"className":6458,"style":1542},[1383],[1095,6460,2585],{"className":6461},[1546],[1095,6463],{"className":6464,"style":1542},[1383],[1095,6466,6468,6471,6474,6477,6480,6483,6486,6489],{"className":6467},[1141],[1095,6469],{"className":6470,"style":1146},[1145],[1095,6472,2598],{"className":6473,"style":2671},[1150,2197],[1095,6475,1121],{"className":6476},[1156],[1095,6478,2603],{"className":6479},[1150],[1095,6481,1349],{"className":6482},[1379],[1095,6484],{"className":6485,"style":1384},[1383],[1095,6487,2608],{"className":6488,"style":2687},[1150,1151],[1095,6490,1127],{"className":6491},[1163],[1091,6493,6494],{},[1172,6495,6496],{},"不可微路径",[1091,6498,6499],{},[1095,6500,6502,6534],{"className":6501},[1098],[1095,6503,6505],{"className":6504},[1102],[1104,6506,6507],{"xmlns":1106},[1108,6508,6509,6531],{},[1111,6510,6511,6513,6515,6517,6519,6521,6523,6529],{},[1114,6512,1352],{},[1118,6514,2585],{},[1114,6516,2598],{"mathvariant":2129},[1118,6518,1121],{"stretchy":1120},[1114,6520,2443],{},[1118,6522,1349],{"separator":1137},[2171,6524,6525,6527],{},[1114,6526,2477],{},[1490,6528,2177],{},[1118,6530,1127],{"stretchy":1120},[1129,6532,6533],{"encoding":1131},"z \\sim \\mathcal{N}(\\mu, 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\\approx -\\log p_\\theta(x | z^{(l)}) + D_{KL}(q_\\phi(z|x) \\| p(z)), \\quad z^{(l)} = \\mu + \\sigma \\odot 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",[1095,7884,7886,7914],{"className":7885},[1098],[1095,7887,7889],{"className":7888},[1102],[1104,7890,7891],{"xmlns":1106},[1108,7892,7893,7911],{},[1111,7894,7895,7901,7903,7905,7907,7909],{},[1465,7896,7897,7899],{},[1114,7898,3445],{},[1114,7900,1987],{},[1118,7902,1121],{"stretchy":1120},[1114,7904,1352],{},[1118,7906,1230],{},[1114,7908,1124],{},[1118,7910,1127],{"stretchy":1120},[1129,7912,7913],{"encoding":1131},"q_\\phi(z \\mid x)",[1095,7915,7917,7978],{"className":7916,"ariaHidden":1137},[1136],[1095,7918,7920,7923,7963,7966,7969,7972,7975],{"className":7919},[1141],[1095,7921],{"className":7922,"style":2058},[1145],[1095,7924,7926,7929],{"className":7925},[1150],[1095,7927,3445],{"className":7928,"style":1256},[1150,1151],[1095,7930,7932],{"className":7931},[1570],[1095,7933,7935,7955],{"className":7934},[1574,1575],[1095,7936,7938,7952],{"className":7937},[1579],[1095,7939,7941],{"className":7940,"style":1923},[1583],[1095,7942,7943,7946],{"style":2079},[1095,7944],{"className":7945,"style":1592},[1591],[1095,7947,7949],{"className":7948},[1596,1597,1598,1599],[1095,7950,1987],{"className":7951},[1150,1151,1599],[1095,7953,1607],{"className":7954},[1606],[1095,7956,7958],{"className":7957},[1579],[1095,7959,7961],{"className":7960,"style":2098},[1583],[1095,7962],{},[1095,7964,1121],{"className":7965},[1156],[1095,7967,1352],{"className":7968,"style":1388},[1150,1151],[1095,7970],{"className":7971,"style":1542},[1383],[1095,7973,1230],{"className":7974},[1546],[1095,7976],{"className":7977,"style":1542},[1383],[1095,7979,7981,7984,7987],{"className":7980},[1141],[1095,7982],{"className":7983,"style":1146},[1145],[1095,7985,1124],{"className":7986},[1150,1151],[1095,7988,1127],{"className":7989},[1163],[1433,7991,7992,7993],{},"输出 ",[1095,7994,7996,8022],{"className":7995},[1098],[1095,7997,7999],{"className":7998},[1102],[1104,8000,8001],{"xmlns":1106},[1108,8002,8003,8019],{},[1111,8004,8005,8007,8009,8011,8013],{},[1114,8006,2443],{},[1118,8008,1349],{"separator":1137},[1114,8010,3640],{},[1118,8012,3643],{},[2171,8014,8015,8017],{},[1114,8016,2477],{},[1490,8018,2177],{},[1129,8020,8021],{"encoding":1131},"\\mu, \\log\\sigma^2",[1095,8023,8025],{"className":8024,"ariaHidden":1137},[1136],[1095,8026,8028,8032,8035,8038,8041,8046,8049],{"className":8027},[1141],[1095,8029],{"className":8030,"style":8031},[1145],"height:1.0085em;vertical-align:-0.1944em;",[1095,8033,2443],{"className":8034},[1150,1151],[1095,8036,1349],{"className":8037},[1379],[1095,8039],{"className":8040,"style":1384},[1383],[1095,8042,3799,8044],{"className":8043},[1560],[1095,8045,1984],{"style":3802},[1095,8047],{"className":8048,"style":1384},[1383],[1095,8050,8052,8055],{"className":8051},[1150],[1095,8053,2477],{"className":8054,"style":1256},[1150,1151],[1095,8056,8058],{"className":8057},[1570],[1095,8059,8061],{"className":8060},[1574],[1095,8062,8064],{"className":8063},[1579],[1095,8065,8067],{"className":8066,"style":2389},[1583],[1095,8068,8069,8072],{"style":2392},[1095,8070],{"className":8071,"style":1592},[1591],[1095,8073,8075],{"className":8074},[1596,1597,1598,1599],[1095,8076,2177],{"className":8077},[1150,1599],[1433,8079,8080],{},"近似后验推断",[1412,8082,8083,8193,8196],{},[1433,8084,8085,8086],{},"解码器 ",[1095,8087,8089,8117],{"className":8088},[1098],[1095,8090,8092],{"className":8091},[1102],[1104,8093,8094],{"xmlns":1106},[1108,8095,8096,8114],{},[1111,8097,8098,8104,8106,8108,8110,8112],{},[1465,8099,8100,8102],{},[1114,8101,1091],{},[1114,8103,1866],{},[1118,8105,1121],{"stretchy":1120},[1114,8107,1124],{},[1118,8109,1230],{},[1114,8111,1352],{},[1118,8113,1127],{"stretchy":1120},[1129,8115,8116],{"encoding":1131},"p_\\theta(x \\mid z)",[1095,8118,8120,8181],{"className":8119,"ariaHidden":1137},[1136],[1095,8121,8123,8126,8166,8169,8172,8175,8178],{"className":8122},[1141],[1095,8124],{"className":8125,"style":1146},[1145],[1095,8127,8129,8132],{"className":8128},[1150],[1095,8130,1091],{"className":8131},[1150,1151],[1095,8133,8135],{"className":8134},[1570],[1095,8136,8138,8158],{"className":8137},[1574,1575],[1095,8139,8141,8155],{"className":8140},[1579],[1095,8142,8144],{"className":8143,"style":1923},[1583],[1095,8145,8146,8149],{"style":1647},[1095,8147],{"className":8148,"style":1592},[1591],[1095,8150,8152],{"className":8151},[1596,1597,1598,1599],[1095,8153,1866],{"className":8154,"style":1936},[1150,1151,1599],[1095,8156,1607],{"className":8157},[1606],[1095,8159,8161],{"className":8160},[1579],[1095,8162,8164],{"className":8163,"style":1666},[1583],[1095,8165],{},[1095,8167,1121],{"className":8168},[1156],[1095,8170,1124],{"className":8171},[1150,1151],[1095,8173],{"className":8174,"style":1542},[1383],[1095,8176,1230],{"className":8177},[1546],[1095,8179],{"className":8180,"style":1542},[1383],[1095,8182,8184,8187,8190],{"className":8183},[1141],[1095,8185],{"className":8186,"style":1146},[1145],[1095,8188,1352],{"className":8189,"style":1388},[1150,1151],[1095,8191,1127],{"className":8192},[1163],[1433,8194,8195],{},"Bernoulli（二值图像）或 Gaussian",[1433,8197,8198],{},"由隐变量重建数据",[1412,8200,8201,8248,8306],{},[1433,8202,8203,8204],{},"先验 ",[1095,8205,8207,8227],{"className":8206},[1098],[1095,8208,8210],{"className":8209},[1102],[1104,8211,8212],{"xmlns":1106},[1108,8213,8214,8224],{},[1111,8215,8216,8218,8220,8222],{},[1114,8217,1091],{},[1118,8219,1121],{"stretchy":1120},[1114,8221,1352],{},[1118,8223,1127],{"stretchy":1120},[1129,8225,8226],{"encoding":1131},"p(z)",[1095,8228,8230],{"className":8229,"ariaHidden":1137},[1136],[1095,8231,8233,8236,8239,8242,8245],{"className":8232},[1141],[1095,8234],{"className":8235,"style":1146},[1145],[1095,8237,1091],{"className":8238},[1150,1151],[1095,8240,1121],{"className":8241},[1156],[1095,8243,1352],{"className":8244,"style":1388},[1150,1151],[1095,8246,1127],{"className":8247},[1163],[1433,8249,8250],{},[1095,8251,8253,8276],{"className":8252},[1098],[1095,8254,8256],{"className":8255},[1102],[1104,8257,8258],{"xmlns":1106},[1108,8259,8260,8274],{},[1111,8261,8262,8264,8266,8268,8270,8272],{},[1114,8263,2598],{"mathvariant":2129},[1118,8265,1121],{"stretchy":1120},[1490,8267,2603],{},[1118,8269,1349],{"separator":1137},[1114,8271,2608],{},[1118,8273,1127],{"stretchy":1120},[1129,8275,5200],{"encoding":1131},[1095,8277,8279],{"className":8278,"ariaHidden":1137},[1136],[1095,8280,8282,8285,8288,8291,8294,8297,8300,8303],{"className":8281},[1141],[1095,8283],{"className":8284,"style":1146},[1145],[1095,8286,2598],{"className":8287,"style":2671},[1150,2197],[1095,8289,1121],{"className":8290},[1156],[1095,8292,2603],{"className":8293},[1150],[1095,8295,1349],{"className":8296},[1379],[1095,8298],{"className":8299,"style":1384},[1383],[1095,8301,2608],{"className":8302,"style":2687},[1150,1151],[1095,8304,1127],{"className":8305},[1163],[1433,8307,8308],{},"正则化隐空间",[1412,8310,8311,8314,8317],{},[1433,8312,8313],{},"重建损失",[1433,8315,8316],{},"交叉熵或 MSE",[1433,8318,8319],{},"保证重建质量",[1412,8321,8322,8325,8328],{},[1433,8323,8324],{},"KL 损失",[1433,8326,8327],{},"解析公式",[1433,8329,8330],{},"保证隐空间连续可采样",[1830,8332],{},[1189,8334,8336],{"id":8335},"三生成对抗网络gan","三、生成对抗网络（GAN）",[1194,8338,8340],{"id":8339},"_31-基本思想","3.1 基本思想",[1091,8342,8343],{},"GAN 的核心思想来源于博弈论：训练两个相互对抗的网络。",[1091,8345,8346],{},[1172,8347,8348],{},"生成器 G（Generator）",[1166,8350,8351,8463,8511],{},[1169,8352,8353,8354,8462],{},"输入：随机噪声 ",[1095,8355,8357,8385],{"className":8356},[1098],[1095,8358,8360],{"className":8359},[1102],[1104,8361,8362],{"xmlns":1106},[1108,8363,8364,8382],{},[1111,8365,8366,8368,8370,8376,8378,8380],{},[1114,8367,1352],{},[1118,8369,2585],{},[1465,8371,8372,8374],{},[1114,8373,1091],{},[1114,8375,1352],{},[1118,8377,1121],{"stretchy":1120},[1114,8379,1352],{},[1118,8381,1127],{"stretchy":1120},[1129,8383,8384],{"encoding":1131},"z \\sim p_z(z)",[1095,8386,8388,8406],{"className":8387,"ariaHidden":1137},[1136],[1095,8389,8391,8394,8397,8400,8403],{"className":8390},[1141],[1095,8392],{"className":8393,"style":1885},[1145],[1095,8395,1352],{"className":8396,"style":1388},[1150,1151],[1095,8398],{"className":8399,"style":1542},[1383],[1095,8401,2585],{"className":8402},[1546],[1095,8404],{"className":8405,"style":1542},[1383],[1095,8407,8409,8412,8453,8456,8459],{"className":8408},[1141],[1095,8410],{"className":8411,"style":1146},[1145],[1095,8413,8415,8418],{"className":8414},[1150],[1095,8416,1091],{"className":8417},[1150,1151],[1095,8419,8421],{"className":8420},[1570],[1095,8422,8424,8445],{"className":8423},[1574,1575],[1095,8425,8427,8442],{"className":8426},[1579],[1095,8428,8431],{"className":8429,"style":8430},[1583],"height:0.1514em;",[1095,8432,8433,8436],{"style":1647},[1095,8434],{"className":8435,"style":1592},[1591],[1095,8437,8439],{"className":8438},[1596,1597,1598,1599],[1095,8440,1352],{"className":8441,"style":1388},[1150,1151,1599],[1095,8443,1607],{"className":8444},[1606],[1095,8446,8448],{"className":8447},[1579],[1095,8449,8451],{"className":8450,"style":1666},[1583],[1095,8452],{},[1095,8454,1121],{"className":8455},[1156],[1095,8457,1352],{"className":8458,"style":1388},[1150,1151],[1095,8460,1127],{"className":8461},[1163],"（通常为高斯或均匀分布）",[1169,8464,8465,8466],{},"输出：伪造样本 ",[1095,8467,8469,8490],{"className":8468},[1098],[1095,8470,8472],{"className":8471},[1102],[1104,8473,8474],{"xmlns":1106},[1108,8475,8476,8487],{},[1111,8477,8478,8481,8483,8485],{},[1114,8479,8480],{},"G",[1118,8482,1121],{"stretchy":1120},[1114,8484,1352],{},[1118,8486,1127],{"stretchy":1120},[1129,8488,8489],{"encoding":1131},"G(z)",[1095,8491,8493],{"className":8492,"ariaHidden":1137},[1136],[1095,8494,8496,8499,8502,8505,8508],{"className":8495},[1141],[1095,8497],{"className":8498,"style":1146},[1145],[1095,8500,8480],{"className":8501},[1150,1151],[1095,8503,1121],{"className":8504},[1156],[1095,8506,1352],{"className":8507,"style":1388},[1150,1151],[1095,8509,1127],{"className":8510},[1163],[1169,8512,8513],{},"目标：生成尽可能逼真的样本，欺骗判别器",[1091,8515,8516],{},[1172,8517,8518],{},"判别器 D（Discriminator）",[1166,8520,8521,8567,8660],{},[1169,8522,8523,8524],{},"输入：真实样本 x 或生成样本 ",[1095,8525,8527,8546],{"className":8526},[1098],[1095,8528,8530],{"className":8529},[1102],[1104,8531,8532],{"xmlns":1106},[1108,8533,8534,8544],{},[1111,8535,8536,8538,8540,8542],{},[1114,8537,8480],{},[1118,8539,1121],{"stretchy":1120},[1114,8541,1352],{},[1118,8543,1127],{"stretchy":1120},[1129,8545,8489],{"encoding":1131},[1095,8547,8549],{"className":8548,"ariaHidden":1137},[1136],[1095,8550,8552,8555,8558,8561,8564],{"className":8551},[1141],[1095,8553],{"className":8554,"style":1146},[1145],[1095,8556,8480],{"className":8557},[1150,1151],[1095,8559,1121],{"className":8560},[1156],[1095,8562,1352],{"className":8563,"style":1388},[1150,1151],[1095,8565,1127],{"className":8566},[1163],[1169,8568,8569,8570],{},"输出：样本为真实的概率 ",[1095,8571,8573,8606],{"className":8572},[1098],[1095,8574,8576],{"className":8575},[1102],[1104,8577,8578],{"xmlns":1106},[1108,8579,8580,8603],{},[1111,8581,8582,8584,8586,8588,8590,8593,8595,8597,8599,8601],{},[1114,8583,3738],{},[1118,8585,1121],{"stretchy":1120},[1114,8587,1124],{},[1118,8589,1127],{"stretchy":1120},[1118,8591,8592],{},"∈",[1118,8594,3685],{"stretchy":1120},[1490,8596,2603],{},[1118,8598,1349],{"separator":1137},[1490,8600,1492],{},[1118,8602,3730],{"stretchy":1120},[1129,8604,8605],{"encoding":1131},"D(x) \\in [0, 1]",[1095,8607,8609,8636],{"className":8608,"ariaHidden":1137},[1136],[1095,8610,8612,8615,8618,8621,8624,8627,8630,8633],{"className":8611},[1141],[1095,8613],{"className":8614,"style":1146},[1145],[1095,8616,3738],{"className":8617,"style":1936},[1150,1151],[1095,8619,1121],{"className":8620},[1156],[1095,8622,1124],{"className":8623},[1150,1151],[1095,8625,1127],{"className":8626},[1163],[1095,8628],{"className":8629,"style":1542},[1383],[1095,8631,8592],{"className":8632},[1546],[1095,8634],{"className":8635,"style":1542},[1383],[1095,8637,8639,8642,8645,8648,8651,8654,8657],{"className":8638},[1141],[1095,8640],{"className":8641,"style":1146},[1145],[1095,8643,3685],{"className":8644},[1156],[1095,8646,2603],{"className":8647},[1150],[1095,8649,1349],{"className":8650},[1379],[1095,8652],{"className":8653,"style":1384},[1383],[1095,8655,1492],{"className":8656},[1150],[1095,8658,3730],{"className":8659},[1163],[1169,8661,8662],{},"目标：准确区分真实样本和伪造样本",[1194,8664,8666],{"id":8665},"_32-目标函数minimax-game","3.2 目标函数（Minimax Game）",[1091,8668,8669],{},[1172,8670,8671],{},"GAN 目标函数",[1091,8673,8674],{},[1095,8675,8677,8827],{"className":8676},[1098],[1095,8678,8680],{"className":8679},[1102],[1104,8681,8682],{"xmlns":1106},[1108,8683,8684,8824],{},[1111,8685,8686,8697,8708,8710,8712,8714,8716,8718,8720,8722,8754,8756,8758,8760,8762,8764,8766,8768,8770,8772,8794,8796,8798,8800,8802,8804,8806,8808,8810,8812,8814,8816,8818,8820,8822],{},[1465,8687,8688,8695],{},[1111,8689,8690,8693],{},[1114,8691,8692],{},"min",[1118,8694,3643],{},[1114,8696,8480],{},[1465,8698,8699,8706],{},[1111,8700,8701,8704],{},[1114,8702,8703],{},"max",[1118,8705,3643],{},[1114,8707,3738],{},[1114,8709,6804],{},[1118,8711,1121],{"stretchy":1120},[1114,8713,3738],{},[1118,8715,1349],{"separator":1137},[1114,8717,8480],{},[1118,8719,1127],{"stretchy":1120},[1118,8721,1463],{},[1465,8723,8724,8726],{},[1114,8725,2138],{"mathvariant":3662},[1111,8727,8728,8730,8732,8748,8750,8752],{},[1114,8729,1124],{},[1118,8731,2585],{},[1465,8733,8734,8736],{},[1114,8735,1091],{},[1111,8737,8738,8740,8743,8746],{},[1114,8739,2875],{},[1114,8741,8742],{},"a",[1114,8744,8745],{},"t",[1114,8747,8742],{},[1118,8749,1121],{"stretchy":1120},[1114,8751,1124],{},[1118,8753,1127],{"stretchy":1120},[1118,8755,3685],{"stretchy":1120},[1114,8757,3640],{},[1118,8759,3643],{},[1114,8761,3738],{},[1118,8763,1121],{"stretchy":1120},[1114,8765,1124],{},[1118,8767,1127],{"stretchy":1120},[1118,8769,3730],{"stretchy":1120},[1118,8771,3733],{},[1465,8773,8774,8776],{},[1114,8775,2138],{"mathvariant":3662},[1111,8777,8778,8780,8782,8788,8790,8792],{},[1114,8779,1352],{},[1118,8781,2585],{},[1465,8783,8784,8786],{},[1114,8785,1091],{},[1114,8787,1352],{},[1118,8789,1121],{"stretchy":1120},[1114,8791,1352],{},[1118,8793,1127],{"stretchy":1120},[1118,8795,3685],{"stretchy":1120},[1114,8797,3640],{},[1118,8799,3643],{},[1118,8801,1121],{"stretchy":1120},[1490,8803,1492],{},[1118,8805,1510],{},[1114,8807,3738],{},[1118,8809,1121],{"stretchy":1120},[1114,8811,8480],{},[1118,8813,1121],{"stretchy":1120},[1114,8815,1352],{},[1118,8817,1127],{"stretchy":1120},[1118,8819,1127],{"stretchy":1120},[1118,8821,1127],{"stretchy":1120},[1118,8823,3730],{"stretchy":1120},[1129,8825,8826],{"encoding":1131},"\\min_G \\max_D V(D, G) = \\mathbb{E}_{x \\sim p_{data}(x)}[\\log D(x)] + \\mathbb{E}_{z \\sim p_z(z)}[\\log(1 - D(G(z)))]",[1095,8828,8830,8953,9100,9227],{"className":8829,"ariaHidden":1137},[1136],[1095,8831,8833,8836,8877,8880,8920,8923,8926,8929,8932,8935,8938,8941,8944,8947,8950],{"className":8832},[1141],[1095,8834],{"className":8835,"style":1146},[1145],[1095,8837,8839,8842],{"className":8838},[1560],[1095,8840,8692],{"className":8841},[1560],[1095,8843,8845],{"className":8844},[1570],[1095,8846,8848,8869],{"className":8847},[1574,1575],[1095,8849,8851,8866],{"className":8850},[1579],[1095,8852,8854],{"className":8853,"style":2210},[1583],[1095,8855,8857,8860],{"style":8856},"top:-2.55em;margin-right:0.05em;",[1095,8858],{"className":8859,"style":1592},[1591],[1095,8861,8863],{"className":8862},[1596,1597,1598,1599],[1095,8864,8480],{"className":8865},[1150,1151,1599],[1095,8867,1607],{"className":8868},[1606],[1095,8870,8872],{"className":8871},[1579],[1095,8873,8875],{"className":8874,"style":1666},[1583],[1095,8876],{},[1095,8878],{"className":8879,"style":1384},[1383],[1095,8881,8883,8886],{"className":8882},[1560],[1095,8884,8703],{"className":8885},[1560],[1095,8887,8889],{"className":8888},[1570],[1095,8890,8892,8912],{"className":8891},[1574,1575],[1095,8893,8895,8909],{"className":8894},[1579],[1095,8896,8898],{"className":8897,"style":2210},[1583],[1095,8899,8900,8903],{"style":8856},[1095,8901],{"className":8902,"style":1592},[1591],[1095,8904,8906],{"className":8905},[1596,1597,1598,1599],[1095,8907,3738],{"className":8908,"style":1936},[1150,1151,1599],[1095,8910,1607],{"className":8911},[1606],[1095,8913,8915],{"className":8914},[1579],[1095,8916,8918],{"className":8917,"style":1666},[1583],[1095,8919],{},[1095,8921],{"className":8922,"style":1384},[1383],[1095,8924,6804],{"className":8925,"style":2264},[1150,1151],[1095,8927,1121],{"className":8928},[1156],[1095,8930,3738],{"className":8931,"style":1936},[1150,1151],[1095,8933,1349],{"className":8934},[1379],[1095,8936],{"className":8937,"style":1384},[1383],[1095,8939,8480],{"className":8940},[1150,1151],[1095,8942,1127],{"className":8943},[1163],[1095,8945],{"className":8946,"style":1542},[1383],[1095,8948,1463],{"className":8949},[1546],[1095,8951],{"className":8952,"style":1542},[1383],[1095,8954,8956,8960,9068,9071,9076,9079,9082,9085,9088,9091,9094,9097],{"className":8955},[1141],[1095,8957],{"className":8958,"style":8959},[1145],"height:1.1052em;vertical-align:-0.3552em;",[1095,8961,8963,8966],{"className":8962},[1150],[1095,8964,2138],{"className":8965},[1150,3877],[1095,8967,8969],{"className":8968},[1570],[1095,8970,8972,9059],{"className":8971},[1574,1575],[1095,8973,8975,9056],{"className":8974},[1579],[1095,8976,8978],{"className":8977,"style":3279},[1583],[1095,8979,8980,8983],{"style":3892},[1095,8981],{"className":8982,"style":1592},[1591],[1095,8984,8986],{"className":8985},[1596,1597,1598,1599],[1095,8987,8989,8992,8995,9047,9050,9053],{"className":8988},[1150,1599],[1095,8990,1124],{"className":8991},[1150,1151,1599],[1095,8993,2585],{"className":8994},[1546,1599],[1095,8996,8998,9001],{"className":8997},[1150,1599],[1095,8999,1091],{"className":9000},[1150,1151,1599],[1095,9002,9004],{"className":9003},[1570],[1095,9005,9007,9039],{"className":9006},[1574,1575],[1095,9008,9010,9036],{"className":9009},[1579],[1095,9011,9013],{"className":9012,"style":3279},[1583],[1095,9014,9015,9018],{"style":3282},[1095,9016],{"className":9017,"style":3286},[1591],[1095,9019,9021],{"className":9020},[1596,3290,3291,1599],[1095,9022,9024,9027,9030,9033],{"className":9023},[1150,1599],[1095,9025,2875],{"className":9026},[1150,1151,1599],[1095,9028,8742],{"className":9029},[1150,1151,1599],[1095,9031,8745],{"className":9032},[1150,1151,1599],[1095,9034,8742],{"className":9035},[1150,1151,1599],[1095,9037,1607],{"className":9038},[1606],[1095,9040,9042],{"className":9041},[1579],[1095,9043,9045],{"className":9044,"style":3304},[1583],[1095,9046],{},[1095,9048,1121],{"className":9049},[1156,1599],[1095,9051,1124],{"className":9052},[1150,1151,1599],[1095,9054,1127],{"className":9055},[1163,1599],[1095,9057,1607],{"className":9058},[1606],[1095,9060,9062],{"className":9061},[1579],[1095,9063,9066],{"className":9064,"style":9065},[1583],"height:0.3552em;",[1095,9067],{},[1095,9069,3685],{"className":9070},[1156],[1095,9072,3799,9074],{"className":9073},[1560],[1095,9075,1984],{"style":3802},[1095,9077],{"className":9078,"style":1384},[1383],[1095,9080,3738],{"className":9081,"style":1936},[1150,1151],[1095,9083,1121],{"className":9084},[1156],[1095,9086,1124],{"className":9087},[1150,1151],[1095,9089,4869],{"className":9090},[1163],[1095,9092],{"className":9093,"style":2264},[1383],[1095,9095,3733],{"className":9096},[1779],[1095,9098],{"className":9099,"style":2264},[1383],[1095,9101,9103,9106,9204,9207,9212,9215,9218,9221,9224],{"className":9102},[1141],[1095,9104],{"className":9105,"style":8959},[1145],[1095,9107,9109,9112],{"className":9108},[1150],[1095,9110,2138],{"className":9111},[1150,3877],[1095,9113,9115],{"className":9114},[1570],[1095,9116,9118,9196],{"className":9117},[1574,1575],[1095,9119,9121,9193],{"className":9120},[1579],[1095,9122,9124],{"className":9123,"style":3279},[1583],[1095,9125,9126,9129],{"style":3892},[1095,9127],{"className":9128,"style":1592},[1591],[1095,9130,9132],{"className":9131},[1596,1597,1598,1599],[1095,9133,9135,9138,9141,9184,9187,9190],{"className":9134},[1150,1599],[1095,9136,1352],{"className":9137,"style":1388},[1150,1151,1599],[1095,9139,2585],{"className":9140},[1546,1599],[1095,9142,9144,9147],{"className":9143},[1150,1599],[1095,9145,1091],{"className":9146},[1150,1151,1599],[1095,9148,9150],{"className":9149},[1570],[1095,9151,9153,9175],{"className":9152},[1574,1575],[1095,9154,9156,9172],{"className":9155},[1579],[1095,9157,9160],{"className":9158,"style":9159},[1583],"height:0.1645em;",[1095,9161,9163,9166],{"style":9162},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[1095,9164],{"className":9165,"style":3286},[1591],[1095,9167,9169],{"className":9168},[1596,3290,3291,1599],[1095,9170,1352],{"className":9171,"style":1388},[1150,1151,1599],[1095,9173,1607],{"className":9174},[1606],[1095,9176,9178],{"className":9177},[1579],[1095,9179,9182],{"className":9180,"style":9181},[1583],"height:0.143em;",[1095,9183],{},[1095,9185,1121],{"className":9186},[1156,1599],[1095,9188,1352],{"className":9189,"style":1388},[1150,1151,1599],[1095,9191,1127],{"className":9192},[1163,1599],[1095,9194,1607],{"className":9195},[1606],[1095,9197,9199],{"className":9198},[1579],[1095,9200,9202],{"className":9201,"style":9065},[1583],[1095,9203],{},[1095,9205,3685],{"className":9206},[1156],[1095,9208,3799,9210],{"className":9209},[1560],[1095,9211,1984],{"style":3802},[1095,9213,1121],{"className":9214},[1156],[1095,9216,1492],{"className":9217},[1150],[1095,9219],{"className":9220,"style":2264},[1383],[1095,9222,1510],{"className":9223},[1779],[1095,9225],{"className":9226,"style":2264},[1383],[1095,9228,9230,9233,9236,9239,9242,9245,9248],{"className":9229},[1141],[1095,9231],{"className":9232,"style":1146},[1145],[1095,9234,3738],{"className":9235,"style":1936},[1150,1151],[1095,9237,1121],{"className":9238},[1156],[1095,9240,8480],{"className":9241},[1150,1151],[1095,9243,1121],{"className":9244},[1156],[1095,9246,1352],{"className":9247,"style":1388},[1150,1151],[1095,9249,9251],{"className":9250},[1163],")))]",[1166,9253,9254,9318],{},[1169,9255,9256,9257,9260,9317],{},"判别器 D 试图",[1172,9258,9259],{},"最大化",[1095,9261,9263,9287],{"className":9262},[1098],[1095,9264,9266],{"className":9265},[1102],[1104,9267,9268],{"xmlns":1106},[1108,9269,9270,9284],{},[1111,9271,9272,9274,9276,9278,9280,9282],{},[1114,9273,6804],{},[1118,9275,1121],{"stretchy":1120},[1114,9277,3738],{},[1118,9279,1349],{"separator":1137},[1114,9281,8480],{},[1118,9283,1127],{"stretchy":1120},[1129,9285,9286],{"encoding":1131},"V(D,G)",[1095,9288,9290],{"className":9289,"ariaHidden":1137},[1136],[1095,9291,9293,9296,9299,9302,9305,9308,9311,9314],{"className":9292},[1141],[1095,9294],{"className":9295,"style":1146},[1145],[1095,9297,6804],{"className":9298,"style":2264},[1150,1151],[1095,9300,1121],{"className":9301},[1156],[1095,9303,3738],{"className":9304,"style":1936},[1150,1151],[1095,9306,1349],{"className":9307},[1379],[1095,9309],{"className":9310,"style":1384},[1383],[1095,9312,8480],{"className":9313},[1150,1151],[1095,9315,1127],{"className":9316},[1163],"：正确分类真假样本",[1169,9319,9320,9321,9324,9380,9381,9437],{},"生成器 G 试图",[1172,9322,9323],{},"最小化",[1095,9325,9327,9350],{"className":9326},[1098],[1095,9328,9330],{"className":9329},[1102],[1104,9331,9332],{"xmlns":1106},[1108,9333,9334,9348],{},[1111,9335,9336,9338,9340,9342,9344,9346],{},[1114,9337,6804],{},[1118,9339,1121],{"stretchy":1120},[1114,9341,3738],{},[1118,9343,1349],{"separator":1137},[1114,9345,8480],{},[1118,9347,1127],{"stretchy":1120},[1129,9349,9286],{"encoding":1131},[1095,9351,9353],{"className":9352,"ariaHidden":1137},[1136],[1095,9354,9356,9359,9362,9365,9368,9371,9374,9377],{"className":9355},[1141],[1095,9357],{"className":9358,"style":1146},[1145],[1095,9360,6804],{"className":9361,"style":2264},[1150,1151],[1095,9363,1121],{"className":9364},[1156],[1095,9366,3738],{"className":9367,"style":1936},[1150,1151],[1095,9369,1349],{"className":9370},[1379],[1095,9372],{"className":9373,"style":1384},[1383],[1095,9375,8480],{"className":9376},[1150,1151],[1095,9378,1127],{"className":9379},[1163],"：让 ",[1095,9382,9384,9410],{"className":9383},[1098],[1095,9385,9387],{"className":9386},[1102],[1104,9388,9389],{"xmlns":1106},[1108,9390,9391,9407],{},[1111,9392,9393,9395,9397,9399,9401,9403,9405],{},[1114,9394,3738],{},[1118,9396,1121],{"stretchy":1120},[1114,9398,8480],{},[1118,9400,1121],{"stretchy":1120},[1114,9402,1352],{},[1118,9404,1127],{"stretchy":1120},[1118,9406,1127],{"stretchy":1120},[1129,9408,9409],{"encoding":1131},"D(G(z))",[1095,9411,9413],{"className":9412,"ariaHidden":1137},[1136],[1095,9414,9416,9419,9422,9425,9428,9431,9434],{"className":9415},[1141],[1095,9417],{"className":9418,"style":1146},[1145],[1095,9420,3738],{"className":9421,"style":1936},[1150,1151],[1095,9423,1121],{"className":9424},[1156],[1095,9426,8480],{"className":9427},[1150,1151],[1095,9429,1121],{"className":9430},[1156],[1095,9432,1352],{"className":9433,"style":1388},[1150,1151],[1095,9435,2370],{"className":9436},[1163]," 尽可能大",[1194,9439,9441],{"id":9440},"_33-最优判别器","3.3 最优判别器",[1091,9443,9444,9445,9502],{},"固定 G，对 ",[1095,9446,9448,9472],{"className":9447},[1098],[1095,9449,9451],{"className":9450},[1102],[1104,9452,9453],{"xmlns":1106},[1108,9454,9455,9469],{},[1111,9456,9457,9459,9461,9463,9465,9467],{},[1114,9458,6804],{},[1118,9460,1121],{"stretchy":1120},[1114,9462,3738],{},[1118,9464,1349],{"separator":1137},[1114,9466,8480],{},[1118,9468,1127],{"stretchy":1120},[1129,9470,9471],{"encoding":1131},"V(D, G)",[1095,9473,9475],{"className":9474,"ariaHidden":1137},[1136],[1095,9476,9478,9481,9484,9487,9490,9493,9496,9499],{"className":9477},[1141],[1095,9479],{"className":9480,"style":1146},[1145],[1095,9482,6804],{"className":9483,"style":2264},[1150,1151],[1095,9485,1121],{"className":9486},[1156],[1095,9488,3738],{"className":9489,"style":1936},[1150,1151],[1095,9491,1349],{"className":9492},[1379],[1095,9494],{"className":9495,"style":1384},[1383],[1095,9497,8480],{"className":9498},[1150,1151],[1095,9500,1127],{"className":9501},[1163]," 关于 D 求最优解：",[1091,9504,9505],{},[1095,9506,9508,9595],{"className":9507},[1098],[1095,9509,9511],{"className":9510},[1102],[1104,9512,9513],{"xmlns":1106},[1108,9514,9515,9592],{},[1111,9516,9517,9524,9526,9528,9530,9532],{},[2171,9518,9519,9521],{},[1114,9520,3738],{},[1118,9522,9523],{},"∗",[1118,9525,1121],{"stretchy":1120},[1114,9527,1124],{},[1118,9529,1127],{"stretchy":1120},[1118,9531,1463],{},[3104,9533,9534,9556],{},[1111,9535,9536,9550,9552,9554],{},[1465,9537,9538,9540],{},[1114,9539,1091],{},[1111,9541,9542,9544,9546,9548],{},[1114,9543,2875],{},[1114,9545,8742],{},[1114,9547,8745],{},[1114,9549,8742],{},[1118,9551,1121],{"stretchy":1120},[1114,9553,1124],{},[1118,9555,1127],{"stretchy":1120},[1111,9557,9558,9572,9574,9576,9578,9580,9586,9588,9590],{},[1465,9559,9560,9562],{},[1114,9561,1091],{},[1111,9563,9564,9566,9568,9570],{},[1114,9565,2875],{},[1114,9567,8742],{},[1114,9569,8745],{},[1114,9571,8742],{},[1118,9573,1121],{"stretchy":1120},[1114,9575,1124],{},[1118,9577,1127],{"stretchy":1120},[1118,9579,3733],{},[1465,9581,9582,9584],{},[1114,9583,1091],{},[1114,9585,1984],{},[1118,9587,1121],{"stretchy":1120},[1114,9589,1124],{},[1118,9591,1127],{"stretchy":1120},[1129,9593,9594],{"encoding":1131},"D^*(x) = \\frac{p_{data}(x)}{p_{data}(x) + p_g(x)}",[1095,9596,9598,9652],{"className":9597,"ariaHidden":1137},[1136],[1095,9599,9601,9604,9634,9637,9640,9643,9646,9649],{"className":9600},[1141],[1095,9602],{"className":9603,"style":1146},[1145],[1095,9605,9607,9610],{"className":9606},[1150],[1095,9608,3738],{"className":9609,"style":1936},[1150,1151],[1095,9611,9613],{"className":9612},[1570],[1095,9614,9616],{"className":9615},[1574],[1095,9617,9619],{"className":9618},[1579],[1095,9620,9623],{"className":9621,"style":9622},[1583],"height:0.6887em;",[1095,9624,9625,9628],{"style":2392},[1095,9626],{"className":9627,"style":1592},[1591],[1095,9629,9631],{"className":9630},[1596,1597,1598,1599],[1095,9632,9523],{"className":9633},[1779,1599],[1095,9635,1121],{"className":9636},[1156],[1095,9638,1124],{"className":9639},[1150,1151],[1095,9641,1127],{"className":9642},[1163],[1095,9644],{"className":9645,"style":1542},[1383],[1095,9647,1463],{"className":9648},[1546],[1095,9650],{"className":9651,"style":1542},[1383],[1095,9653,9655,9659],{"className":9654},[1141],[1095,9656],{"className":9657,"style":9658},[1145],"height:1.5523em;vertical-align:-0.5423em;",[1095,9660,9662,9665,9894],{"className":9661},[1150],[1095,9663],{"className":9664},[1156,3235],[1095,9666,9668],{"className":9667},[3104],[1095,9669,9671,9885],{"className":9670},[1574,1575],[1095,9672,9674,9882],{"className":9673},[1579],[1095,9675,9677,9802,9810],{"className":9676,"style":3248},[1583],[1095,9678,9679,9682],{"style":3251},[1095,9680],{"className":9681,"style":2026},[1591],[1095,9683,9685],{"className":9684},[1596,1597,1598,1599],[1095,9686,9688,9740,9743,9746,9749,9752,9793,9796,9799],{"className":9687},[1150,1599],[1095,9689,9691,9694],{"className":9690},[1150,1599],[1095,9692,1091],{"className":9693},[1150,1151,1599],[1095,9695,9697],{"className":9696},[1570],[1095,9698,9700,9732],{"className":9699},[1574,1575],[1095,9701,9703,9729],{"className":9702},[1579],[1095,9704,9706],{"className":9705,"style":3279},[1583],[1095,9707,9708,9711],{"style":3282},[1095,9709],{"className":9710,"style":3286},[1591],[1095,9712,9714],{"className":9713},[1596,3290,3291,1599],[1095,9715,9717,9720,9723,9726],{"className":9716},[1150,1599],[1095,9718,2875],{"className":9719},[1150,1151,1599],[1095,9721,8742],{"className":9722},[1150,1151,1599],[1095,9724,8745],{"className":9725},[1150,1151,1599],[1095,9727,8742],{"className":9728},[1150,1151,1599],[1095,9730,1607],{"className":9731},[1606],[1095,9733,9735],{"className":9734},[1579],[1095,9736,9738],{"className":9737,"style":3304},[1583],[1095,9739],{},[1095,9741,1121],{"className":9742},[1156,1599],[1095,9744,1124],{"className":9745},[1150,1151,1599],[1095,9747,1127],{"className":9748},[1163,1599],[1095,9750,3733],{"className":9751},[1779,1599],[1095,9753,9755,9758],{"className":9754},[1150,1599],[1095,9756,1091],{"className":9757},[1150,1151,1599],[1095,9759,9761],{"className":9760},[1570],[1095,9762,9764,9784],{"className":9763},[1574,1575],[1095,9765,9767,9781],{"className":9766},[1579],[1095,9768,9770],{"className":9769,"style":9159},[1583],[1095,9771,9772,9775],{"style":9162},[1095,9773],{"className":9774,"style":3286},[1591],[1095,9776,9778],{"className":9777},[1596,3290,3291,1599],[1095,9779,1984],{"className":9780,"style":1256},[1150,1151,1599],[1095,9782,1607],{"className":9783},[1606],[1095,9785,9787],{"className":9786},[1579],[1095,9788,9791],{"className":9789,"style":9790},[1583],"height:0.2819em;",[1095,9792],{},[1095,9794,1121],{"className":9795},[1156,1599],[1095,9797,1124],{"className":9798},[1150,1151,1599],[1095,9800,1127],{"className":9801},[1163,1599],[1095,9803,9804,9807],{"style":3318},[1095,9805],{"className":9806,"style":2026},[1591],[1095,9808],{"className":9809,"style":3326},[3325],[1095,9811,9812,9815],{"style":3329},[1095,9813],{"className":9814,"style":2026},[1591],[1095,9816,9818],{"className":9817},[1596,1597,1598,1599],[1095,9819,9821,9873,9876,9879],{"className":9820},[1150,1599],[1095,9822,9824,9827],{"className":9823},[1150,1599],[1095,9825,1091],{"className":9826},[1150,1151,1599],[1095,9828,9830],{"className":9829},[1570],[1095,9831,9833,9865],{"className":9832},[1574,1575],[1095,9834,9836,9862],{"className":9835},[1579],[1095,9837,9839],{"className":9838,"style":3279},[1583],[1095,9840,9841,9844],{"style":3282},[1095,9842],{"className":9843,"style":3286},[1591],[1095,9845,9847],{"className":9846},[1596,3290,3291,1599],[1095,9848,9850,9853,9856,9859],{"className":9849},[1150,1599],[1095,9851,2875],{"className":9852},[1150,1151,1599],[1095,9854,8742],{"className":9855},[1150,1151,1599],[1095,9857,8745],{"className":9858},[1150,1151,1599],[1095,9860,8742],{"className":9861},[1150,1151,1599],[1095,9863,1607],{"className":9864},[1606],[1095,9866,9868],{"className":9867},[1579],[1095,9869,9871],{"className":9870,"style":3304},[1583],[1095,9872],{},[1095,9874,1121],{"className":9875},[1156,1599],[1095,9877,1124],{"className":9878},[1150,1151,1599],[1095,9880,1127],{"className":9881},[1163,1599],[1095,9883,1607],{"className":9884},[1606],[1095,9886,9888],{"className":9887},[1579],[1095,9889,9892],{"className":9890,"style":9891},[1583],"height:0.5423em;",[1095,9893],{},[1095,9895],{"className":9896},[1163,3235],[1091,9898,9899,9902,9903,9931,9932,9976,9977,10266],{},[1172,9900,9901],{},"推导","：对于任意 x，",[1095,9904,9906,9919],{"className":9905},[1098],[1095,9907,9909],{"className":9908},[1102],[1104,9910,9911],{"xmlns":1106},[1108,9912,9913,9917],{},[1111,9914,9915],{},[1114,9916,6804],{},[1129,9918,6804],{"encoding":1131},[1095,9920,9922],{"className":9921,"ariaHidden":1137},[1136],[1095,9923,9925,9928],{"className":9924},[1141],[1095,9926],{"className":9927,"style":5154},[1145],[1095,9929,6804],{"className":9930,"style":2264},[1150,1151]," 关于 ",[1095,9933,9935,9955],{"className":9934},[1098],[1095,9936,9938],{"className":9937},[1102],[1104,9939,9940],{"xmlns":1106},[1108,9941,9942,9952],{},[1111,9943,9944,9946,9948,9950],{},[1114,9945,3738],{},[1118,9947,1121],{"stretchy":1120},[1114,9949,1124],{},[1118,9951,1127],{"stretchy":1120},[1129,9953,9954],{"encoding":1131},"D(x)",[1095,9956,9958],{"className":9957,"ariaHidden":1137},[1136],[1095,9959,9961,9964,9967,9970,9973],{"className":9960},[1141],[1095,9962],{"className":9963,"style":1146},[1145],[1095,9965,3738],{"className":9966,"style":1936},[1150,1151],[1095,9968,1121],{"className":9969},[1156],[1095,9971,1124],{"className":9972},[1150,1151],[1095,9974,1127],{"className":9975},[1163]," 的被积函数为 ",[1095,9978,9980,10056],{"className":9979},[1098],[1095,9981,9983],{"className":9982},[1102],[1104,9984,9985],{"xmlns":1106},[1108,9986,9987,10053],{},[1111,9988,9989,9991,9993,9995,9997,9999,10013,10015,10017,10019,10021,10023,10025,10027,10033,10035,10037,10039,10041,10043,10045,10047,10049,10051],{},[1114,9990,1863],{},[1118,9992,1121],{"stretchy":1120},[1114,9994,3738],{},[1118,9996,1127],{"stretchy":1120},[1118,9998,1463],{},[1465,10000,10001,10003],{},[1114,10002,1091],{},[1111,10004,10005,10007,10009,10011],{},[1114,10006,2875],{},[1114,10008,8742],{},[1114,10010,8745],{},[1114,10012,8742],{},[1118,10014,1121],{"stretchy":1120},[1114,10016,1124],{},[1118,10018,1127],{"stretchy":1120},[1114,10020,3640],{},[1118,10022,3643],{},[1114,10024,3738],{},[1118,10026,3733],{},[1465,10028,10029,10031],{},[1114,10030,1091],{},[1114,10032,1984],{},[1118,10034,1121],{"stretchy":1120},[1114,10036,1124],{},[1118,10038,1127],{"stretchy":1120},[1114,10040,3640],{},[1118,10042,3643],{},[1118,10044,1121],{"stretchy":1120},[1490,10046,1492],{},[1118,10048,1510],{},[1114,10050,3738],{},[1118,10052,1127],{"stretchy":1120},[1129,10054,10055],{"encoding":1131},"f(D) = p_{data}(x)\\log D + p_g(x)\\log(1-D)",[1095,10057,10059,10086,10176,10254],{"className":10058,"ariaHidden":1137},[1136],[1095,10060,10062,10065,10068,10071,10074,10077,10080,10083],{"className":10061},[1141],[1095,10063],{"className":10064,"style":1146},[1145],[1095,10066,1863],{"className":10067,"style":1910},[1150,1151],[1095,10069,1121],{"className":10070},[1156],[1095,10072,3738],{"className":10073,"style":1936},[1150,1151],[1095,10075,1127],{"className":10076},[1163],[1095,10078],{"className":10079,"style":1542},[1383],[1095,10081,1463],{"className":10082},[1546],[1095,10084],{"className":10085,"style":1542},[1383],[1095,10087,10089,10092,10144,10147,10150,10153,10156,10161,10164,10167,10170,10173],{"className":10088},[1141],[1095,10090],{"className":10091,"style":1146},[1145],[1095,10093,10095,10098],{"className":10094},[1150],[1095,10096,1091],{"className":10097},[1150,1151],[1095,10099,10101],{"className":10100},[1570],[1095,10102,10104,10136],{"className":10103},[1574,1575],[1095,10105,10107,10133],{"className":10106},[1579],[1095,10108,10110],{"className":10109,"style":1923},[1583],[1095,10111,10112,10115],{"style":1647},[1095,10113],{"className":10114,"style":1592},[1591],[1095,10116,10118],{"className":10117},[1596,1597,1598,1599],[1095,10119,10121,10124,10127,10130],{"className":10120},[1150,1599],[1095,10122,2875],{"className":10123},[1150,1151,1599],[1095,10125,8742],{"className":10126},[1150,1151,1599],[1095,10128,8745],{"className":10129},[1150,1151,1599],[1095,10131,8742],{"className":10132},[1150,1151,1599],[1095,10134,1607],{"className":10135},[1606],[1095,10137,10139],{"className":10138},[1579],[1095,10140,10142],{"className":10141,"style":1666},[1583],[1095,10143],{},[1095,10145,1121],{"className":10146},[1156],[1095,10148,1124],{"className":10149},[1150,1151],[1095,10151,1127],{"className":10152},[1163],[1095,10154],{"className":10155,"style":1384},[1383],[1095,10157,3799,10159],{"className":10158},[1560],[1095,10160,1984],{"style":3802},[1095,10162],{"className":10163,"style":1384},[1383],[1095,10165,3738],{"className":10166,"style":1936},[1150,1151],[1095,10168],{"className":10169,"style":2264},[1383],[1095,10171,3733],{"className":10172},[1779],[1095,10174],{"className":10175,"style":2264},[1383],[1095,10177,10179,10182,10222,10225,10228,10231,10234,10239,10242,10245,10248,10251],{"className":10178},[1141],[1095,10180],{"className":10181,"style":2058},[1145],[1095,10183,10185,10188],{"className":10184},[1150],[1095,10186,1091],{"className":10187},[1150,1151],[1095,10189,10191],{"className":10190},[1570],[1095,10192,10194,10214],{"className":10193},[1574,1575],[1095,10195,10197,10211],{"className":10196},[1579],[1095,10198,10200],{"className":10199,"style":8430},[1583],[1095,10201,10202,10205],{"style":1647},[1095,10203],{"className":10204,"style":1592},[1591],[1095,10206,10208],{"className":10207},[1596,1597,1598,1599],[1095,10209,1984],{"className":10210,"style":1256},[1150,1151,1599],[1095,10212,1607],{"className":10213},[1606],[1095,10215,10217],{"className":10216},[1579],[1095,10218,10220],{"className":10219,"style":2098},[1583],[1095,10221],{},[1095,10223,1121],{"className":10224},[1156],[1095,10226,1124],{"className":10227},[1150,1151],[1095,10229,1127],{"className":10230},[1163],[1095,10232],{"className":10233,"style":1384},[1383],[1095,10235,3799,10237],{"className":10236},[1560],[1095,10238,1984],{"style":3802},[1095,10240,1121],{"className":10241},[1156],[1095,10243,1492],{"className":10244},[1150],[1095,10246],{"className":10247,"style":2264},[1383],[1095,10249,1510],{"className":10250},[1779],[1095,10252],{"className":10253,"style":2264},[1383],[1095,10255,10257,10260,10263],{"className":10256},[1141],[1095,10258],{"className":10259,"style":1146},[1145],[1095,10261,3738],{"className":10262,"style":1936},[1150,1151],[1095,10264,1127],{"className":10265},[1163],"，对 D 求导令其为零：",[1091,10268,10269],{},[1095,10270,10272,10422],{"className":10271},[1098],[1095,10273,10275],{"className":10274},[1102],[1104,10276,10277],{"xmlns":1106},[1108,10278,10279,10419],{},[1111,10280,10281,10307,10309,10333,10335,10337,10340,10343,10345,10351,10353,10355,10357,10359],{},[3104,10282,10283,10305],{},[1111,10284,10285,10299,10301,10303],{},[1465,10286,10287,10289],{},[1114,10288,1091],{},[1111,10290,10291,10293,10295,10297],{},[1114,10292,2875],{},[1114,10294,8742],{},[1114,10296,8745],{},[1114,10298,8742],{},[1118,10300,1121],{"stretchy":1120},[1114,10302,1124],{},[1118,10304,1127],{"stretchy":1120},[1114,10306,3738],{},[1118,10308,1510],{},[3104,10310,10311,10325],{},[1111,10312,10313,10319,10321,10323],{},[1465,10314,10315,10317],{},[1114,10316,1091],{},[1114,10318,1984],{},[1118,10320,1121],{"stretchy":1120},[1114,10322,1124],{},[1118,10324,1127],{"stretchy":1120},[1111,10326,10327,10329,10331],{},[1490,10328,1492],{},[1118,10330,1510],{},[1114,10332,3738],{},[1118,10334,1463],{},[1490,10336,2603],{},[2870,10338,10339],{},"  ",[1118,10341,10342],{},"⟹",[2870,10344,10339],{},[2171,10346,10347,10349],{},[1114,10348,3738],{},[1118,10350,9523],{},[1118,10352,1121],{"stretchy":1120},[1114,10354,1124],{},[1118,10356,1127],{"stretchy":1120},[1118,10358,1463],{},[3104,10360,10361,10383],{},[1111,10362,10363,10377,10379,10381],{},[1465,10364,10365,10367],{},[1114,10366,1091],{},[1111,10368,10369,10371,10373,10375],{},[1114,10370,2875],{},[1114,10372,8742],{},[1114,10374,8745],{},[1114,10376,8742],{},[1118,10378,1121],{"stretchy":1120},[1114,10380,1124],{},[1118,10382,1127],{"stretchy":1120},[1111,10384,10385,10399,10401,10403,10405,10407,10413,10415,10417],{},[1465,10386,10387,10389],{},[1114,10388,1091],{},[1111,10390,10391,10393,10395,10397],{},[1114,10392,2875],{},[1114,10394,8742],{},[1114,10396,8745],{},[1114,10398,8742],{},[1118,10400,1121],{"stretchy":1120},[1114,10402,1124],{},[1118,10404,1127],{"stretchy":1120},[1118,10406,3733],{},[1465,10408,10409,10411],{},[1114,10410,1091],{},[1114,10412,1984],{},[1118,10414,1121],{"stretchy":1120},[1114,10416,1124],{},[1118,10418,1127],{"stretchy":1120},[1129,10420,10421],{"encoding":1131},"\\frac{p_{data}(x)}{D} - \\frac{p_g(x)}{1-D} = 0 \\implies D^*(x) = \\frac{p_{data}(x)}{p_{data}(x) + p_g(x)}",[1095,10423,10425,10567,10706,10731,10784],{"className":10424,"ariaHidden":1137},[1136],[1095,10426,10428,10432,10558,10561,10564],{"className":10427},[1141],[1095,10429],{"className":10430,"style":10431},[1145],"height:1.355em;vertical-align:-0.345em;",[1095,10433,10435,10438,10555],{"className":10434},[1150],[1095,10436],{"className":10437},[1156,3235],[1095,10439,10441],{"className":10440},[3104],[1095,10442,10444,10547],{"className":10443},[1574,1575],[1095,10445,10447,10544],{"className":10446},[1579],[1095,10448,10450,10464,10472],{"className":10449,"style":3248},[1583],[1095,10451,10452,10455],{"style":3251},[1095,10453],{"className":10454,"style":2026},[1591],[1095,10456,10458],{"className":10457},[1596,1597,1598,1599],[1095,10459,10461],{"className":10460},[1150,1599],[1095,10462,3738],{"className":10463,"style":1936},[1150,1151,1599],[1095,10465,10466,10469],{"style":3318},[1095,10467],{"className":10468,"style":2026},[1591],[1095,10470],{"className":10471,"style":3326},[3325],[1095,10473,10474,10477],{"style":3329},[1095,10475],{"className":10476,"style":2026},[1591],[1095,10478,10480],{"className":10479},[1596,1597,1598,1599],[1095,10481,10483,10535,10538,10541],{"className":10482},[1150,1599],[1095,10484,10486,10489],{"className":10485},[1150,1599],[1095,10487,1091],{"className":10488},[1150,1151,1599],[1095,10490,10492],{"className":10491},[1570],[1095,10493,10495,10527],{"className":10494},[1574,1575],[1095,10496,10498,10524],{"className":10497},[1579],[1095,10499,10501],{"className":10500,"style":3279},[1583],[1095,10502,10503,10506],{"style":3282},[1095,10504],{"className":10505,"style":3286},[1591],[1095,10507,10509],{"className":10508},[1596,3290,3291,1599],[1095,10510,10512,10515,10518,10521],{"className":10511},[1150,1599],[1095,10513,2875],{"className":10514},[1150,1151,1599],[1095,10516,8742],{"className":10517},[1150,1151,1599],[1095,10519,8745],{"className":10520},[1150,1151,1599],[1095,10522,8742],{"className":10523},[1150,1151,1599],[1095,10525,1607],{"className":10526},[1606],[1095,10528,10530],{"className":10529},[1579],[1095,10531,10533],{"className":10532,"style":3304},[1583],[1095,10534],{},[1095,10536,1121],{"className":10537},[1156,1599],[1095,10539,1124],{"className":10540},[1150,1151,1599],[1095,10542,1127],{"className":10543},[1163,1599],[1095,10545,1607],{"className":10546},[1606],[1095,10548,10550],{"className":10549},[1579],[1095,10551,10553],{"className":10552,"style":5866},[1583],[1095,10554],{},[1095,10556],{"className":10557},[1163,3235],[1095,10559],{"className":10560,"style":2264},[1383],[1095,10562,1510],{"className":10563},[1779],[1095,10565],{"className":10566,"style":2264},[1383],[1095,10568,10570,10574,10697,10700,10703],{"className":10569},[1141],[1095,10571],{"className":10572,"style":10573},[1145],"height:1.4357em;vertical-align:-0.4033em;",[1095,10575,10577,10580,10694],{"className":10576},[1150],[1095,10578],{"className":10579},[1156,3235],[1095,10581,10583],{"className":10582},[3104],[1095,10584,10586,10685],{"className":10585},[1574,1575],[1095,10587,10589,10682],{"className":10588},[1579],[1095,10590,10593,10613,10621],{"className":10591,"style":10592},[1583],"height:1.0323em;",[1095,10594,10595,10598],{"style":3251},[1095,10596],{"className":10597,"style":2026},[1591],[1095,10599,10601],{"className":10600},[1596,1597,1598,1599],[1095,10602,10604,10607,10610],{"className":10603},[1150,1599],[1095,10605,1492],{"className":10606},[1150,1599],[1095,10608,1510],{"className":10609},[1779,1599],[1095,10611,3738],{"className":10612,"style":1936},[1150,1151,1599],[1095,10614,10615,10618],{"style":3318},[1095,10616],{"className":10617,"style":2026},[1591],[1095,10619],{"className":10620,"style":3326},[3325],[1095,10622,10624,10627],{"style":10623},"top:-3.5073em;",[1095,10625],{"className":10626,"style":2026},[1591],[1095,10628,10630],{"className":10629},[1596,1597,1598,1599],[1095,10631,10633,10673,10676,10679],{"className":10632},[1150,1599],[1095,10634,10636,10639],{"className":10635},[1150,1599],[1095,10637,1091],{"className":10638},[1150,1151,1599],[1095,10640,10642],{"className":10641},[1570],[1095,10643,10645,10665],{"className":10644},[1574,1575],[1095,10646,10648,10662],{"className":10647},[1579],[1095,10649,10651],{"className":10650,"style":9159},[1583],[1095,10652,10653,10656],{"style":9162},[1095,10654],{"className":10655,"style":3286},[1591],[1095,10657,10659],{"className":10658},[1596,3290,3291,1599],[1095,10660,1984],{"className":10661,"style":1256},[1150,1151,1599],[1095,10663,1607],{"className":10664},[1606],[1095,10666,10668],{"className":10667},[1579],[1095,10669,10671],{"className":10670,"style":9790},[1583],[1095,10672],{},[1095,10674,1121],{"className":10675},[1156,1599],[1095,10677,1124],{"className":10678},[1150,1151,1599],[1095,10680,1127],{"className":10681},[1163,1599],[1095,10683,1607],{"className":10684},[1606],[1095,10686,10688],{"className":10687},[1579],[1095,10689,10692],{"className":10690,"style":10691},[1583],"height:0.4033em;",[1095,10693],{},[1095,10695],{"className":10696},[1163,3235],[1095,10698],{"className":10699,"style":1542},[1383],[1095,10701,1463],{"className":10702},[1546],[1095,10704],{"className":10705,"style":1542},[1383],[1095,10707,10709,10713,10716,10719,10722,10725,10728],{"className":10708},[1141],[1095,10710],{"className":10711,"style":10712},[1145],"height:0.6684em;vertical-align:-0.024em;",[1095,10714,2603],{"className":10715},[1150],[1095,10717],{"className":10718,"style":1542},[1383],[1095,10720],{"className":10721,"style":1542},[1383],[1095,10723,10342],{"className":10724},[1546],[1095,10726],{"className":10727,"style":1542},[1383],[1095,10729],{"className":10730,"style":1542},[1383],[1095,10732,10734,10737,10766,10769,10772,10775,10778,10781],{"className":10733},[1141],[1095,10735],{"className":10736,"style":1146},[1145],[1095,10738,10740,10743],{"className":10739},[1150],[1095,10741,3738],{"className":10742,"style":1936},[1150,1151],[1095,10744,10746],{"className":10745},[1570],[1095,10747,10749],{"className":10748},[1574],[1095,10750,10752],{"className":10751},[1579],[1095,10753,10755],{"className":10754,"style":9622},[1583],[1095,10756,10757,10760],{"style":2392},[1095,10758],{"className":10759,"style":1592},[1591],[1095,10761,10763],{"className":10762},[1596,1597,1598,1599],[1095,10764,9523],{"className":10765},[1779,1599],[1095,10767,1121],{"className":10768},[1156],[1095,10770,1124],{"className":10771},[1150,1151],[1095,10773,1127],{"className":10774},[1163],[1095,10776],{"className":10777,"style":1542},[1383],[1095,10779,1463],{"className":10780},[1546],[1095,10782],{"className":10783,"style":1542},[1383],[1095,10785,10787,10790],{"className":10786},[1141],[1095,10788],{"className":10789,"style":9658},[1145],[1095,10791,10793,10796,11023],{"className":10792},[1150],[1095,10794],{"className":10795},[1156,3235],[1095,10797,10799],{"className":10798},[3104],[1095,10800,10802,11015],{"className":10801},[1574,1575],[1095,10803,10805,11012],{"className":10804},[1579],[1095,10806,10808,10932,10940],{"className":10807,"style":3248},[1583],[1095,10809,10810,10813],{"style":3251},[1095,10811],{"className":10812,"style":2026},[1591],[1095,10814,10816],{"className":10815},[1596,1597,1598,1599],[1095,10817,10819,10871,10874,10877,10880,10883,10923,10926,10929],{"className":10818},[1150,1599],[1095,10820,10822,10825],{"className":10821},[1150,1599],[1095,10823,1091],{"className":10824},[1150,1151,1599],[1095,10826,10828],{"className":10827},[1570],[1095,10829,10831,10863],{"className":10830},[1574,1575],[1095,10832,10834,10860],{"className":10833},[1579],[1095,10835,10837],{"className":10836,"style":3279},[1583],[1095,10838,10839,10842],{"style":3282},[1095,10840],{"className":10841,"style":3286},[1591],[1095,10843,10845],{"className":10844},[1596,3290,3291,1599],[1095,10846,10848,10851,10854,10857],{"className":10847},[1150,1599],[1095,10849,2875],{"className":10850},[1150,1151,1599],[1095,10852,8742],{"className":10853},[1150,1151,1599],[1095,10855,8745],{"className":10856},[1150,1151,1599],[1095,10858,8742],{"className":10859},[1150,1151,1599],[1095,10861,1607],{"className":10862},[1606],[1095,10864,10866],{"className":10865},[1579],[1095,10867,10869],{"className":10868,"style":3304},[1583],[1095,10870],{},[1095,10872,1121],{"className":10873},[1156,1599],[1095,10875,1124],{"className":10876},[1150,1151,1599],[1095,10878,1127],{"className":10879},[1163,1599],[1095,10881,3733],{"className":10882},[1779,1599],[1095,10884,10886,10889],{"className":10885},[1150,1599],[1095,10887,1091],{"className":10888},[1150,1151,1599],[1095,10890,10892],{"className":10891},[1570],[1095,10893,10895,10915],{"className":10894},[1574,1575],[1095,10896,10898,10912],{"className":10897},[1579],[1095,10899,10901],{"className":10900,"style":9159},[1583],[1095,10902,10903,10906],{"style":9162},[1095,10904],{"className":10905,"style":3286},[1591],[1095,10907,10909],{"className":10908},[1596,3290,3291,1599],[1095,10910,1984],{"className":10911,"style":1256},[1150,1151,1599],[1095,10913,1607],{"className":10914},[1606],[1095,10916,10918],{"className":10917},[1579],[1095,10919,10921],{"className":10920,"style":9790},[1583],[1095,10922],{},[1095,10924,1121],{"className":10925},[1156,1599],[1095,10927,1124],{"className":10928},[1150,1151,1599],[1095,10930,1127],{"className":10931},[1163,1599],[1095,10933,10934,10937],{"style":3318},[1095,10935],{"className":10936,"style":2026},[1591],[1095,10938],{"className":10939,"style":3326},[3325],[1095,10941,10942,10945],{"style":3329},[1095,10943],{"className":10944,"style":2026},[1591],[1095,10946,10948],{"className":10947},[1596,1597,1598,1599],[1095,10949,10951,11003,11006,11009],{"className":10950},[1150,1599],[1095,10952,10954,10957],{"className":10953},[1150,1599],[1095,10955,1091],{"className":10956},[1150,1151,1599],[1095,10958,10960],{"className":10959},[1570],[1095,10961,10963,10995],{"className":10962},[1574,1575],[1095,10964,10966,10992],{"className":10965},[1579],[1095,10967,10969],{"className":10968,"style":3279},[1583],[1095,10970,10971,10974],{"style":3282},[1095,10972],{"className":10973,"style":3286},[1591],[1095,10975,10977],{"className":10976},[1596,3290,3291,1599],[1095,10978,10980,10983,10986,10989],{"className":10979},[1150,1599],[1095,10981,2875],{"className":10982},[1150,1151,1599],[1095,10984,8742],{"className":10985},[1150,1151,1599],[1095,10987,8745],{"className":10988},[1150,1151,1599],[1095,10990,8742],{"className":10991},[1150,1151,1599],[1095,10993,1607],{"className":10994},[1606],[1095,10996,10998],{"className":10997},[1579],[1095,10999,11001],{"className":11000,"style":3304},[1583],[1095,11002],{},[1095,11004,1121],{"className":11005},[1156,1599],[1095,11007,1124],{"className":11008},[1150,1151,1599],[1095,11010,1127],{"className":11011},[1163,1599],[1095,11013,1607],{"className":11014},[1606],[1095,11016,11018],{"className":11017},[1579],[1095,11019,11021],{"className":11020,"style":9891},[1583],[1095,11022],{},[1095,11024],{"className":11025},[1163,3235],[1194,11027,11029],{"id":11028},"_34-全局最优与-js-散度","3.4 全局最优与 JS 散度",[1091,11031,11032,11033,11092,11093,4359],{},"将 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-\\log 4 + 2 \\cdot D_{JS}(p_{data} \\| p_g)",[1095,12245,12247,12260,12293,12312],{"className":12246,"ariaHidden":1137},[1136],[1095,12248,12250,12254,12257],{"className":12249},[1141],[1095,12251],{"className":12252,"style":12253},[1145],"height:0.3669em;",[1095,12255,1463],{"className":12256},[1546],[1095,12258],{"className":12259,"style":1542},[1383],[1095,12261,12263,12267,12270,12273,12278,12281,12284,12287,12290],{"className":12262},[1141],[1095,12264],{"className":12265,"style":12266},[1145],"height:0.8889em;vertical-align:-0.1944em;",[1095,12268,1510],{"className":12269},[1150],[1095,12271],{"className":12272,"style":1384},[1383],[1095,12274,3799,12276],{"className":12275},[1560],[1095,12277,1984],{"style":3802},[1095,12279],{"className":12280,"style":1384},[1383],[1095,12282,12196],{"className":12283},[1150],[1095,12285],{"className":12286,"style":2264},[1383],[1095,12288,3733],{"className":12289},[1779],[1095,12291],{"className":12292,"style":2264},[1383],[1095,12294,12296,12300,12303,12306,12309],{"className":12295},[1141],[1095,12297],{"className":12298,"style":12299},[1145],"height:0.6444em;",[1095,12301,2177],{"className":12302},[1150],[1095,12304],{"className":12305,"style":2264},[1383],[1095,12307,12203],{"className":12308},[1779],[1095,12310],{"className":12311,"style":2264},[1383],[1095,12313,12315,12318,12364,12367,12419,12422,12462],{"className":12314},[1141],[1095,12316],{"className":12317,"style":2058},[1145],[1095,12319,12321,12324],{"className":12320},[1150],[1095,12322,3738],{"className":12323,"style":1936},[1150,1151],[1095,12325,12327],{"className":12326},[1570],[1095,12328,12330,12356],{"className":12329},[1574,1575],[1095,12331,12333,12353],{"className":12332},[1579],[1095,12334,12336],{"className":12335,"style":2210},[1583],[1095,12337,12338,12341],{"style":4209},[1095,12339],{"className":12340,"style":1592},[1591],[1095,12342,12344],{"className":12343},[1596,1597,1598,1599],[1095,12345,12347,12350],{"className":12346},[1150,1599],[1095,12348,5608],{"className":12349,"style":5930},[1150,1151,1599],[1095,12351,12214],{"className":12352,"style":2228},[1150,1151,1599],[1095,12354,1607],{"className":12355},[1606],[1095,12357,12359],{"className":12358},[1579],[1095,12360,12362],{"className":12361,"style":1666},[1583],[1095,12363],{},[1095,12365,1121],{"className":12366},[1156],[1095,12368,12370,12373],{"className":12369},[1150],[1095,12371,1091],{"className":12372},[1150,1151],[1095,12374,12376],{"className":12375},[1570],[1095,12377,12379,12411],{"className":12378},[1574,1575],[1095,12380,12382,12408],{"className":12381},[1579],[1095,12383,12385],{"className":12384,"style":1923},[1583],[1095,12386,12387,12390],{"style":1647},[1095,12388],{"className":12389,"style":1592},[1591],[1095,12391,12393],{"className":12392},[1596,1597,1598,1599],[1095,12394,12396,12399,12402,12405],{"className":12395},[1150,1599],[1095,12397,2875],{"className":12398},[1150,1151,1599],[1095,12400,8742],{"className":12401},[1150,1151,1599],[1095,12403,8745],{"className":12404},[1150,1151,1599],[1095,12406,8742],{"className":12407},[1150,1151,1599],[1095,12409,1607],{"className":12410},[1606],[1095,12412,12414],{"className":12413},[1579],[1095,12415,12417],{"className":12416,"style":1666},[1583],[1095,12418],{},[1095,12420,2143],{"className":12421},[1150],[1095,12423,12425,12428],{"className":12424},[1150],[1095,12426,1091],{"className":12427},[1150,1151],[1095,12429,12431],{"className":12430},[1570],[1095,12432,12434,12454],{"className":12433},[1574,1575],[1095,12435,12437,12451],{"className":12436},[1579],[1095,12438,12440],{"className":12439,"style":8430},[1583],[1095,12441,12442,12445],{"style":1647},[1095,12443],{"className":12444,"style":1592},[1591],[1095,12446,12448],{"className":12447},[1596,1597,1598,1599],[1095,12449,1984],{"className":12450,"style":1256},[1150,1151,1599],[1095,12452,1607],{"className":12453},[1606],[1095,12455,12457],{"className":12456},[1579],[1095,12458,12460],{"className":12459,"style":2098},[1583],[1095,12461],{},[1095,12463,1127],{"className":12464},[1163],[1091,12466,12467,12470,12471,12561,12562,12633,12634,12787,12788,12874,12875,2550],{},[1172,12468,12469],{},"关键结论","：在最优判别器下，最小化生成器的目标等价于最小化 ",[1095,12472,12474,12500],{"className":12473},[1098],[1095,12475,12477],{"className":12476},[1102],[1104,12478,12479],{"xmlns":1106},[1108,12480,12481,12497],{},[1111,12482,12483],{},[1465,12484,12485,12487],{},[1114,12486,1091],{},[1111,12488,12489,12491,12493,12495],{},[1114,12490,2875],{},[1114,12492,8742],{},[1114,12494,8745],{},[1114,12496,8742],{},[1129,12498,12499],{"encoding":1131},"p_{data}",[1095,12501,12503],{"className":12502,"ariaHidden":1137},[1136],[1095,12504,12506,12509],{"className":12505},[1141],[1095,12507],{"className":12508,"style":2456},[1145],[1095,12510,12512,12515],{"className":12511},[1150],[1095,12513,1091],{"className":12514},[1150,1151],[1095,12516,12518],{"className":12517},[1570],[1095,12519,12521,12553],{"className":12520},[1574,1575],[1095,12522,12524,12550],{"className":12523},[1579],[1095,12525,12527],{"className":12526,"style":1923},[1583],[1095,12528,12529,12532],{"style":1647},[1095,12530],{"className":12531,"style":1592},[1591],[1095,12533,12535],{"className":12534},[1596,1597,1598,1599],[1095,12536,12538,12541,12544,12547],{"className":12537},[1150,1599],[1095,12539,2875],{"className":12540},[1150,1151,1599],[1095,12542,8742],{"className":12543},[1150,1151,1599],[1095,12545,8745],{"className":12546},[1150,1151,1599],[1095,12548,8742],{"className":12549},[1150,1151,1599],[1095,12551,1607],{"className":12552},[1606],[1095,12554,12556],{"className":12555},[1579],[1095,12557,12559],{"className":12558,"style":1666},[1583],[1095,12560],{}," 与 ",[1095,12563,12565,12583],{"className":12564},[1098],[1095,12566,12568],{"className":12567},[1102],[1104,12569,12570],{"xmlns":1106},[1108,12571,12572,12580],{},[1111,12573,12574],{},[1465,12575,12576,12578],{},[1114,12577,1091],{},[1114,12579,1984],{},[1129,12581,12582],{"encoding":1131},"p_g",[1095,12584,12586],{"className":12585,"ariaHidden":1137},[1136],[1095,12587,12589,12593],{"className":12588},[1141],[1095,12590],{"className":12591,"style":12592},[1145],"height:0.7167em;vertical-align:-0.2861em;",[1095,12594,12596,12599],{"className":12595},[1150],[1095,12597,1091],{"className":12598},[1150,1151],[1095,12600,12602],{"className":12601},[1570],[1095,12603,12605,12625],{"className":12604},[1574,1575],[1095,12606,12608,12622],{"className":12607},[1579],[1095,12609,12611],{"className":12610,"style":8430},[1583],[1095,12612,12613,12616],{"style":1647},[1095,12614],{"className":12615,"style":1592},[1591],[1095,12617,12619],{"className":12618},[1596,1597,1598,1599],[1095,12620,1984],{"className":12621,"style":1256},[1150,1151,1599],[1095,12623,1607],{"className":12624},[1606],[1095,12626,12628],{"className":12627},[1579],[1095,12629,12631],{"className":12630,"style":2098},[1583],[1095,12632],{}," 之间的 Jensen-Shannon 散度。当且仅当 ",[1095,12635,12637,12671],{"className":12636},[1098],[1095,12638,12640],{"className":12639},[1102],[1104,12641,12642],{"xmlns":1106},[1108,12643,12644,12668],{},[1111,12645,12646,12652,12654],{},[1465,12647,12648,12650],{},[1114,12649,1091],{},[1114,12651,1984],{},[1118,12653,1463],{},[1465,12655,12656,12658],{},[1114,12657,1091],{},[1111,12659,12660,12662,12664,12666],{},[1114,12661,2875],{},[1114,12663,8742],{},[1114,12665,8745],{},[1114,12667,8742],{},[1129,12669,12670],{"encoding":1131},"p_g = p_{data}",[1095,12672,12674,12729],{"className":12673,"ariaHidden":1137},[1136],[1095,12675,12677,12680,12720,12723,12726],{"className":12676},[1141],[1095,12678],{"className":12679,"style":12592},[1145],[1095,12681,12683,12686],{"className":12682},[1150],[1095,12684,1091],{"className":12685},[1150,1151],[1095,12687,12689],{"className":12688},[1570],[1095,12690,12692,12712],{"className":12691},[1574,1575],[1095,12693,12695,12709],{"className":12694},[1579],[1095,12696,12698],{"className":12697,"style":8430},[1583],[1095,12699,12700,12703],{"style":1647},[1095,12701],{"className":12702,"style":1592},[1591],[1095,12704,12706],{"className":12705},[1596,1597,1598,1599],[1095,12707,1984],{"className":12708,"style":1256},[1150,1151,1599],[1095,12710,1607],{"className":12711},[1606],[1095,12713,12715],{"className":12714},[1579],[1095,12716,12718],{"className":12717,"style":2098},[1583],[1095,12719],{},[1095,12721],{"className":12722,"style":1542},[1383],[1095,12724,1463],{"className":12725},[1546],[1095,12727],{"className":12728,"style":1542},[1383],[1095,12730,12732,12735],{"className":12731},[1141],[1095,12733],{"className":12734,"style":2456},[1145],[1095,12736,12738,12741],{"className":12737},[1150],[1095,12739,1091],{"className":12740},[1150,1151],[1095,12742,12744],{"className":12743},[1570],[1095,12745,12747,12779],{"className":12746},[1574,1575],[1095,12748,12750,12776],{"className":12749},[1579],[1095,12751,12753],{"className":12752,"style":1923},[1583],[1095,12754,12755,12758],{"style":1647},[1095,12756],{"className":12757,"style":1592},[1591],[1095,12759,12761],{"className":12760},[1596,1597,1598,1599],[1095,12762,12764,12767,12770,12773],{"className":12763},[1150,1599],[1095,12765,2875],{"className":12766},[1150,1151,1599],[1095,12768,8742],{"className":12769},[1150,1151,1599],[1095,12771,8745],{"className":12772},[1150,1151,1599],[1095,12774,8742],{"className":12775},[1150,1151,1599],[1095,12777,1607],{"className":12778},[1606],[1095,12780,12782],{"className":12781},[1579],[1095,12783,12785],{"className":12784,"style":1666},[1583],[1095,12786],{}," 时，",[1095,12789,12791,12818],{"className":12790},[1098],[1095,12792,12794],{"className":12793},[1102],[1104,12795,12796],{"xmlns":1106},[1108,12797,12798,12816],{},[1111,12799,12800,12802,12804,12810,12812,12814],{},[1114,12801,6804],{},[1118,12803,1121],{"stretchy":1120},[2171,12805,12806,12808],{},[1114,12807,3738],{},[1118,12809,9523],{},[1118,12811,1349],{"separator":1137},[1114,12813,8480],{},[1118,12815,1127],{"stretchy":1120},[1129,12817,11123],{"encoding":1131},[1095,12819,12821],{"className":12820,"ariaHidden":1137},[1136],[1095,12822,12824,12827,12830,12833,12862,12865,12868,12871],{"className":12823},[1141],[1095,12825],{"className":12826,"style":1146},[1145],[1095,12828,6804],{"className":12829,"style":2264},[1150,1151],[1095,12831,1121],{"className":12832},[1156],[1095,12834,12836,12839],{"className":12835},[1150],[1095,12837,3738],{"className":12838,"style":1936},[1150,1151],[1095,12840,12842],{"className":12841},[1570],[1095,12843,12845],{"className":12844},[1574],[1095,12846,12848],{"className":12847},[1579],[1095,12849,12851],{"className":12850,"style":9622},[1583],[1095,12852,12853,12856],{"style":2392},[1095,12854],{"className":12855,"style":1592},[1591],[1095,12857,12859],{"className":12858},[1596,1597,1598,1599],[1095,12860,9523],{"className":12861},[1779,1599],[1095,12863,1349],{"className":12864},[1379],[1095,12866],{"className":12867,"style":1384},[1383],[1095,12869,8480],{"className":12870},[1150,1151],[1095,12872,1127],{"className":12873},[1163]," 达到全局最小值 ",[1095,12876,12878,12898],{"className":12877},[1098],[1095,12879,12881],{"className":12880},[1102],[1104,12882,12883],{"xmlns":1106},[1108,12884,12885,12895],{},[1111,12886,12887,12889,12891,12893],{},[1118,12888,1510],{},[1114,12890,3640],{},[1118,12892,3643],{},[1490,12894,12196],{},[1129,12896,12897],{"encoding":1131},"-\\log 4",[1095,12899,12901],{"className":12900,"ariaHidden":1137},[1136],[1095,12902,12904,12907,12910,12913,12918,12921],{"className":12903},[1141],[1095,12905],{"className":12906,"style":12266},[1145],[1095,12908,1510],{"className":12909},[1150],[1095,12911],{"className":12912,"style":1384},[1383],[1095,12914,3799,12916],{"className":12915},[1560],[1095,12917,1984],{"style":3802},[1095,12919],{"className":12920,"style":1384},[1383],[1095,12922,12196],{"className":12923},[1150],[1194,12925,12927],{"id":12926},"_35-训练算法","3.5 训练算法",[1091,12929,12930],{},"GAN 的训练采用交替优化：",[2564,12932,12933,13100,13262,13763,13924],{},[1169,12934,12935,12936],{},"从真实数据采样 mini-batch ",[1095,12937,12939,12993],{"className":12938},[1098],[1095,12940,12942],{"className":12941},[1102],[1104,12943,12944],{"xmlns":1106},[1108,12945,12946,12990],{},[1111,12947,12948,12951,12963,12965,12968,12970,12972,12974,12987],{},[1118,12949,12950],{"stretchy":1120},"{",[2171,12952,12953,12955],{},[1114,12954,1124],{},[1111,12956,12957,12959,12961],{},[1118,12958,1121],{"stretchy":1120},[1490,12960,1492],{},[1118,12962,1127],{"stretchy":1120},[1118,12964,1349],{"separator":1137},[1114,12966,12967],{"mathvariant":1229},".",[1114,12969,12967],{"mathvariant":1229},[1114,12971,12967],{"mathvariant":1229},[1118,12973,1349],{"separator":1137},[2171,12975,12976,12978],{},[1114,12977,1124],{},[1111,12979,12980,12982,12985],{},[1118,12981,1121],{"stretchy":1120},[1114,12983,12984],{},"m",[1118,12986,1127],{"stretchy":1120},[1118,12988,12989],{"stretchy":1120},"}",[1129,12991,12992],{"encoding":1131},"\\{x^{(1)}, ..., x^{(m)}\\}",[1095,12994,12996],{"className":12995,"ariaHidden":1137},[1136],[1095,12997,12999,13002,13005,13043,13046,13049,13053,13056,13059,13097],{"className":12998},[1141],[1095,13000],{"className":13001,"style":7483},[1145],[1095,13003,12950],{"className":13004},[1156],[1095,13006,13008,13011],{"className":13007},[1150],[1095,13009,1124],{"className":13010},[1150,1151],[1095,13012,13014],{"className":13013},[1570],[1095,13015,13017],{"className":13016},[1574],[1095,13018,13020],{"className":13019},[1579],[1095,13021,13023],{"className":13022,"style":7565},[1583],[1095,13024,13025,13028],{"style":2392},[1095,13026],{"className":13027,"style":1592},[1591],[1095,13029,13031],{"className":13030},[1596,1597,1598,1599],[1095,13032,13034,13037,13040],{"className":13033},[1150,1599],[1095,13035,1121],{"className":13036},[1156,1599],[1095,13038,1492],{"className":13039},[1150,1599],[1095,13041,1127],{"className":13042},[1163,1599],[1095,13044,1349],{"className":13045},[1379],[1095,13047],{"className":13048,"style":1384},[1383],[1095,13050,13052],{"className":13051},[1150],"...",[1095,13054,1349],{"className":13055},[1379],[1095,13057],{"className":13058,"style":1384},[1383],[1095,13060,13062,13065],{"className":13061},[1150],[1095,13063,1124],{"className":13064},[1150,1151],[1095,13066,13068],{"className":13067},[1570],[1095,13069,13071],{"className":13070},[1574],[1095,13072,13074],{"className":13073},[1579],[1095,13075,13077],{"className":13076,"style":7565},[1583],[1095,13078,13079,13082],{"style":2392},[1095,13080],{"className":13081,"style":1592},[1591],[1095,13083,13085],{"className":13084},[1596,1597,1598,1599],[1095,13086,13088,13091,13094],{"className":13087},[1150,1599],[1095,13089,1121],{"className":13090},[1156,1599],[1095,13092,12984],{"className":13093},[1150,1151,1599],[1095,13095,1127],{"className":13096},[1163,1599],[1095,13098,12989],{"className":13099},[1163],[1169,13101,13102,13103],{},"从噪声分布采样 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z^{(m)}\\}",[1095,13157,13159],{"className":13158,"ariaHidden":1137},[1136],[1095,13160,13162,13165,13168,13206,13209,13212,13215,13218,13221,13259],{"className":13161},[1141],[1095,13163],{"className":13164,"style":7483},[1145],[1095,13166,12950],{"className":13167},[1156],[1095,13169,13171,13174],{"className":13170},[1150],[1095,13172,1352],{"className":13173,"style":1388},[1150,1151],[1095,13175,13177],{"className":13176},[1570],[1095,13178,13180],{"className":13179},[1574],[1095,13181,13183],{"className":13182},[1579],[1095,13184,13186],{"className":13185,"style":7565},[1583],[1095,13187,13188,13191],{"style":2392},[1095,13189],{"className":13190,"style":1592},[1591],[1095,13192,13194],{"className":13193},[1596,1597,1598,1599],[1095,13195,13197,13200,13203],{"className":13196},[1150,1599],[1095,13198,1121],{"className":13199},[1156,1599],[1095,13201,1492],{"className":13202},[1150,1599],[1095,13204,1127],{"className":13205},[1163,1599],[1095,13207,1349],{"className":13208},[1379],[1095,13210],{"className":13211,"style":1384},[1383],[1095,13213,13052],{"className":13214},[1150],[1095,13216,1349],{"className":13217},[1379],[1095,13219],{"className":13220,"style":1384},[1383],[1095,13222,13224,13227],{"className":13223},[1150],[1095,13225,1352],{"className":13226,"style":1388},[1150,1151],[1095,13228,13230],{"className":13229},[1570],[1095,13231,13233],{"className":13232},[1574],[1095,13234,13236],{"className":13235},[1579],[1095,13237,13239],{"className":13238,"style":7565},[1583],[1095,13240,13241,13244],{"style":2392},[1095,13242],{"className":13243,"style":1592},[1591],[1095,13245,13247],{"className":13246},[1596,1597,1598,1599],[1095,13248,13250,13253,13256],{"className":13249},[1150,1599],[1095,13251,1121],{"className":13252},[1156,1599],[1095,13254,12984],{"className":13255},[1150,1151,1599],[1095,13257,1127],{"className":13258},[1163,1599],[1095,13260,12989],{"className":13261},[1163],[1169,13263,13264,13267,13268],{},[1172,13265,13266],{},"更新判别器","（梯度上升）：",[1095,13269,13271,13380],{"className":13270},[1098],[1095,13272,13274],{"className":13273},[1102],[1104,13275,13276],{"xmlns":1106},[1108,13277,13278,13377],{},[1111,13279,13280,13291,13297,13311],{},[1465,13281,13282,13285],{},[1114,13283,13284],{"mathvariant":1229},"∇",[1465,13286,13287,13289],{},[1114,13288,1866],{},[1114,13290,2875],{},[3104,13292,13293,13295],{},[1490,13294,1492],{},[1114,13296,12984],{},[5592,13298,13299,13301,13309],{},[1118,13300,5596],{},[1111,13302,13303,13305,13307],{},[1114,13304,1472],{},[1118,13306,1463],{},[1490,13308,1492],{},[1114,13310,12984],{},[1111,13312,13313,13315,13317,13319,13321,13323,13335,13337,13339,13341,13343,13345,13347,13349,13351,13353,13355,13357,13369,13371,13373,13375],{},[1118,13314,3685],{"fence":1137},[1114,13316,3640],{},[1118,13318,3643],{},[1114,13320,3738],{},[1118,13322,1121],{"stretchy":1120},[2171,13324,13325,13327],{},[1114,13326,1124],{},[1111,13328,13329,13331,13333],{},[1118,13330,1121],{"stretchy":1120},[1114,13332,1472],{},[1118,13334,1127],{"stretchy":1120},[1118,13336,1127],{"stretchy":1120},[1118,13338,3733],{},[1114,13340,3640],{},[1118,13342,3643],{},[1118,13344,1121],{"stretchy":1120},[1490,13346,1492],{},[1118,13348,1510],{},[1114,13350,3738],{},[1118,13352,1121],{"stretchy":1120},[1114,13354,8480],{},[1118,13356,1121],{"stretchy":1120},[2171,13358,13359,13361],{},[1114,13360,1352],{},[1111,13362,13363,13365,13367],{},[1118,13364,1121],{"stretchy":1120},[1114,13366,1472],{},[1118,13368,1127],{"stretchy":1120},[1118,13370,1127],{"stretchy":1120},[1118,13372,1127],{"stretchy":1120},[1118,13374,1127],{"stretchy":1120},[1118,13376,3730],{"fence":1137},[1129,13378,13379],{"encoding":1131},"\\nabla_{\\theta_d} \\frac{1}{m} \\sum_{i=1}^{m} \\left[\\log D(x^{(i)}) + \\log(1 - D(G(z^{(i)})))\\right]",[1095,13381,13383],{"className":13382,"ariaHidden":1137},[1136],[1095,13384,13386,13390,13472,13540,13543,13607,13610],{"className":13385},[1141],[1095,13387],{"className":13388,"style":13389},[1145],"height:1.238em;vertical-align:-0.35em;",[1095,13391,13393,13396],{"className":13392},[1150],[1095,13394,13284],{"className":13395},[1150],[1095,13397,13399],{"className":13398},[1570],[1095,13400,13402,13463],{"className":13401},[1574,1575],[1095,13403,13405,13460],{"className":13404},[1579],[1095,13406,13408],{"className":13407,"style":1923},[1583],[1095,13409,13410,13413],{"style":1647},[1095,13411],{"className":13412,"style":1592},[1591],[1095,13414,13416],{"className":13415},[1596,1597,1598,1599],[1095,13417,13419],{"className":13418},[1150,1599],[1095,13420,13422,13425],{"className":13421},[1150,1599],[1095,13423,1866],{"className":13424,"style":1936},[1150,1151,1599],[1095,13426,13428],{"className":13427},[1570],[1095,13429,13431,13452],{"className":13430},[1574,1575],[1095,13432,13434,13449],{"className":13433},[1579],[1095,13435,13437],{"className":13436,"style":3279},[1583],[1095,13438,13440,13443],{"style":13439},"top:-2.3488em;margin-left:-0.0278em;margin-right:0.0714em;",[1095,13441],{"className":13442,"style":3286},[1591],[1095,13444,13446],{"className":13445},[1596,3290,3291,1599],[1095,13447,2875],{"className":13448},[1150,1151,1599],[1095,13450,1607],{"className":13451},[1606],[1095,13453,13455],{"className":13454},[1579],[1095,13456,13458],{"className":13457,"style":3304},[1583],[1095,13459],{},[1095,13461,1607],{"className":13462},[1606],[1095,13464,13466],{"className":13465},[1579],[1095,13467,13470],{"className":13468,"style":13469},[1583],"height:0.2559em;",[1095,13471],{},[1095,13473,13475,13478,13537],{"className":13474},[1150],[1095,13476],{"className":13477},[1156,3235],[1095,13479,13481],{"className":13480},[3104],[1095,13482,13484,13529],{"className":13483},[1574,1575],[1095,13485,13487,13526],{"className":13486},[1579],[1095,13488,13490,13504,13512],{"className":13489,"style":5819},[1583],[1095,13491,13492,13495],{"style":3251},[1095,13493],{"className":13494,"style":2026},[1591],[1095,13496,13498],{"className":13497},[1596,1597,1598,1599],[1095,13499,13501],{"className":13500},[1150,1599],[1095,13502,12984],{"className":13503},[1150,1151,1599],[1095,13505,13506,13509],{"style":3318},[1095,13507],{"className":13508,"style":2026},[1591],[1095,13510],{"className":13511,"style":3326},[3325],[1095,13513,13514,13517],{"style":5844},[1095,13515],{"className":13516,"style":2026},[1591],[1095,13518,13520],{"className":13519},[1596,1597,1598,1599],[1095,13521,13523],{"className":13522},[1150,1599],[1095,13524,1492],{"className":13525},[1150,1599],[1095,13527,1607],{"className":13528},[1606],[1095,13530,13532],{"className":13531},[1579],[1095,13533,13535],{"className":13534,"style":5866},[1583],[1095,13536],{},[1095,13538],{"className":13539},[1163,3235],[1095,13541],{"className":13542,"style":1384},[1383],[1095,13544,13546,13549],{"className":13545},[1560],[1095,13547,5596],{"className":13548,"style":1566},[1560,1564,1565],[1095,13550,13552],{"className":13551},[1570],[1095,13553,13555,13599],{"className":13554},[1574,1575],[1095,13556,13558,13596],{"className":13557},[1579],[1095,13559,13562,13582],{"className":13560,"style":13561},[1583],"height:0.8043em;",[1095,13563,13564,13567],{"style":1587},[1095,13565],{"className":13566,"style":1592},[1591],[1095,13568,13570],{"className":13569},[1596,1597,1598,1599],[1095,13571,13573,13576,13579],{"className":13572},[1150,1599],[1095,13574,1472],{"className":13575},[1150,1151,1599],[1095,13577,1463],{"className":13578},[1546,1599],[1095,13580,1492],{"className":13581},[1150,1599],[1095,13583,13584,13587],{"style":5917},[1095,13585],{"className":13586,"style":1592},[1591],[1095,13588,13590],{"className":13589},[1596,1597,1598,1599],[1095,13591,13593],{"className":13592},[1150,1599],[1095,13594,12984],{"className":13595},[1150,1151,1599],[1095,13597,1607],{"className":13598},[1606],[1095,13600,13602],{"className":13601},[1579],[1095,13603,13605],{"className":13604,"style":1614},[1583],[1095,13606],{},[1095,13608],{"className":13609,"style":1384},[1383],[1095,13611,13613,13619,13624,13627,13630,13633,13671,13674,13677,13680,13683,13688,13691,13694,13697,13700,13703,13706,13709,13712,13715,13753,13757],{"className":13612},[1734],[1095,13614,13616],{"className":13615,"style":3981},[1156,3980],[1095,13617,3685],{"className":13618},[3985,3291],[1095,13620,3799,13622],{"className":13621},[1560],[1095,13623,1984],{"style":3802},[1095,13625],{"className":13626,"style":1384},[1383],[1095,13628,3738],{"className":13629,"style":1936},[1150,1151],[1095,13631,1121],{"className":13632},[1156],[1095,13634,13636,13639],{"className":13635},[1150],[1095,13637,1124],{"className":13638},[1150,1151],[1095,13640,13642],{"className":13641},[1570],[1095,13643,13645],{"className":13644},[1574],[1095,13646,13648],{"className":13647},[1579],[1095,13649,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\\frac{1}{m} \\sum_{i=1}^{m} \\log(1 - D(G(z^{(i)})))",[1095,14012,14014,14259],{"className":14013,"ariaHidden":1137},[1136],[1095,14015,14017,14021,14102,14170,14173,14236,14239,14244,14247,14250,14253,14256],{"className":14016},[1141],[1095,14018],{"className":14019,"style":14020},[1145],"height:1.1924em;vertical-align:-0.3473em;",[1095,14022,14024,14027],{"className":14023},[1150],[1095,14025,13284],{"className":14026},[1150],[1095,14028,14030],{"className":14029},[1570],[1095,14031,14033,14094],{"className":14032},[1574,1575],[1095,14034,14036,14091],{"className":14035},[1579],[1095,14037,14039],{"className":14038,"style":1923},[1583],[1095,14040,14041,14044],{"style":1647},[1095,14042],{"className":14043,"style":1592},[1591],[1095,14045,14047],{"className":14046},[1596,1597,1598,1599],[1095,14048,14050],{"className":14049},[1150,1599],[1095,14051,14053,14056],{"className":14052},[1150,1599],[1095,14054,1866],{"className":14055,"style":1936},[1150,1151,1599],[1095,14057,14059],{"className":14058},[1570],[1095,14060,14062,14083],{"className":14061},[1574,1575],[1095,14063,14065,14080],{"className":14064},[1579],[1095,14066,14068],{"className":14067,"style":9159},[1583],[1095,14069,14071,14074],{"style":14070},"top:-2.357em;margin-left:-0.0278em;margin-right:0.0714em;",[1095,14072],{"className":14073,"style":3286},[1591],[1095,14075,14077],{"className":14076},[1596,3290,3291,1599],[1095,14078,1984],{"className":14079,"style":1256},[1150,1151,1599],[1095,14081,1607],{"className":14082},[1606],[1095,14084,14086],{"className":14085},[1579],[1095,14087,14089],{"className":14088,"style":9790},[1583],[1095,14090],{},[1095,14092,1607],{"className":14093},[1606],[1095,14095,14097],{"className":14096},[1579],[1095,14098,14100],{"className":14099,"style":11919},[1583],[1095,14101],{},[1095,14103,14105,14108,14167],{"className":14104},[1150],[1095,14106],{"className":14107},[1156,3235],[1095,14109,14111],{"className":14110},[3104],[1095,14112,14114,14159],{"className":14113},[1574,1575],[1095,14115,14117,14156],{"className":14116},[1579],[1095,14118,14120,14134,14142],{"className":14119,"style":5819},[1583],[1095,14121,14122,14125],{"style":3251},[1095,14123],{"className":14124,"style":2026},[1591],[1095,14126,14128],{"className":14127},[1596,1597,1598,1599],[1095,14129,14131],{"className":14130},[1150,1599],[1095,14132,12984],{"className":14133},[1150,1151,1599],[1095,14135,14136,14139],{"style":3318},[1095,14137],{"className":14138,"style":2026},[1591],[1095,14140],{"className":14141,"style":3326},[3325],[1095,14143,14144,14147],{"style":5844},[1095,14145],{"className":14146,"style":2026},[1591],[1095,14148,14150],{"className":14149},[1596,1597,1598,1599],[1095,14151,14153],{"className":14152},[1150,1599],[1095,14154,1492],{"className":14155},[1150,1599],[1095,14157,1607],{"className":14158},[1606],[1095,14160,14162],{"className":14161},[1579],[1095,14163,14165],{"className":14164,"style":5866},[1583],[1095,14166],{},[1095,14168],{"className":14169},[1163,3235],[1095,14171],{"className":14172,"style":1384},[1383],[1095,14174,14176,14179],{"className":14175},[1560],[1095,14177,5596],{"className":14178,"style":1566},[1560,1564,1565],[1095,14180,14182],{"className":14181},[1570],[1095,14183,14185,14228],{"className":14184},[1574,1575],[1095,14186,14188,14225],{"className":14187},[1579],[1095,14189,14191,14211],{"className":14190,"style":13561},[1583],[1095,14192,14193,14196],{"style":1587},[1095,14194],{"className":14195,"style":1592},[1591],[1095,14197,14199],{"className":14198},[1596,1597,1598,1599],[1095,14200,14202,14205,14208],{"className":14201},[1150,1599],[1095,14203,1472],{"className":14204},[1150,1151,1599],[1095,14206,1463],{"className":14207},[1546,1599],[1095,14209,1492],{"className":14210},[1150,1599],[1095,14212,14213,14216],{"style":5917},[1095,14214],{"className":14215,"style":1592},[1591],[1095,14217,14219],{"className":14218},[1596,1597,1598,1599],[1095,14220,14222],{"className":14221},[1150,1599],[1095,14223,12984],{"className":14224},[1150,1151,1599],[1095,14226,1607],{"className":14227},[1606],[1095,14229,14231],{"className":14230},[1579],[1095,14232,14234],{"className":14233,"style":1614},[1583],[1095,14235],{},[1095,14237],{"className":14238,"style":1384},[1383],[1095,14240,3799,14242],{"className":14241},[1560],[1095,14243,1984],{"style":3802},[1095,14245,1121],{"className":14246},[1156],[1095,14248,1492],{"className":14249},[1150],[1095,14251],{"className":14252,"style":2264},[1383],[1095,14254,1510],{"className":14255},[1779],[1095,14257],{"className":14258,"style":2264},[1383],[1095,14260,14262,14265,14268,14271,14274,14277,14315],{"className":14261},[1141],[1095,14263],{"className":14264,"style":7483},[1145],[1095,14266,3738],{"className":14267,"style":1936},[1150,1151],[1095,14269,1121],{"className":14270},[1156],[1095,14272,8480],{"className":14273},[1150,1151],[1095,14275,1121],{"className":14276},[1156],[1095,14278,14280,14283],{"className":14279},[1150],[1095,14281,1352],{"className":14282,"style":1388},[1150,1151],[1095,14284,14286],{"className":14285},[1570],[1095,14287,14289],{"className":14288},[1574],[1095,14290,14292],{"className":14291},[1579],[1095,14293,14295],{"className":14294,"style":7565},[1583],[1095,14296,14297,14300],{"style":2392},[1095,14298],{"className":14299,"style":1592},[1591],[1095,14301,14303],{"className":14302},[1596,1597,1598,1599],[1095,14304,14306,14309,14312],{"className":14305},[1150,1599],[1095,14307,1121],{"className":14308},[1156,1599],[1095,14310,1472],{"className":14311},[1150,1151,1599],[1095,14313,1127],{"className":14314},[1163,1599],[1095,14316,13756],{"className":14317},[1163],[1091,14319,14320,14323,14324,14352,14353,14431,14432,14526,14527,14529,14530,14598,14599,14692],{},[1172,14321,14322],{},"实践技巧","：在训练初期，",[1095,14325,14327,14340],{"className":14326},[1098],[1095,14328,14330],{"className":14329},[1102],[1104,14331,14332],{"xmlns":1106},[1108,14333,14334,14338],{},[1111,14335,14336],{},[1114,14337,8480],{},[1129,14339,8480],{"encoding":1131},[1095,14341,14343],{"className":14342,"ariaHidden":1137},[1136],[1095,14344,14346,14349],{"className":14345},[1141],[1095,14347],{"className":14348,"style":5154},[1145],[1095,14350,8480],{"className":14351},[1150,1151]," 很弱，",[1095,14354,14356,14386],{"className":14355},[1098],[1095,14357,14359],{"className":14358},[1102],[1104,14360,14361],{"xmlns":1106},[1108,14362,14363,14383],{},[1111,14364,14365,14367,14369,14371,14373,14375,14377,14379,14381],{},[1114,14366,3738],{},[1118,14368,1121],{"stretchy":1120},[1114,14370,8480],{},[1118,14372,1121],{"stretchy":1120},[1114,14374,1352],{},[1118,14376,1127],{"stretchy":1120},[1118,14378,1127],{"stretchy":1120},[1118,14380,7339],{},[1490,14382,2603],{},[1129,14384,14385],{"encoding":1131},"D(G(z)) \\approx 0",[1095,14387,14389,14422],{"className":14388,"ariaHidden":1137},[1136],[1095,14390,14392,14395,14398,14401,14404,14407,14410,14413,14416,14419],{"className":14391},[1141],[1095,14393],{"className":14394,"style":1146},[1145],[1095,14396,3738],{"className":14397,"style":1936},[1150,1151],[1095,14399,1121],{"className":14400},[1156],[1095,14402,8480],{"className":14403},[1150,1151],[1095,14405,1121],{"className":14406},[1156],[1095,14408,1352],{"className":14409,"style":1388},[1150,1151],[1095,14411,2370],{"className":14412},[1163],[1095,14414],{"className":14415,"style":1542},[1383],[1095,14417,7339],{"className":14418},[1546],[1095,14420],{"className":14421,"style":1542},[1383],[1095,14423,14425,14428],{"className":14424},[1141],[1095,14426],{"className":14427,"style":12299},[1145],[1095,14429,2603],{"className":14430},[1150],"，此时 ",[1095,14433,14435,14473],{"className":14434},[1098],[1095,14436,14438],{"className":14437},[1102],[1104,14439,14440],{"xmlns":1106},[1108,14441,14442,14470],{},[1111,14443,14444,14446,14448,14450,14452,14454,14456,14458,14460,14462,14464,14466,14468],{},[1114,14445,3640],{},[1118,14447,3643],{},[1118,14449,1121],{"stretchy":1120},[1490,14451,1492],{},[1118,14453,1510],{},[1114,14455,3738],{},[1118,14457,1121],{"stretchy":1120},[1114,14459,8480],{},[1118,14461,1121],{"stretchy":1120},[1114,14463,1352],{},[1118,14465,1127],{"stretchy":1120},[1118,14467,1127],{"stretchy":1120},[1118,14469,1127],{"stretchy":1120},[1129,14471,14472],{"encoding":1131},"\\log(1-D(G(z)))",[1095,14474,14476,14502],{"className":14475,"ariaHidden":1137},[1136],[1095,14477,14479,14482,14487,14490,14493,14496,14499],{"className":14478},[1141],[1095,14480],{"className":14481,"style":1146},[1145],[1095,14483,3799,14485],{"className":14484},[1560],[1095,14486,1984],{"style":3802},[1095,14488,1121],{"className":14489},[1156],[1095,14491,1492],{"className":14492},[1150],[1095,14494],{"className":14495,"style":2264},[1383],[1095,14497,1510],{"className":14498},[1779],[1095,14500],{"className":14501,"style":2264},[1383],[1095,14503,14505,14508,14511,14514,14517,14520,14523],{"className":14504},[1141],[1095,14506],{"className":14507,"style":1146},[1145],[1095,14509,3738],{"className":14510,"style":1936},[1150,1151],[1095,14512,1121],{"className":14513},[1156],[1095,14515,8480],{"className":14516},[1150,1151],[1095,14518,1121],{"className":14519},[1156],[1095,14521,1352],{"className":14522,"style":1388},[1150,1151],[1095,14524,13756],{"className":14525},[1163]," 的梯度饱和（接近于 0）。实践中",[1172,14528,9259],{}," ",[1095,14531,14533,14563],{"className":14532},[1098],[1095,14534,14536],{"className":14535},[1102],[1104,14537,14538],{"xmlns":1106},[1108,14539,14540,14560],{},[1111,14541,14542,14544,14546,14548,14550,14552,14554,14556,14558],{},[1114,14543,3640],{},[1118,14545,3643],{},[1114,14547,3738],{},[1118,14549,1121],{"stretchy":1120},[1114,14551,8480],{},[1118,14553,1121],{"stretchy":1120},[1114,14555,1352],{},[1118,14557,1127],{"stretchy":1120},[1118,14559,1127],{"stretchy":1120},[1129,14561,14562],{"encoding":1131},"\\log D(G(z))",[1095,14564,14566],{"className":14565,"ariaHidden":1137},[1136],[1095,14567,14569,14572,14577,14580,14583,14586,14589,14592,14595],{"className":14568},[1141],[1095,14570],{"className":14571,"style":1146},[1145],[1095,14573,3799,14575],{"className":14574},[1560],[1095,14576,1984],{"style":3802},[1095,14578],{"className":14579,"style":1384},[1383],[1095,14581,3738],{"className":14582,"style":1936},[1150,1151],[1095,14584,1121],{"className":14585},[1156],[1095,14587,8480],{"className":14588},[1150,1151],[1095,14590,1121],{"className":14591},[1156],[1095,14593,1352],{"className":14594,"style":1388},[1150,1151],[1095,14596,2370],{"className":14597},[1163]," 代替最小化 ",[1095,14600,14602,14639],{"className":14601},[1098],[1095,14603,14605],{"className":14604},[1102],[1104,14606,14607],{"xmlns":1106},[1108,14608,14609,14637],{},[1111,14610,14611,14613,14615,14617,14619,14621,14623,14625,14627,14629,14631,14633,14635],{},[1114,14612,3640],{},[1118,14614,3643],{},[1118,14616,1121],{"stretchy":1120},[1490,14618,1492],{},[1118,14620,1510],{},[1114,14622,3738],{},[1118,14624,1121],{"stretchy":1120},[1114,14626,8480],{},[1118,14628,1121],{"stretchy":1120},[1114,14630,1352],{},[1118,14632,1127],{"stretchy":1120},[1118,14634,1127],{"stretchy":1120},[1118,14636,1127],{"stretchy":1120},[1129,14638,14472],{"encoding":1131},[1095,14640,14642,14668],{"className":14641,"ariaHidden":1137},[1136],[1095,14643,14645,14648,14653,14656,14659,14662,14665],{"className":14644},[1141],[1095,14646],{"className":14647,"style":1146},[1145],[1095,14649,3799,14651],{"className":14650},[1560],[1095,14652,1984],{"style":3802},[1095,14654,1121],{"className":14655},[1156],[1095,14657,1492],{"className":14658},[1150],[1095,14660],{"className":14661,"style":2264},[1383],[1095,14663,1510],{"className":14664},[1779],[1095,14666],{"className":14667,"style":2264},[1383],[1095,14669,14671,14674,14677,14680,14683,14686,14689],{"className":14670},[1141],[1095,14672],{"className":14673,"style":1146},[1145],[1095,14675,3738],{"className":14676,"style":1936},[1150,1151],[1095,14678,1121],{"className":14679},[1156],[1095,14681,8480],{"className":14682},[1150,1151],[1095,14684,1121],{"className":14685},[1156],[1095,14687,1352],{"className":14688,"style":1388},[1150,1151],[1095,14690,13756],{"className":14691},[1163],"，能提供更强的梯度信号。",[1194,14694,14696],{"id":14695},"_36-gan-的主要问题","3.6 GAN 的主要问题",[1406,14698,14699,14711],{},[1409,14700,14701],{},[1412,14702,14703,14705,14708],{},[1415,14704,6195],{},[1415,14706,14707],{},"描述",[1415,14709,14710],{},"表现",[1428,14712,14713,14730,14743,14756],{},[1412,14714,14715,14724,14727],{},[1433,14716,14717,14720,14723],{},[1172,14718,14719],{},"模式崩塌",[14721,14722],"br",{},"Mode Collapse",[1433,14725,14726],{},"生成器只学会生成少数几种样本，忽略数据分布的多样性",[1433,14728,14729],{},"生成的图像缺乏多样性",[1412,14731,14732,14737,14740],{},[1433,14733,14734],{},[1172,14735,14736],{},"训练不稳定",[1433,14738,14739],{},"G 和 D 的平衡难以维持，容易出现振荡",[1433,14741,14742],{},"损失曲线震荡不收敛",[1412,14744,14745,14750,14753],{},[1433,14746,14747],{},[1172,14748,14749],{},"无收敛保证",[1433,14751,14752],{},"minimax 博弈在一般神经网络参数化下不保证收敛到纳什均衡",[1433,14754,14755],{},"训练难以判断何时终止",[1412,14757,14758,14763,14766],{},[1433,14759,14760],{},[1172,14761,14762],{},"评估困难",[1433,14764,14765],{},"缺乏明确的量化指标判断生成质量",[1433,14767,14768],{},"需要 FID、IS 等辅助指标",[1830,14770],{},[1189,14772,14774],{"id":14773},"四gan-变体","四、GAN 变体",[1194,14776,14778],{"id":14777},"_41-dcgandeep-convolutional-gan","4.1 DCGAN（Deep Convolutional GAN）",[1091,14780,14781],{},"DCGAN 将卷积网络引入 GAN 框架，是第一个成功稳定训练 GAN 的卷积架构。",[1091,14783,14784],{},[1172,14785,14786],{},"DCGAN 架构指南",[1166,14788,14789,14796,14802,14805,14808],{},[1169,14790,14791,14792,14795],{},"用",[1172,14793,14794],{},"步幅卷积","（strided convolution）替代池化层",[1169,14797,14798,14799],{},"G 和 D 中均使用 ",[1172,14800,14801],{},"Batch Normalization",[1169,14803,14804],{},"去除全连接层（最后一层除外）",[1169,14806,14807],{},"生成器使用 ReLU 激活（最后一层 Tanh）",[1169,14809,14810],{},"判别器使用 LeakyReLU 激活",[1091,14812,14813,14816,14817,14904],{},[1172,14814,14815],{},"生成器结构","：噪声向量 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经过多层转置卷积（反卷积）逐步上采样为图像：",[1091,14906,14907],{},[1095,14908,14910,15031],{"className":14909},[1098],[1095,14911,14913],{"className":14912},[1102],[1104,14914,14915],{"xmlns":1106},[1108,14916,14917,15028],{},[1111,14918,14919,14921,14935,14937,14940,14942,14944,14947,14956,14959,14961,14963,14965,14968,14976,14979,14981,14983,14985,14988,14996,14999,15001,15003,15005,15008,15016,15019,15021,15023,15025],{},[1114,14920,1352],{},[1971,14922,14923,14927],{},[1118,14924,14926],{"stretchy":1137,"minsize":14925},"3.0em","→",[14928,14929,14932],"mpadded",{"width":14930,"lspace":14931},"+0.6em","0.3em",[2870,14933,14934],{},"Reshape",[1490,14936,12196],{},[1118,14938,14939],{},"×",[1490,14941,12196],{},[1118,14943,14939],{},[1490,14945,14946],{},"1024",[1971,14948,14949,14951],{},[1118,14950,14926],{"stretchy":1137,"minsize":14925},[14928,14952,14953],{"width":14930,"lspace":14931},[2870,14954,14955],{},"DeConv",[1490,14957,14958],{},"8",[1118,14960,14939],{},[1490,14962,14958],{},[1118,14964,14939],{},[1490,14966,14967],{},"512",[1971,14969,14970,14972],{},[1118,14971,14926],{"stretchy":1137,"minsize":14925},[14928,14973,14974],{"width":14930,"lspace":14931},[2870,14975,14955],{},[1490,14977,14978],{},"16",[1118,14980,14939],{},[1490,14982,14978],{},[1118,14984,14939],{},[1490,14986,14987],{},"256",[1971,14989,14990,14992],{},[1118,14991,14926],{"stretchy":1137,"minsize":14925},[14928,14993,14994],{"width":14930,"lspace":14931},[2870,14995,14955],{},[1490,14997,14998],{},"32",[1118,15000,14939],{},[1490,15002,14998],{},[1118,15004,14939],{},[1490,15006,15007],{},"128",[1971,15009,15010,15012],{},[1118,15011,14926],{"stretchy":1137,"minsize":14925},[14928,15013,15014],{"width":14930,"lspace":14931},[2870,15015,14955],{},[1490,15017,15018],{},"64",[1118,15020,14939],{},[1490,15022,15018],{},[1118,15024,14939],{},[1490,15026,15027],{},"3",[1129,15029,15030],{"encoding":1131},"z \\xrightarrow{\\text{Reshape}} 4\\times4\\times1024 \\xrightarrow{\\text{DeConv}} 8\\times8\\times512 \\xrightarrow{\\text{DeConv}} 16\\times16\\times256 \\xrightarrow{\\text{DeConv}} 32\\times32\\times128 \\xrightarrow{\\text{DeConv}} 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WGAN（Wasserstein GAN）",[2556,15583,15585],{"id":15584},"js-散度的缺陷","JS 散度的缺陷",[1091,15587,15588,15590,15591,6744,15680,15749,15750,15791],{},[1172,15589,6195],{},"：当 ",[1095,15592,15594,15619],{"className":15593},[1098],[1095,15595,15597],{"className":15596},[1102],[1104,15598,15599],{"xmlns":1106},[1108,15600,15601,15617],{},[1111,15602,15603],{},[1465,15604,15605,15607],{},[1114,15606,1091],{},[1111,15608,15609,15611,15613,15615],{},[1114,15610,2875],{},[1114,15612,8742],{},[1114,15614,8745],{},[1114,15616,8742],{},[1129,15618,12499],{"encoding":1131},[1095,15620,15622],{"className":15621,"ariaHidden":1137},[1136],[1095,15623,15625,15628],{"className":15624},[1141],[1095,15626],{"className":15627,"style":2456},[1145],[1095,15629,15631,15634],{"className":15630},[1150],[1095,15632,1091],{"className":15633},[1150,1151],[1095,15635,15637],{"className":15636},[1570],[1095,15638,15640,15672],{"className":15639},[1574,1575],[1095,15641,15643,15669],{"className":15642},[1579],[1095,15644,15646],{"className":15645,"style":1923},[1583],[1095,15647,15648,15651],{"style":1647},[1095,15649],{"className":15650,"style":1592},[1591],[1095,15652,15654],{"className":15653},[1596,1597,1598,1599],[1095,15655,15657,15660,15663,15666],{"className":15656},[1150,1599],[1095,15658,2875],{"className":15659},[1150,1151,1599],[1095,15661,8742],{"className":15662},[1150,1151,1599],[1095,15664,8745],{"className":15665},[1150,1151,1599],[1095,15667,8742],{"className":15668},[1150,1151,1599],[1095,15670,1607],{"className":15671},[1606],[1095,15673,15675],{"className":15674},[1579],[1095,15676,15678],{"className":15677,"style":1666},[1583],[1095,15679],{},[1095,15681,15683,15700],{"className":15682},[1098],[1095,15684,15686],{"className":15685},[1102],[1104,15687,15688],{"xmlns":1106},[1108,15689,15690,15698],{},[1111,15691,15692],{},[1465,15693,15694,15696],{},[1114,15695,1091],{},[1114,15697,1984],{},[1129,15699,12582],{"encoding":1131},[1095,15701,15703],{"className":15702,"ariaHidden":1137},[1136],[1095,15704,15706,15709],{"className":15705},[1141],[1095,15707],{"className":15708,"style":12592},[1145],[1095,15710,15712,15715],{"className":15711},[1150],[1095,15713,1091],{"className":15714},[1150,1151],[1095,15716,15718],{"className":15717},[1570],[1095,15719,15721,15741],{"className":15720},[1574,1575],[1095,15722,15724,15738],{"className":15723},[1579],[1095,15725,15727],{"className":15726,"style":8430},[1583],[1095,15728,15729,15732],{"style":1647},[1095,15730],{"className":15731,"style":1592},[1591],[1095,15733,15735],{"className":15734},[1596,1597,1598,1599],[1095,15736,1984],{"className":15737,"style":1256},[1150,1151,1599],[1095,15739,1607],{"className":15740},[1606],[1095,15742,15744],{"className":15743},[1579],[1095,15745,15747],{"className":15746,"style":2098},[1583],[1095,15748],{}," 的支撑集不重叠时（高维空间中几乎总是如此），JS 散度恒等于 ",[1095,15751,15753,15771],{"className":15752},[1098],[1095,15754,15756],{"className":15755},[1102],[1104,15757,15758],{"xmlns":1106},[1108,15759,15760,15768],{},[1111,15761,15762,15764,15766],{},[1114,15763,3640],{},[1118,15765,3643],{},[1490,15767,2177],{},[1129,15769,15770],{"encoding":1131},"\\log 2",[1095,15772,15774],{"className":15773,"ariaHidden":1137},[1136],[1095,15775,15777,15780,15785,15788],{"className":15776},[1141],[1095,15778],{"className":15779,"style":12266},[1145],[1095,15781,3799,15783],{"className":15782},[1560],[1095,15784,1984],{"style":3802},[1095,15786],{"className":15787,"style":1384},[1383],[1095,15789,2177],{"className":15790},[1150],"，梯度为 0，导致生成器无法学习。",[2556,15793,15795],{"id":15794},"wasserstein-距离","Wasserstein 距离",[1091,15797,15798,15801],{},[1172,15799,15800],{},"Earth Mover's Distance（推土机距离）","：衡量将一个分布\"搬运\"成另一个分布所需的最小工作量：",[1091,15803,15804],{},[1095,15805,15807,15929],{"className":15806},[1098],[1095,15808,15810],{"className":15809},[1102],[1104,15811,15812],{"xmlns":1106},[1108,15813,15814,15926],{},[1111,15815,15816,15819,15821,15835,15837,15843,15845,15847,15892,15912,15914,15916,15918,15920,15922,15924],{},[1114,15817,15818],{},"W",[1118,15820,1121],{"stretchy":1120},[1465,15822,15823,15825],{},[1114,15824,1091],{},[1111,15826,15827,15829,15831,15833],{},[1114,15828,2875],{},[1114,15830,8742],{},[1114,15832,8745],{},[1114,15834,8742],{},[1118,15836,1349],{"separator":1137},[1465,15838,15839,15841],{},[1114,15840,1091],{},[1114,15842,1984],{},[1118,15844,1127],{"stretchy":1120},[1118,15846,1463],{},[1465,15848,15849,15856],{},[1111,15850,15851,15854],{},[1114,15852,15853],{},"inf",[1118,15855,3643],{},[1111,15857,15858,15861,15863,15866,15868,15882,15884,15890],{},[1114,15859,15860],{},"γ",[1118,15862,8592],{},[1114,15864,15865],{"mathvariant":1229},"Π",[1118,15867,1121],{"stretchy":1120},[1465,15869,15870,15872],{},[1114,15871,1091],{},[1111,15873,15874,15876,15878,15880],{},[1114,15875,2875],{},[1114,15877,8742],{},[1114,15879,8745],{},[1114,15881,8742],{},[1118,15883,1349],{"separator":1137},[1465,15885,15886,15888],{},[1114,15887,1091],{},[1114,15889,1984],{},[1118,15891,1127],{"stretchy":1120},[1465,15893,15894,15896],{},[1114,15895,2138],{"mathvariant":3662},[1111,15897,15898,15900,15902,15904,15906,15908,15910],{},[1118,15899,1121],{"stretchy":1120},[1114,15901,1124],{},[1118,15903,1349],{"separator":1137},[1114,15905,1226],{},[1118,15907,1127],{"stretchy":1120},[1118,15909,2585],{},[1114,15911,15860],{},[1118,15913,3685],{"stretchy":1120},[1114,15915,2143],{"mathvariant":1229},[1114,15917,1124],{},[1118,15919,1510],{},[1114,15921,1226],{},[1114,15923,2143],{"mathvariant":1229},[1118,15925,3730],{"stretchy":1120},[1129,15927,15928],{"encoding":1131},"W(p_{data}, p_g) = \\inf_{\\gamma \\in \\Pi(p_{data}, p_g)} \\mathbb{E}_{(x,y) \\sim \\gamma}[\\|x - y\\|]",[1095,15930,15932,16054,16300],{"className":15931,"ariaHidden":1137},[1136],[1095,15933,15935,15938,15941,15944,15996,15999,16002,16042,16045,16048,16051],{"className":15934},[1141],[1095,15936],{"className":15937,"style":2058},[1145],[1095,15939,15818],{"className":15940,"style":1152},[1150,1151],[1095,15942,1121],{"className":15943},[1156],[1095,15945,15947,15950],{"className":15946},[1150],[1095,15948,1091],{"className":15949},[1150,1151],[1095,15951,15953],{"className":15952},[1570],[1095,15954,15956,15988],{"className":15955},[1574,1575],[1095,15957,15959,15985],{"className":15958},[1579],[1095,15960,15962],{"className":15961,"style":1923},[1583],[1095,15963,15964,15967],{"style":1647},[1095,15965],{"className":15966,"style":1592},[1591],[1095,15968,15970],{"className":15969},[1596,1597,1598,1599],[1095,15971,15973,15976,15979,15982],{"className":15972},[1150,1599],[1095,15974,2875],{"className":15975},[1150,1151,1599],[1095,15977,8742],{"className":15978},[1150,1151,1599],[1095,15980,8745],{"className":15981},[1150,1151,1599],[1095,15983,8742],{"className":15984},[1150,1151,1599],[1095,15986,1607],{"className":15987},[1606],[1095,15989,15991],{"className":15990},[1579],[1095,15992,15994],{"className":15993,"style":1666},[1583],[1095,15995],{},[1095,15997,1349],{"className":15998},[1379],[1095,16000],{"className":16001,"style":1384},[1383],[1095,16003,16005,16008],{"className":16004},[1150],[1095,16006,1091],{"className":16007},[1150,1151],[1095,16009,16011],{"className":16010},[1570],[1095,16012,16014,16034],{"className":16013},[1574,1575],[1095,16015,16017,16031],{"className":16016},[1579],[1095,16018,16020],{"className":16019,"style":8430},[1583],[1095,16021,16022,16025],{"style":1647},[1095,16023],{"className":16024,"style":1592},[1591],[1095,16026,16028],{"className":16027},[1596,1597,1598,1599],[1095,16029,1984],{"className":16030,"style":1256},[1150,1151,1599],[1095,16032,1607],{"className":16033},[1606],[1095,16035,16037],{"className":16036},[1579],[1095,16038,16040],{"className":16039,"style":2098},[1583],[1095,16041],{},[1095,16043,1127],{"className":16044},[1163],[1095,16046],{"className":16047,"style":1542},[1383],[1095,16049,1463],{"className":16050},[1546],[1095,16052],{"className":16053,"style":1542},[1383],[1095,16055,16057,16061,16218,16221,16282,16285,16288,16291,16294,16297],{"className":16056},[1141],[1095,16058],{"className":16059,"style":16060},[1145],"height:1.1275em;vertical-align:-0.3775em;",[1095,16062,16064,16071],{"className":16063},[1560],[1095,16065,16067,16068],{"className":16066},[1560],"in",[1095,16069,1863],{"style":16070},"margin-right:0.0778em;",[1095,16072,16074],{"className":16073},[1570],[1095,16075,16077,16209],{"className":16076},[1574,1575],[1095,16078,16080,16206],{"className":16079},[1579],[1095,16081,16083],{"className":16082,"style":3279},[1583],[1095,16084,16086,16089],{"style":16085},"top:-2.5198em;margin-right:0.05em;",[1095,16087],{"className":16088,"style":1592},[1591],[1095,16090,16092],{"className":16091},[1596,1597,1598,1599],[1095,16093,16095,16099,16102,16105,16108,16160,16163,16203],{"className":16094},[1150,1599],[1095,16096,15860],{"className":16097,"style":16098},[1150,1151,1599],"margin-right:0.0556em;",[1095,16100,8592],{"className":16101},[1546,1599],[1095,16103,15865],{"className":16104},[1150,1599],[1095,16106,1121],{"className":16107},[1156,1599],[1095,16109,16111,16114],{"className":16110},[1150,1599],[1095,16112,1091],{"className":16113},[1150,1151,1599],[1095,16115,16117],{"className":16116},[1570],[1095,16118,16120,16152],{"className":16119},[1574,1575],[1095,16121,16123,16149],{"className":16122},[1579],[1095,16124,16126],{"className":16125,"style":3279},[1583],[1095,16127,16128,16131],{"style":3282},[1095,16129],{"className":16130,"style":3286},[1591],[1095,16132,16134],{"className":16133},[1596,3290,3291,1599],[1095,16135,16137,16140,16143,16146],{"className":16136},[1150,1599],[1095,16138,2875],{"className":16139},[1150,1151,1599],[1095,16141,8742],{"className":16142},[1150,1151,1599],[1095,16144,8745],{"className":16145},[1150,1151,1599],[1095,16147,8742],{"className":16148},[1150,1151,1599],[1095,16150,1607],{"className":16151},[1606],[1095,16153,16155],{"className":16154},[1579],[1095,16156,16158],{"className":16157,"style":3304},[1583],[1095,16159],{},[1095,16161,1349],{"className":16162},[1379,1599],[1095,16164,16166,16169],{"className":16165},[1150,1599],[1095,16167,1091],{"className":16168},[1150,1151,1599],[1095,16170,16172],{"className":16171},[1570],[1095,16173,16175,16195],{"className":16174},[1574,1575],[1095,16176,16178,16192],{"className":16177},[1579],[1095,16179,16181],{"className":16180,"style":9159},[1583],[1095,16182,16183,16186],{"style":9162},[1095,16184],{"className":16185,"style":3286},[1591],[1095,16187,16189],{"className":16188},[1596,3290,3291,1599],[1095,16190,1984],{"className":16191,"style":1256},[1150,1151,1599],[1095,16193,1607],{"className":16194},[1606],[1095,16196,16198],{"className":16197},[1579],[1095,16199,16201],{"className":16200,"style":9790},[1583],[1095,16202],{},[1095,16204,1127],{"className":16205},[1163,1599],[1095,16207,1607],{"className":16208},[1606],[1095,16210,16212],{"className":16211},[1579],[1095,16213,16216],{"className":16214,"style":16215},[1583],"height:0.3775em;",[1095,16217],{},[1095,16219],{"className":16220,"style":1384},[1383],[1095,16222,16224,16227],{"className":16223},[1150],[1095,16225,2138],{"className":16226},[1150,3877],[1095,16228,16230],{"className":16229},[1570],[1095,16231,16233,16274],{"className":16232},[1574,1575],[1095,16234,16236,16271],{"className":16235},[1579],[1095,16237,16239],{"className":16238,"style":3279},[1583],[1095,16240,16241,16244],{"style":3892},[1095,16242],{"className":16243,"style":1592},[1591],[1095,16245,16247],{"className":16246},[1596,1597,1598,1599],[1095,16248,16250,16253,16256,16259,16262,16265,16268],{"className":16249},[1150,1599],[1095,16251,1121],{"className":16252},[1156,1599],[1095,16254,1124],{"className":16255},[1150,1151,1599],[1095,16257,1349],{"className":16258},[1379,1599],[1095,16260,1226],{"className":16261,"style":1256},[1150,1151,1599],[1095,16263,1127],{"className":16264},[1163,1599],[1095,16266,2585],{"className":16267},[1546,1599],[1095,16269,15860],{"className":16270,"style":16098},[1150,1151,1599],[1095,16272,1607],{"className":16273},[1606],[1095,16275,16277],{"className":16276},[1579],[1095,16278,16280],{"className":16279,"style":9065},[1583],[1095,16281],{},[1095,16283,3685],{"className":16284},[1156],[1095,16286,2143],{"className":16287},[1150],[1095,16289,1124],{"className":16290},[1150,1151],[1095,16292],{"className":16293,"style":2264},[1383],[1095,16295,1510],{"className":16296},[1779],[1095,16298],{"className":16299,"style":2264},[1383],[1095,16301,16303,16306,16309,16312],{"className":16302},[1141],[1095,16304],{"className":16305,"style":1146},[1145],[1095,16307,1226],{"className":16308,"style":1256},[1150,1151],[1095,16310,2143],{"className":16311},[1150],[1095,16313,3730],{"className":16314},[1163],[1091,16316,6157,16317,16476,16477,6744,16566,16635],{},[1095,16318,16320,16360],{"className":16319},[1098],[1095,16321,16323],{"className":16322},[1102],[1104,16324,16325],{"xmlns":1106},[1108,16326,16327,16357],{},[1111,16328,16329,16331,16333,16347,16349,16355],{},[1114,16330,15865],{"mathvariant":1229},[1118,16332,1121],{"stretchy":1120},[1465,16334,16335,16337],{},[1114,16336,1091],{},[1111,16338,16339,16341,16343,16345],{},[1114,16340,2875],{},[1114,16342,8742],{},[1114,16344,8745],{},[1114,16346,8742],{},[1118,16348,1349],{"separator":1137},[1465,16350,16351,16353],{},[1114,16352,1091],{},[1114,16354,1984],{},[1118,16356,1127],{"stretchy":1120},[1129,16358,16359],{"encoding":1131},"\\Pi(p_{data}, p_g)",[1095,16361,16363],{"className":16362,"ariaHidden":1137},[1136],[1095,16364,16366,16369,16372,16375,16427,16430,16433,16473],{"className":16365},[1141],[1095,16367],{"className":16368,"style":2058},[1145],[1095,16370,15865],{"className":16371},[1150],[1095,16373,1121],{"className":16374},[1156],[1095,16376,16378,16381],{"className":16377},[1150],[1095,16379,1091],{"className":16380},[1150,1151],[1095,16382,16384],{"className":16383},[1570],[1095,16385,16387,16419],{"className":16386},[1574,1575],[1095,16388,16390,16416],{"className":16389},[1579],[1095,16391,16393],{"className":16392,"style":1923},[1583],[1095,16394,16395,16398],{"style":1647},[1095,16396],{"className":16397,"style":1592},[1591],[1095,16399,16401],{"className":16400},[1596,1597,1598,1599],[1095,16402,16404,16407,16410,16413],{"className":16403},[1150,1599],[1095,16405,2875],{"className":16406},[1150,1151,1599],[1095,16408,8742],{"className":16409},[1150,1151,1599],[1095,16411,8745],{"className":16412},[1150,1151,1599],[1095,16414,8742],{"className":16415},[1150,1151,1599],[1095,16417,1607],{"className":16418},[1606],[1095,16420,16422],{"className":16421},[1579],[1095,16423,16425],{"className":16424,"style":1666},[1583],[1095,16426],{},[1095,16428,1349],{"className":16429},[1379],[1095,16431],{"className":16432,"style":1384},[1383],[1095,16434,16436,16439],{"className":16435},[1150],[1095,16437,1091],{"className":16438},[1150,1151],[1095,16440,16442],{"className":16441},[1570],[1095,16443,16445,16465],{"className":16444},[1574,1575],[1095,16446,16448,16462],{"className":16447},[1579],[1095,16449,16451],{"className":16450,"style":8430},[1583],[1095,16452,16453,16456],{"style":1647},[1095,16454],{"className":16455,"style":1592},[1591],[1095,16457,16459],{"className":16458},[1596,1597,1598,1599],[1095,16460,1984],{"className":16461,"style":1256},[1150,1151,1599],[1095,16463,1607],{"className":16464},[1606],[1095,16466,16468],{"className":16467},[1579],[1095,16469,16471],{"className":16470,"style":2098},[1583],[1095,16472],{},[1095,16474,1127],{"className":16475},[1163]," 是所有以 ",[1095,16478,16480,16505],{"className":16479},[1098],[1095,16481,16483],{"className":16482},[1102],[1104,16484,16485],{"xmlns":1106},[1108,16486,16487,16503],{},[1111,16488,16489],{},[1465,16490,16491,16493],{},[1114,16492,1091],{},[1111,16494,16495,16497,16499,16501],{},[1114,16496,2875],{},[1114,16498,8742],{},[1114,16500,8745],{},[1114,16502,8742],{},[1129,16504,12499],{"encoding":1131},[1095,16506,16508],{"className":16507,"ariaHidden":1137},[1136],[1095,16509,16511,16514],{"className":16510},[1141],[1095,16512],{"className":16513,"style":2456},[1145],[1095,16515,16517,16520],{"className":16516},[1150],[1095,16518,1091],{"className":16519},[1150,1151],[1095,16521,16523],{"className":16522},[1570],[1095,16524,16526,16558],{"className":16525},[1574,1575],[1095,16527,16529,16555],{"className":16528},[1579],[1095,16530,16532],{"className":16531,"style":1923},[1583],[1095,16533,16534,16537],{"style":1647},[1095,16535],{"className":16536,"style":1592},[1591],[1095,16538,16540],{"className":16539},[1596,1597,1598,1599],[1095,16541,16543,16546,16549,16552],{"className":16542},[1150,1599],[1095,16544,2875],{"className":16545},[1150,1151,1599],[1095,16547,8742],{"className":16548},[1150,1151,1599],[1095,16550,8745],{"className":16551},[1150,1151,1599],[1095,16553,8742],{"className":16554},[1150,1151,1599],[1095,16556,1607],{"className":16557},[1606],[1095,16559,16561],{"className":16560},[1579],[1095,16562,16564],{"className":16563,"style":1666},[1583],[1095,16565],{},[1095,16567,16569,16586],{"className":16568},[1098],[1095,16570,16572],{"className":16571},[1102],[1104,16573,16574],{"xmlns":1106},[1108,16575,16576,16584],{},[1111,16577,16578],{},[1465,16579,16580,16582],{},[1114,16581,1091],{},[1114,16583,1984],{},[1129,16585,12582],{"encoding":1131},[1095,16587,16589],{"className":16588,"ariaHidden":1137},[1136],[1095,16590,16592,16595],{"className":16591},[1141],[1095,16593],{"className":16594,"style":12592},[1145],[1095,16596,16598,16601],{"className":16597},[1150],[1095,16599,1091],{"className":16600},[1150,1151],[1095,16602,16604],{"className":16603},[1570],[1095,16605,16607,16627],{"className":16606},[1574,1575],[1095,16608,16610,16624],{"className":16609},[1579],[1095,16611,16613],{"className":16612,"style":8430},[1583],[1095,16614,16615,16618],{"style":1647},[1095,16616],{"className":16617,"style":1592},[1591],[1095,16619,16621],{"className":16620},[1596,1597,1598,1599],[1095,16622,1984],{"className":16623,"style":1256},[1150,1151,1599],[1095,16625,1607],{"className":16626},[1606],[1095,16628,16630],{"className":16629},[1579],[1095,16631,16633],{"className":16632,"style":2098},[1583],[1095,16634],{}," 为边际分布的联合分布集合。",[2556,16637,16639],{"id":16638},"wgan-目标函数","WGAN 目标函数",[1091,16641,16642],{},"利用 Kantorovich-Rubinstein 对偶性：",[1091,16644,16645],{},[1095,16646,16648,16782],{"className":16647},[1098],[1095,16649,16651],{"className":16650},[1102],[1104,16652,16653],{"xmlns":1106},[1108,16654,16655,16779],{},[1111,16656,16657,16659,16661,16675,16677,16683,16685,16687,16713,16737,16739,16741,16743,16745,16747,16749,16751,16767,16769,16771,16773,16775,16777],{},[1114,16658,15818],{},[1118,16660,1121],{"stretchy":1120},[1465,16662,16663,16665],{},[1114,16664,1091],{},[1111,16666,16667,16669,16671,16673],{},[1114,16668,2875],{},[1114,16670,8742],{},[1114,16672,8745],{},[1114,16674,8742],{},[1118,16676,1349],{"separator":1137},[1465,16678,16679,16681],{},[1114,16680,1091],{},[1114,16682,1984],{},[1118,16684,1127],{"stretchy":1120},[1118,16686,1463],{},[1465,16688,16689,16696],{},[1111,16690,16691,16694],{},[1114,16692,16693],{},"sup",[1118,16695,3643],{},[1111,16697,16698,16700,16702,16708,16711],{},[1114,16699,2143],{"mathvariant":1229},[1114,16701,1863],{},[1465,16703,16704,16706],{},[1114,16705,2143],{"mathvariant":1229},[1114,16707,2130],{},[1118,16709,16710],{},"≤",[1490,16712,1492],{},[1465,16714,16715,16717],{},[1114,16716,2138],{"mathvariant":3662},[1111,16718,16719,16721,16723],{},[1114,16720,1124],{},[1118,16722,2585],{},[1465,16724,16725,16727],{},[1114,16726,1091],{},[1111,16728,16729,16731,16733,16735],{},[1114,16730,2875],{},[1114,16732,8742],{},[1114,16734,8745],{},[1114,16736,8742],{},[1118,16738,3685],{"stretchy":1120},[1114,16740,1863],{},[1118,16742,1121],{"stretchy":1120},[1114,16744,1124],{},[1118,16746,1127],{"stretchy":1120},[1118,16748,3730],{"stretchy":1120},[1118,16750,1510],{},[1465,16752,16753,16755],{},[1114,16754,2138],{"mathvariant":3662},[1111,16756,16757,16759,16761],{},[1114,16758,1124],{},[1118,16760,2585],{},[1465,16762,16763,16765],{},[1114,16764,1091],{},[1114,16766,1984],{},[1118,16768,3685],{"stretchy":1120},[1114,16770,1863],{},[1118,16772,1121],{"stretchy":1120},[1114,16774,1124],{},[1118,16776,1127],{"stretchy":1120},[1118,16778,3730],{"stretchy":1120},[1129,16780,16781],{"encoding":1131},"W(p_{data}, p_g) = \\sup_{\\|f\\|_L \\leq 1} \\mathbb{E}_{x \\sim p_{data}}[f(x)] - \\mathbb{E}_{x \\sim p_g}[f(x)]",[1095,16783,16785,16907,17136],{"className":16784,"ariaHidden":1137},[1136],[1095,16786,16788,16791,16794,16797,16849,16852,16855,16895,16898,16901,16904],{"className":16787},[1141],[1095,16789],{"className":16790,"style":2058},[1145],[1095,16792,15818],{"className":16793,"style":1152},[1150,1151],[1095,16795,1121],{"className":16796},[1156],[1095,16798,16800,16803],{"className":16799},[1150],[1095,16801,1091],{"className":16802},[1150,1151],[1095,16804,16806],{"className":16805},[1570],[1095,16807,16809,16841],{"className":16808},[1574,1575],[1095,16810,16812,16838],{"className":16811},[1579],[1095,16813,16815],{"className":16814,"style":1923},[1583],[1095,16816,16817,16820],{"style":1647},[1095,16818],{"className":16819,"style":1592},[1591],[1095,16821,16823],{"className":16822},[1596,1597,1598,1599],[1095,16824,16826,16829,16832,16835],{"className":16825},[1150,1599],[1095,16827,2875],{"className":16828},[1150,1151,1599],[1095,16830,8742],{"className":16831},[1150,1151,1599],[1095,16833,8745],{"className":16834},[1150,1151,1599],[1095,16836,8742],{"className":16837},[1150,1151,1599],[1095,16839,1607],{"className":16840},[1606],[1095,16842,16844],{"className":16843},[1579],[1095,16845,16847],{"className":16846,"style":1666},[1583],[1095,16848],{},[1095,16850,1349],{"className":16851},[1379],[1095,16853],{"className":16854,"style":1384},[1383],[1095,16856,16858,16861],{"className":16857},[1150],[1095,16859,1091],{"className":16860},[1150,1151],[1095,16862,16864],{"className":16863},[1570],[1095,16865,16867,16887],{"className":16866},[1574,1575],[1095,16868,16870,16884],{"className":16869},[1579],[1095,16871,16873],{"className":16872,"style":8430},[1583],[1095,16874,16875,16878],{"style":1647},[1095,16876],{"className":16877,"style":1592},[1591],[1095,16879,16881],{"className":16880},[1596,1597,1598,1599],[1095,16882,1984],{"className":16883,"style":1256},[1150,1151,1599],[1095,16885,1607],{"className":16886},[1606],[1095,16888,16890],{"className":16889},[1579],[1095,16891,16893],{"className":16892,"style":2098},[1583],[1095,16894],{},[1095,16896,1127],{"className":16897},[1163],[1095,16899],{"className":16900,"style":1542},[1383],[1095,16902,1463],{"className":16903},[1546],[1095,16905],{"className":16906,"style":1542},[1383],[1095,16908,16910,16914,17011,17014,17112,17115,17118,17121,17124,17127,17130,17133],{"className":16909},[1141],[1095,16911],{"className":16912,"style":16913},[1145],"height:1.1691em;vertical-align:-0.4191em;",[1095,16915,16917,16920],{"className":16916},[1560],[1095,16918,16693],{"className":16919},[1560],[1095,16921,16923],{"className":16922},[1570],[1095,16924,16926,17002],{"className":16925},[1574,1575],[1095,16927,16929,16999],{"className":16928},[1579],[1095,16930,16933],{"className":16931,"style":16932},[1583],"height:0.2809em;",[1095,16934,16936,16939],{"style":16935},"top:-2.4559em;margin-right:0.05em;",[1095,16937],{"className":16938,"style":1592},[1591],[1095,16940,16942],{"className":16941},[1596,1597,1598,1599],[1095,16943,16945,16948,16951,16993,16996],{"className":16944},[1150,1599],[1095,16946,2143],{"className":16947},[1150,1599],[1095,16949,1863],{"className":16950,"style":1910},[1150,1151,1599],[1095,16952,16954,16957],{"className":16953},[1150,1599],[1095,16955,2143],{"className":16956},[1150,1599],[1095,16958,16960],{"className":16959},[1570],[1095,16961,16963,16984],{"className":16962},[1574,1575],[1095,16964,16966,16981],{"className":16965},[1579],[1095,16967,16969],{"className":16968,"style":3279},[1583],[1095,16970,16972,16975],{"style":16971},"top:-2.3567em;margin-left:0em;margin-right:0.0714em;",[1095,16973],{"className":16974,"style":3286},[1591],[1095,16976,16978],{"className":16977},[1596,3290,3291,1599],[1095,16979,2130],{"className":16980},[1150,1151,1599],[1095,16982,1607],{"className":16983},[1606],[1095,16985,16987],{"className":16986},[1579],[1095,16988,16991],{"className":16989,"style":16990},[1583],"height:0.1433em;",[1095,16992],{},[1095,16994,16710],{"className":16995},[1546,1599],[1095,16997,1492],{"className":16998},[1150,1599],[1095,17000,1607],{"className":17001},[1606],[1095,17003,17005],{"className":17004},[1579],[1095,17006,17009],{"className":17007,"style":17008},[1583],"height:0.4191em;",[1095,17010],{},[1095,17012],{"className":17013,"style":1384},[1383],[1095,17015,17017,17020],{"className":17016},[1150],[1095,17018,2138],{"className":17019},[1150,3877],[1095,17021,17023],{"className":17022},[1570],[1095,17024,17026,17104],{"className":17025},[1574,1575],[1095,17027,17029,17101],{"className":17028},[1579],[1095,17030,17032],{"className":17031,"style":8430},[1583],[1095,17033,17034,17037],{"style":1647},[1095,17035],{"className":17036,"style":1592},[1591],[1095,17038,17040],{"className":17039},[1596,1597,1598,1599],[1095,17041,17043,17046,17049],{"className":17042},[1150,1599],[1095,17044,1124],{"className":17045},[1150,1151,1599],[1095,17047,2585],{"className":17048},[1546,1599],[1095,17050,17052,17055],{"className":17051}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\\max_{\\|D\\|_L \\leq 1} \\mathbb{E}_{x \\sim p_{data}}[D(x)] - \\mathbb{E}_{z \\sim p_z}[D(G(z))]",[1095,17373,17375,17641],{"className":17374,"ariaHidden":1137},[1136],[1095,17376,17378,17381,17421,17424,17516,17519,17617,17620,17623,17626,17629,17632,17635,17638],{"className":17377},[1141],[1095,17379],{"className":17380,"style":8959},[1145],[1095,17382,17384,17387],{"className":17383},[1560],[1095,17385,8692],{"className":17386},[1560],[1095,17388,17390],{"className":17389},[1570],[1095,17391,17393,17413],{"className":17392},[1574,1575],[1095,17394,17396,17410],{"className":17395},[1579],[1095,17397,17399],{"className":17398,"style":2210},[1583],[1095,17400,17401,17404],{"style":8856},[1095,17402],{"className":17403,"style":1592},[1591],[1095,17405,17407],{"className":17406},[1596,1597,1598,1599],[1095,17408,8480],{"className":17409},[1150,1151,1599],[1095,17411,1607],{"className":17412},[1606],[1095,17414,17416],{"className":17415},[1579],[1095,17417,17419],{"className":17418,"style":1666},[1583],[1095,17420],{},[1095,17422],{"className":17423,"style":1384},[1383],[1095,17425,17427,17430],{"className":17426},[1560],[1095,17428,8703],{"className":17429},[1560],[1095,17431,17433],{"className":17432},[1570],[1095,17434,17436,17508],{"className":17435},[1574,1575],[1095,17437,17439,17505],{"className":17438},[1579],[1095,17440,17442],{"className":17441,"style":3279},[1583],[1095,17443,17444,17447],{"style":16085},[1095,17445],{"className":17446,"style":1592},[1591],[1095,17448,17450],{"className":17449},[1596,1597,1598,1599],[1095,17451,17453,17456,17459,17499,17502],{"className":17452},[1150,1599],[1095,17454,2143],{"className":17455},[1150,1599],[1095,17457,3738],{"className":17458,"style":1936},[1150,1151,1599],[1095,17460,17462,17465],{"className":17461},[1150,1599],[1095,17463,2143],{"className":17464},[1150,1599],[1095,17466,17468],{"className":17467},[1570],[1095,17469,17471,17491],{"className":17470},[1574,1575],[1095,17472,17474,17488],{"className":17473},[1579],[1095,17475,17477],{"className":17476,"style":3279},[1583],[1095,17478,17479,17482],{"style":16971},[1095,17480],{"className":17481,"style":3286},[1591],[1095,17483,17485],{"className":17484},[1596,3290,3291,1599],[1095,17486,2130],{"className":17487},[1150,1151,1599],[1095,17489,1607],{"className":17490},[1606],[1095,17492,17494],{"className":17493},[1579],[1095,17495,17497],{"className":17496,"style":16990},[1583],[1095,17498],{},[1095,17500,16710],{"className":17501},[1546,1599],[1095,17503,1492],{"className":17504},[1150,1599],[1095,17506,1607],{"className":17507},[1606],[1095,17509,17511],{"className":17510},[1579],[1095,17512,17514],{"className":17513,"style":9065},[1583],[1095,17515],{},[1095,17517],{"className":17518,"style":1384},[1383],[1095,17520,17522,17525],{"className":17521},[1150],[1095,17523,2138],{"className":17524},[1150,3877],[1095,17526,17528],{"className":17527},[1570],[1095,17529,17531,17609],{"className":17530},[1574,1575],[1095,17532,17534,17606],{"className":17533},[1579],[1095,17535,17537],{"className":17536,"style":8430},[1583],[1095,17538,17539,17542],{"style":1647},[1095,17540],{"className":17541,"style":1592},[1591],[1095,17543,17545],{"className":17544},[1596,1597,1598,1599],[1095,17546,17548,17551,17554],{"className":17547},[1150,1599],[1095,17549,1124],{"className":17550},[1150,1151,1599],[1095,17552,2585],{"className":17553},[1546,1599],[1095,17555,17557,17560],{"className":17556},[1150,1599],[1095,17558,1091],{"className":17559},[1150,1151,1599],[1095,17561,17563],{"className":17562},[1570],[1095,17564,17566,17598],{"className":17565},[1574,1575],[1095,17567,17569,17595],{"className":17568},[1579],[1095,17570,17572],{"className":17571,"style":3279},[1583],[1095,17573,17574,17577],{"style":3282},[1095,17575],{"className":17576,"style":3286},[1591],[1095,17578,17580],{"className":17579},[1596,3290,3291,1599],[1095,17581,17583,17586,17589,17592],{"className":17582},[1150,1599],[1095,17584,2875],{"className":17585},[1150,1151,1599],[1095,17587,8742],{"className":17588},[1150,1151,1599],[1095,17590,8745],{"className":17591},[1150,1151,1599],[1095,17593,8742],{"className":17594},[1150,1151,1599],[1095,17596,1607],{"className":17597},[1606],[1095,17599,17601],{"className":17600},[1579],[1095,17602,17604],{"className":17603,"style":3304},[1583],[1095,17605],{},[1095,17607,1607],{"className":17608},[1606],[1095,17610,17612],{"className":17611},[1579],[1095,17613,17615],{"className":17614,"style":2098},[1583],[1095,17616],{},[1095,17618,3685],{"className":17619},[1156],[1095,17621,3738],{"className":17622,"style":1936},[1150,1151],[1095,17624,1121],{"className":17625},[1156],[1095,17627,1124],{"className":17628},[1150,1151],[1095,17630,4869],{"className":17631},[1163],[1095,17633],{"className":17634,"style":2264},[1383],[1095,17636,1510],{"className":17637},[1779],[1095,17639],{"className":17640,"style":2264},[1383],[1095,17642,17644,17647,17733,17736,17739,17742,17745,17748,17751],{"className":17643},[1141],[1095,17645],{"className":17646,"style":2058},[1145],[1095,17648,17650,17653],{"className"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clipping）",[1095,17763,17765,17795],{"className":17764},[1098],[1095,17766,17768],{"className":17767},[1102],[1104,17769,17770],{"xmlns":1106},[1108,17771,17772,17792],{},[1111,17773,17774,17777,17779,17781,17783,17786,17788,17790],{},[1114,17775,17776],{},"w",[1118,17778,8592],{},[1118,17780,3685],{"stretchy":1120},[1118,17782,1510],{},[1114,17784,17785],{},"c",[1118,17787,1349],{"separator":1137},[1114,17789,17785],{},[1118,17791,3730],{"stretchy":1120},[1129,17793,17794],{"encoding":1131},"w \\in [-c, c]",[1095,17796,17798,17817],{"className":17797,"ariaHidden":1137},[1136],[1095,17799,17801,17804,17808,17811,17814],{"className":17800},[1141],[1095,17802],{"className":17803,"style":14853},[1145],[1095,17805,17776],{"className":17806,"style":17807},[1150,1151],"margin-right:0.0269em;",[1095,17809],{"className":17810,"style":1542},[1383],[1095,17812,8592],{"className":17813},[1546],[1095,17815],{"className":17816,"style":1542},[1383],[1095,17818,17820,17823,17826,17829,17832,17835,17838,17841],{"className":17819},[1141],[1095,17821],{"className":17822,"style":1146},[1145],[1095,17824,3685],{"className":17825},[1156],[1095,17827,1510],{"className":17828},[1150],[1095,17830,17785],{"className":17831},[1150,1151],[1095,17833,1349],{"className":17834},[1379],[1095,17836],{"className":17837,"style":1384},[1383],[1095,17839,17785],{"className":17840},[1150,1151],[1095,17842,3730],{"className":17843},[1163]," 来强制 Lipschitz 约束。",[2556,17846,17848],{"id":17847},"wgan-的优势","WGAN 的优势",[1166,17850,17851,17854,17857],{},[1169,17852,17853],{},"Wasserstein 距离在分布不重叠时仍能提供有意义的梯度",[1169,17855,17856],{},"训练更稳定，损失曲线与生成质量相关",[1169,17858,17859],{},"减少模式崩塌",[1194,17861,17863],{"id":17862},"_43-cganconditional-gan","4.3 CGAN（Conditional GAN）",[1091,17865,17866,17867,17895],{},"通过引入条件信息 ",[1095,17868,17870,17883],{"className":17869},[1098],[1095,17871,17873],{"className":17872},[1102],[1104,17874,17875],{"xmlns":1106},[1108,17876,17877,17881],{},[1111,17878,17879],{},[1114,17880,1226],{},[1129,17882,1226],{"encoding":1131},[1095,17884,17886],{"className":17885,"ariaHidden":1137},[1136],[1095,17887,17889,17892],{"className":17888},[1141],[1095,17890],{"className":17891,"style":2456},[1145],[1095,17893,1226],{"className":17894,"style":1256},[1150,1151],"（如类别标签），控制生成内容：",[1091,17897,17898],{},[1095,17899,17901,18047],{"className":17900},[1098],[1095,17902,17904],{"className":17903},[1102],[1104,17905,17906],{"xmlns":1106},[1108,17907,17908,18044],{},[1111,17909,17910,17920,17930,17932,17934,17936,17938,17940,17942,17944,17968,17970,17972,17974,17976,17978,17980,17982,17984,17986,17988,17990,18006,18008,18010,18012,18014,18016,18018,18020,18022,18024,18026,18028,18030,18032,18034,18036,18038,18040,18042],{},[1465,17911,17912,17918],{},[1111,17913,17914,17916],{},[1114,17915,8692],{},[1118,17917,3643],{},[1114,17919,8480],{},[1465,17921,17922,17928],{},[1111,17923,17924,17926],{},[1114,17925,8703],{},[1118,17927,3643],{},[1114,17929,3738],{},[1114,17931,6804],{},[1118,17933,1121],{"stretchy":1120},[1114,17935,3738],{},[1118,17937,1349],{"separator":1137},[1114,17939,8480],{},[1118,17941,1127],{"stretchy":1120},[1118,17943,1463],{},[1465,17945,17946,17948],{},[1114,17947,2138],{"mathvariant":3662},[1111,17949,17950,17952,17954],{},[1114,17951,1124],{},[1118,17953,2585],{},[1465,17955,17956,17958],{},[1114,17957,1091],{},[1111,17959,17960,17962,17964,17966],{},[1114,17961,2875],{},[1114,17963,8742],{},[1114,17965,8745],{},[1114,17967,8742],{},[1118,17969,3685],{"stretchy":1120},[1114,17971,3640],{},[1118,17973,3643],{},[1114,17975,3738],{},[1118,17977,1121],{"stretchy":1120},[1114,17979,1124],{},[1114,17981,1230],{"mathvariant":1229},[1114,17983,1226],{},[1118,17985,1127],{"stretchy":1120},[1118,17987,3730],{"stretchy":1120},[1118,17989,3733],{},[1465,17991,17992,17994],{},[1114,17993,2138],{"mathvariant":3662},[1111,17995,17996,17998,18000],{},[1114,17997,1352],{},[1118,17999,2585],{},[1465,18001,18002,18004],{},[1114,18003,1091],{},[1114,18005,1352],{},[1118,18007,3685],{"stretchy":1120},[1114,18009,3640],{},[1118,18011,3643],{},[1118,18013,1121],{"stretchy":1120},[1490,18015,1492],{},[1118,18017,1510],{},[1114,18019,3738],{},[1118,18021,1121],{"stretchy":1120},[1114,18023,8480],{},[1118,18025,1121],{"stretchy":1120},[1114,18027,1352],{},[1114,18029,1230],{"mathvariant":1229},[1114,18031,1226],{},[1118,18033,1127],{"stretchy":1120},[1114,18035,1230],{"mathvariant":1229},[1114,18037,1226],{},[1118,18039,1127],{"stretchy":1120},[1118,18041,1127],{"stretchy":1120},[1118,18043,3730],{"stretchy":1120},[1129,18045,18046],{"encoding":1131},"\\min_G \\max_D V(D, G) = \\mathbb{E}_{x \\sim p_{data}}[\\log D(x|y)] + \\mathbb{E}_{z \\sim p_z}[\\log(1 - D(G(z|y)|y))]",[1095,18048,18050,18172,18314,18429],{"className":18049,"ariaHidden":1137},[1136],[1095,18051,18053,18056,18096,18099,18139,18142,18145,18148,18151,18154,18157,18160,18163,18166,18169],{"className":18052},[1141],[1095,18054],{"className":18055,"style":1146},[1145],[1095,18057,18059,18062],{"className":18058},[1560],[1095,18060,8692],{"className":18061},[1560],[1095,18063,18065],{"className":18064},[1570],[1095,18066,18068,18088],{"className":18067},[1574,1575],[1095,18069,18071,18085],{"className":18070},[1579],[1095,18072,18074],{"className":18073,"style":2210},[1583],[1095,18075,18076,18079],{"style":8856},[1095,18077],{"className":18078,"style":1592},[1591],[1095,18080,18082],{"className":18081},[1596,1597,1598,1599],[1095,18083,8480],{"className":18084},[1150,1151,1599],[1095,18086,1607],{"className":18087},[1606],[1095,18089,18091],{"className":18090},[1579],[1095,18092,18094],{"className":18093,"style":1666},[1583],[1095,18095],{},[1095,18097],{"className":18098,"style":1384},[1383],[1095,18100,18102,18105],{"className":18101},[1560],[1095,18103,8703],{"className":18104},[1560],[1095,18106,18108],{"className":18107},[1570],[1095,18109,18111,18131],{"className":18110},[1574,1575],[1095,18112,18114,18128],{"className":18113},[1579],[1095,18115,18117],{"className":18116,"style":2210},[1583],[1095,18118,18119,18122],{"style":8856},[1095,18120],{"className":18121,"style":1592},[1591],[1095,18123,18125],{"className":18124},[1596,1597,1598,1599],[1095,18126,3738],{"className":18127,"style":1936},[1150,1151,1599],[1095,18129,1607],{"className":18130},[1606],[1095,18132,18134],{"className":18133},[1579],[1095,18135,18137],{"className":18136,"style":1666},[1583],[1095,18138],{},[1095,18140],{"className":18141,"style":1384},[1383],[1095,18143,6804],{"className":18144,"style":2264},[1150,1151],[1095,18146,1121],{"className":18147},[1156],[1095,18149,3738],{"className":18150,"style":1936},[1150,1151],[1095,18152,1349],{"className":18153},[1379],[1095,18155],{"className":18156,"style":1384},[1383],[1095,18158,8480],{"className":18159},[1150,1151],[1095,18161,1127],{"className":18162},[1163],[1095,18164],{"className":18165,"style":1542},[1383],[1095,18167,1463],{"className":18168},[1546],[1095,18170],{"className":18171,"style":1542},[1383],[1095,18173,18175,18178,18276,18279,18284,18287,18290,18293,18296,18299,18302,18305,18308,18311],{"className":18174},[1141],[1095,18176],{"className":18177,"style":2058},[1145],[1095,18179,18181,18184],{"className":18180},[1150],[1095,18182,2138],{"className":18183},[1150,3877],[1095,18185,18187],{"className":18186},[1570],[1095,18188,18190,18268],{"className":18189},[1574,1575],[1095,18191,18193,18265],{"className":18192},[1579],[1095,18194,18196],{"className":18195,"style":8430},[1583],[1095,18197,18198,18201],{"style":1647},[1095,18199],{"className":18200,"style":1592},[1591],[1095,18202,18204],{"className":18203},[1596,1597,1598,1599],[1095,18205,18207,18210,18213],{"className":18206},[1150,1599],[1095,18208,1124],{"className":18209},[1150,1151,1599],[1095,18211,2585],{"className":18212},[1546,1599],[1095,18214,18216,18219],{"className":18215},[1150,1599],[1095,18217,1091],{"className":18218},[1150,1151,1599],[1095,18220,18222],{"className":18221},[1570],[1095,18223,18225,18257],{"className":18224},[1574,1575],[1095,18226,18228,18254],{"className":18227},[1579],[1095,18229,18231],{"className":18230,"style":3279},[1583],[1095,18232,18233,18236],{"style":3282},[1095,18234],{"className":18235,"style":3286},[1591],[1095,18237,18239],{"className":18238},[1596,3290,3291,1599],[1095,18240,18242,18245,18248,18251],{"className":18241},[1150,1599],[1095,18243,2875],{"className":18244},[1150,1151,1599],[1095,18246,8742],{"className":18247},[1150,1151,1599],[1095,18249,8745],{"className":18250},[1150,1151,1599],[1095,18252,8742],{"className":18253},[1150,1151,1599],[1095,18255,1607],{"className":18256},[1606],[1095,18258,18260],{"className":18259},[1579],[1095,18261,18263],{"className":18262,"style":3304},[1583],[1095,18264],{},[1095,18266,1607],{"className":18267},[1606],[1095,18269,18271],{"className":18270},[1579],[1095,18272,18274],{"className":18273,"style":2098},[1583],[1095,18275],{},[1095,18277,3685],{"className":18278},[1156],[1095,18280,3799,18282],{"className":18281},[1560],[1095,18283,1984],{"style":3802},[1095,18285],{"className":18286,"style":1384},[1383],[1095,18288,3738],{"className":18289,"style":1936},[1150,1151],[1095,18291,1121],{"className":18292},[1156],[1095,18294,1124],{"className":18295},[1150,1151],[1095,18297,1230],{"className":18298},[1150],[1095,18300,1226],{"className":18301,"style":1256},[1150,1151],[1095,18303,4869],{"className":18304},[1163],[1095,18306],{"className":18307,"style":2264},[1383],[1095,18309,3733],{"className":18310},[1779],[1095,18312],{"className":18313,"style":2264},[1383],[1095,18315,18317,18320,18406,18409,18414,18417,18420,18423,18426],{"className":18316},[1141],[1095,18318],{"className":18319,"style":2058},[1145],[1095,18321,18323,18326],{"className":18322},[1150],[1095,18324,2138],{"className":18325},[1150,3877],[1095,18327,18329],{"className":18328},[1570],[1095,18330,18332,18398],{"className":18331},[1574,1575],[1095,18333,18335,18395],{"className":18334},[1579],[1095,18336,18338],{"className":18337,"style":8430},[1583],[1095,18339,18340,18343],{"style":1647},[1095,18341],{"className":18342,"style":1592},[1591],[1095,18344,18346],{"className":18345},[1596,1597,1598,1599],[1095,18347,18349,18352,18355],{"className":18348},[1150,1599],[1095,18350,1352],{"className":18351,"style":1388},[1150,1151,1599],[1095,18353,2585],{"className":18354},[1546,1599],[1095,18356,18358,18361],{"className":18357},[1150,1599],[1095,18359,1091],{"className":18360},[1150,1151,1599],[1095,18362,18364],{"className":18363},[1570],[1095,18365,18367,18387],{"className":18366},[1574,1575],[1095,18368,18370,18384],{"className":18369},[1579],[1095,18371,18373],{"className":18372,"style":9159},[1583],[1095,18374,18375,18378],{"style":9162},[1095,18376],{"className":18377,"style":3286},[1591],[1095,18379,18381],{"className":18380},[1596,3290,3291,1599],[1095,18382,1352],{"className":18383,"style":1388},[1150,1151,1599],[1095,18385,1607],{"className":18386},[1606],[1095,18388,18390],{"className":18389},[1579],[1095,18391,18393],{"className":18392,"style":9181},[1583],[1095,18394],{},[1095,18396,1607],{"className":18397},[1606],[1095,18399,18401],{"className":18400},[1579],[1095,18402,18404],{"className":18403,"style":2098},[1583],[1095,18405],{},[1095,18407,3685],{"className":18408},[1156],[1095,18410,3799,18412],{"className":18411},[1560],[1095,18413,1984],{"style":3802},[1095,18415,1121],{"className":18416},[1156],[1095,18418,1492],{"className":18419},[1150],[1095,18421],{"className":18422,"style":2264},[1383],[1095,18424,1510],{"className":18425},[1779],[1095,18427],{"className":18428,"style":2264},[1383],[1095,18430,18432,18435,18438,18441,18444,18447,18450,18453,18456,18459,18462,18465],{"className":18431},[1141],[1095,18433],{"className":18434,"style":1146},[1145],[1095,18436,3738],{"className":18437,"style":1936},[1150,1151],[1095,18439,1121],{"className":18440},[1156],[1095,18442,8480],{"className":18443},[1150,1151],[1095,18445,1121],{"className":18446},[1156],[1095,18448,1352],{"className":18449,"style":1388},[1150,1151],[1095,18451,1230],{"className":18452},[1150],[1095,18454,1226],{"className":18455,"style":1256},[1150,1151],[1095,18457,1127],{"className":18458},[1163],[1095,18460,1230],{"className":18461},[1150],[1095,18463,1226],{"className":18464,"style":1256},[1150,1151],[1095,18466,17754],{"className":18467},[1163],[1166,18469,18470,18531,18592],{},[1169,18471,18472,18473,18530],{},"生成器：",[1095,18474,18476,18500],{"className":18475},[1098],[1095,18477,18479],{"className":18478},[1102],[1104,18480,18481],{"xmlns":1106},[1108,18482,18483,18497],{},[1111,18484,18485,18487,18489,18491,18493,18495],{},[1114,18486,8480],{},[1118,18488,1121],{"stretchy":1120},[1114,18490,1352],{},[1118,18492,1349],{"separator":1137},[1114,18494,1226],{},[1118,18496,1127],{"stretchy":1120},[1129,18498,18499],{"encoding":1131},"G(z, y)",[1095,18501,18503],{"className":18502,"ariaHidden":1137},[1136],[1095,18504,18506,18509,18512,18515,18518,18521,18524,18527],{"className":18505},[1141],[1095,18507],{"className":18508,"style":1146},[1145],[1095,18510,8480],{"className":18511},[1150,1151],[1095,18513,1121],{"className":18514},[1156],[1095,18516,1352],{"className":18517,"style":1388},[1150,1151],[1095,18519,1349],{"className":18520},[1379],[1095,18522],{"className":18523,"style":1384},[1383],[1095,18525,1226],{"className":18526,"style":1256},[1150,1151],[1095,18528,1127],{"className":18529},[1163],"，将噪声 z 和条件 y 拼接后生成",[1169,18532,18533,18534,18591],{},"判别器：",[1095,18535,18537,18561],{"className":18536},[1098],[1095,18538,18540],{"className":18539},[1102],[1104,18541,18542],{"xmlns":1106},[1108,18543,18544,18558],{},[1111,18545,18546,18548,18550,18552,18554,18556],{},[1114,18547,3738],{},[1118,18549,1121],{"stretchy":1120},[1114,18551,1124],{},[1118,18553,1349],{"separator":1137},[1114,18555,1226],{},[1118,18557,1127],{"stretchy":1120},[1129,18559,18560],{"encoding":1131},"D(x, y)",[1095,18562,18564],{"className":18563,"ariaHidden":1137},[1136],[1095,18565,18567,18570,18573,18576,18579,18582,18585,18588],{"className":18566},[1141],[1095,18568],{"className":18569,"style":1146},[1145],[1095,18571,3738],{"className":18572,"style":1936},[1150,1151],[1095,18574,1121],{"className":18575},[1156],[1095,18577,1124],{"className":18578},[1150,1151],[1095,18580,1349],{"className":18581},[1379],[1095,18583],{"className":18584,"style":1384},[1383],[1095,18586,1226],{"className":18587,"style":1256},[1150,1151],[1095,18589,1127],{"className":18590},[1163],"，同时接收样本和条件来判断真假",[1169,18593,18594],{},"应用：按类别生成特定数字、按文本描述生成图像",[1194,18596,18598],{"id":18597},"_44-infogan","4.4 InfoGAN",[1091,18600,18601,18602,18605],{},"InfoGAN 通过",[1172,18603,18604],{},"最大化互信息","来学习解耦的隐表示：",[1091,18607,18608,18609,18637,18638,18666,18667,6744,18695,18752],{},"将噪声分为两部分：",[1095,18610,18612,18625],{"className":18611},[1098],[1095,18613,18615],{"className":18614},[1102],[1104,18616,18617],{"xmlns":1106},[1108,18618,18619,18623],{},[1111,18620,18621],{},[1114,18622,1352],{},[1129,18624,1352],{"encoding":1131},[1095,18626,18628],{"className":18627,"ariaHidden":1137},[1136],[1095,18629,18631,18634],{"className":18630},[1141],[1095,18632],{"className":18633,"style":1885},[1145],[1095,18635,1352],{"className":18636,"style":1388},[1150,1151],"（不可压缩噪声）和 ",[1095,18639,18641,18654],{"className":18640},[1098],[1095,18642,18644],{"className":18643},[1102],[1104,18645,18646],{"xmlns":1106},[1108,18647,18648,18652],{},[1111,18649,18650],{},[1114,18651,17785],{},[1129,18653,17785],{"encoding":1131},[1095,18655,18657],{"className":18656,"ariaHidden":1137},[1136],[1095,18658,18660,18663],{"className":18659},[1141],[1095,18661],{"className":18662,"style":1885},[1145],[1095,18664,17785],{"className":18665},[1150,1151],"（隐编码）。目标是使 ",[1095,18668,18670,18683],{"className":18669},[1098],[1095,18671,18673],{"className":18672},[1102],[1104,18674,18675],{"xmlns":1106},[1108,18676,18677,18681],{},[1111,18678,18679],{},[1114,18680,17785],{},[1129,18682,17785],{"encoding":1131},[1095,18684,18686],{"className":18685,"ariaHidden":1137},[1136],[1095,18687,18689,18692],{"className":18688},[1141],[1095,18690],{"className":18691,"style":1885},[1145],[1095,18693,17785],{"className":18694},[1150,1151],[1095,18696,18698,18722],{"className":18697},[1098],[1095,18699,18701],{"className":18700},[1102],[1104,18702,18703],{"xmlns":1106},[1108,18704,18705,18719],{},[1111,18706,18707,18709,18711,18713,18715,18717],{},[1114,18708,8480],{},[1118,18710,1121],{"stretchy":1120},[1114,18712,1352],{},[1118,18714,1349],{"separator":1137},[1114,18716,17785],{},[1118,18718,1127],{"stretchy":1120},[1129,18720,18721],{"encoding":1131},"G(z, c)",[1095,18723,18725],{"className":18724,"ariaHidden":1137},[1136],[1095,18726,18728,18731,18734,18737,18740,18743,18746,18749],{"className":18727},[1141],[1095,18729],{"className":18730,"style":1146},[1145],[1095,18732,8480],{"className":18733},[1150,1151],[1095,18735,1121],{"className":18736},[1156],[1095,18738,1352],{"className":18739,"style":1388},[1150,1151],[1095,18741,1349],{"className":18742},[1379],[1095,18744],{"className":18745,"style":1384},[1383],[1095,18747,17785],{"className":18748},[1150,1151],[1095,18750,1127],{"className":18751},[1163]," 之间的互信息最大：",[1091,18754,18755],{},[1095,18756,18758,18829],{"className":18757},[1098],[1095,18759,18761],{"className":18760},[1102],[1104,18762,18763],{"xmlns":1106},[1108,18764,18765,18826],{},[1111,18766,18767,18777,18787,18789,18791,18793,18795,18797,18799,18801,18804,18806,18808,18810,18812,18814,18816,18818,18820,18822,18824],{},[1465,18768,18769,18775],{},[1111,18770,18771,18773],{},[1114,18772,8692],{},[1118,18774,3643],{},[1114,18776,8480],{},[1465,18778,18779,18785],{},[1111,18780,18781,18783],{},[1114,18782,8703],{},[1118,18784,3643],{},[1114,18786,3738],{},[1114,18788,6804],{},[1118,18790,1121],{"stretchy":1120},[1114,18792,3738],{},[1118,18794,1349],{"separator":1137},[1114,18796,8480],{},[1118,18798,1127],{"stretchy":1120},[1118,18800,1510],{},[1114,18802,18803],{},"λ",[1114,18805,2608],{},[1118,18807,1121],{"stretchy":1120},[1114,18809,17785],{},[1118,18811,6819],{"separator":1137},[1114,18813,8480],{},[1118,18815,1121],{"stretchy":1120},[1114,18817,1352],{},[1118,18819,1349],{"separator":1137},[1114,18821,17785],{},[1118,18823,1127],{"stretchy":1120},[1118,18825,1127],{"stretchy":1120},[1129,18827,18828],{"encoding":1131},"\\min_G \\max_D V(D, G) - \\lambda I(c; G(z, c))",[1095,18830,18832,18954],{"className":18831,"ariaHidden":1137},[1136],[1095,18833,18835,18838,18878,18881,18921,18924,18927,18930,18933,18936,18939,18942,18945,18948,18951],{"className":18834},[1141],[1095,18836],{"className":18837,"style":1146},[1145],[1095,18839,18841,18844],{"className":18840},[1560],[1095,18842,8692],{"className":18843},[1560],[1095,18845,18847],{"className":18846},[1570],[1095,18848,18850,18870],{"className":18849},[1574,1575],[1095,18851,18853,18867],{"className":18852},[1579],[1095,18854,18856],{"className":18855,"style":2210},[1583],[1095,18857,18858,18861],{"style":8856},[1095,18859],{"className":18860,"style":1592},[1591],[1095,18862,18864],{"className":18863},[1596,1597,1598,1599],[1095,18865,8480],{"className":18866},[1150,1151,1599],[1095,18868,1607],{"className":18869},[1606],[1095,18871,18873],{"className":18872},[1579],[1095,18874,18876],{"className":18875,"style":1666},[1583],[1095,18877],{},[1095,18879],{"className":18880,"style":1384},[1383],[1095,18882,18884,18887],{"className":18883},[1560],[1095,18885,8703],{"className":18886},[1560],[1095,18888,18890],{"className":18889},[1570],[1095,18891,18893,18913],{"className":18892},[1574,1575],[1095,18894,18896,18910],{"className":18895},[1579],[1095,18897,18899],{"className":18898,"style":2210},[1583],[1095,18900,18901,18904],{"style":8856},[1095,18902],{"className":18903,"style":1592},[1591],[1095,18905,18907],{"className":18906},[1596,1597,1598,1599],[1095,18908,3738],{"className":18909,"style":1936},[1150,1151,1599],[1095,18911,1607],{"className":18912},[1606],[1095,18914,18916],{"className":18915},[1579],[1095,18917,18919],{"className":18918,"style":1666},[1583],[1095,18920],{},[1095,18922],{"className":18923,"style":1384},[1383],[1095,18925,6804],{"className":18926,"style":2264},[1150,1151],[1095,18928,1121],{"className":18929},[1156],[1095,18931,3738],{"className":18932,"style":1936},[1150,1151],[1095,18934,1349],{"className":18935},[1379],[1095,18937],{"className":18938,"style":1384},[1383],[1095,18940,8480],{"className":18941},[1150,1151],[1095,18943,1127],{"className":18944},[1163],[1095,18946],{"className":18947,"style":2264},[1383],[1095,18949,1510],{"className":18950},[1779],[1095,18952],{"className":18953,"style":2264},[1383],[1095,18955,18957,18960,18963,18966,18969,18972,18975,18978,18981,18984,18987,18990,18993,18996],{"className":18956},[1141],[1095,18958],{"className":18959,"style":1146},[1145],[1095,18961,18803],{"className":18962},[1150,1151],[1095,18964,2608],{"className":18965,"style":2687},[1150,1151],[1095,18967,1121],{"className":18968},[1156],[1095,18970,17785],{"className":18971},[1150,1151],[1095,18973,6819],{"className":18974},[1379],[1095,18976],{"className":18977,"style":1384},[1383],[1095,18979,8480],{"className":18980},[1150,1151],[1095,18982,1121],{"className":18983},[1156],[1095,18985,1352],{"className":18986,"style":1388},[1150,1151],[1095,18988,1349],{"className":18989},[1379],[1095,18991],{"className":18992,"style":1384},[1383],[1095,18994,17785],{"className":18995},[1150,1151],[1095,18997,2370],{"className":18998},[1163],[1091,19000,19001],{},"由于互信息不可直接计算，使用变分下界近似：",[1091,19003,19004],{},[1095,19005,19007,19129],{"className":19006},[1098],[1095,19008,19010],{"className":19009},[1102],[1104,19011,19012],{"xmlns":1106},[1108,19013,19014,19126],{},[1111,19015,19016,19018,19020,19022,19024,19026,19028,19030,19032,19034,19036,19038,19040,19076,19078,19080,19082,19085,19087,19089,19091,19093,19095,19097,19099,19102,19104,19106,19108,19110,19116,19118,19120,19122,19124],{},[1114,19017,2608],{},[1118,19019,1121],{"stretchy":1120},[1114,19021,17785],{},[1118,19023,6819],{"separator":1137},[1114,19025,8480],{},[1118,19027,1121],{"stretchy":1120},[1114,19029,1352],{},[1118,19031,1349],{"separator":1137},[1114,19033,17785],{},[1118,19035,1127],{"stretchy":1120},[1118,19037,1127],{"stretchy":1120},[1118,19039,4397],{},[1465,19041,19042,19044],{},[1114,19043,2138],{"mathvariant":3662},[1111,19045,19046,19048,19050,19052,19054,19056,19058,19060,19062,19064,19066,19068,19070,19072,19074],{},[1114,19047,17785],{},[1118,19049,2585],{},[1114,19051,1091],{},[1118,19053,1121],{"stretchy":1120},[1114,19055,17785],{},[1118,19057,1127],{"stretchy":1120},[1118,19059,1349],{"separator":1137},[1114,19061,1124],{},[1118,19063,2585],{},[1114,19065,8480],{},[1118,19067,1121],{"stretchy":1120},[1114,19069,1352],{},[1118,19071,1349],{"separator":1137},[1114,19073,17785],{},[1118,19075,1127],{"stretchy":1120},[1118,19077,3685],{"stretchy":1120},[1114,19079,3640],{},[1118,19081,3643],{},[1114,19083,19084],{},"Q",[1118,19086,1121],{"stretchy":1120},[1114,19088,17785],{},[1114,19090,1230],{"mathvariant":1229},[1114,19092,1124],{},[1118,19094,1127],{"stretchy":1120},[1118,19096,3730],{"stretchy":1120},[1118,19098,3733],{},[1114,19100,19101],{},"H",[1118,19103,1121],{"stretchy":1120},[1114,19105,17785],{},[1118,19107,1127],{"stretchy":1120},[1118,19109,1463],{},[1465,19111,19112,19114],{},[1114,19113,2130],{},[1114,19115,2608],{},[1118,19117,1121],{"stretchy":1120},[1114,19119,8480],{},[1118,19121,1349],{"separator":1137},[1114,19123,19084],{},[1118,19125,1127],{"stretchy":1120},[1129,19127,19128],{"encoding":1131},"I(c; G(z, c)) \\geq \\mathbb{E}_{c \\sim p(c), x \\sim G(z,c)}[\\log Q(c|x)] + H(c) = L_I(G, Q)",[1095,19130,19132,19183,19312,19340],{"className":19131,"ariaHidden":1137},[1136],[1095,19133,19135,19138,19141,19144,19147,19150,19153,19156,19159,19162,19165,19168,19171,19174,19177,19180],{"className":19134},[1141],[1095,19136],{"className":19137,"style":1146},[1145],[1095,19139,2608],{"className":19140,"style":2687},[1150,1151],[1095,19142,1121],{"className":19143},[1156],[1095,19145,17785],{"className":19146},[1150,1151],[1095,19148,6819],{"className":19149},[1379],[1095,19151],{"className":19152,"style":1384},[1383],[1095,19154,8480],{"className":19155},[1150,1151],[1095,19157,1121],{"className":19158},[1156],[1095,19160,1352],{"className":19161,"style":1388},[1150,1151],[1095,19163,1349],{"className":19164},[1379],[1095,19166],{"className":19167,"style":1384},[1383],[1095,19169,17785],{"className":19170},[1150,1151],[1095,19172,2370],{"className":19173},[1163],[1095,19175],{"className":19176,"style":1542},[1383],[1095,19178,4397],{"className":19179},[1546],[1095,19181],{"className":19182,"style":1542},[1383],[1095,19184,19186,19189,19274,19277,19282,19285,19288,19291,19294,19297,19300,19303,19306,19309],{"className":19185},[1141],[1095,19187],{"className":19188,"style":8959},[1145],[1095,19190,19192,19195],{"className":19191},[1150],[1095,19193,2138],{"className":19194},[1150,3877],[1095,19196,19198],{"className":19197},[1570],[1095,19199,19201,19266],{"className":19200},[1574,1575],[1095,19202,19204,19263],{"className":19203},[1579],[1095,19205,19207],{"className":19206,"style":3279},[1583],[1095,19208,19209,19212],{"style":3892},[1095,19210],{"className":19211,"style":1592},[1591],[1095,19213,19215],{"className":19214},[1596,1597,1598,1599],[1095,19216,19218,19221,19224,19227,19230,19233,19236,19239,19242,19245,19248,19251,19254,19257,19260],{"className":19217},[1150,1599],[1095,19219,17785],{"className":19220},[1150,1151,1599],[1095,19222,2585],{"className":19223},[1546,1599],[1095,19225,1091],{"className":19226},[1150,1151,1599],[1095,19228,1121],{"className":19229},[1156,1599],[1095,19231,17785],{"className":19232},[1150,1151,1599],[1095,19234,1127],{"className":19235},[1163,1599],[1095,19237,1349],{"className":19238},[1379,1599],[1095,19240,1124],{"className":19241},[1150,1151,1599],[1095,19243,2585],{"className":19244},[1546,1599],[1095,19246,8480],{"className":19247},[1150,1151,1599],[1095,19249,1121],{"className":19250},[1156,1599],[1095,19252,1352],{"className":19253,"style":1388},[1150,1151,1599],[1095,19255,1349],{"className":19256},[1379,1599],[1095,19258,17785],{"className":19259},[1150,1151,1599],[1095,19261,1127],{"className":19262},[1163,1599],[1095,19264,1607],{"className":19265},[1606],[1095,19267,19269],{"className":19268},[1579],[1095,19270,19272],{"className":19271,"style":9065},[1583],[1095,19273],{},[1095,19275,3685],{"className":19276},[1156],[1095,19278,3799,19280],{"className":19279},[1560],[1095,19281,1984],{"style":3802},[1095,19283],{"className":19284,"style":1384},[1383],[1095,19286,19084],{"className":19287},[1150,1151],[1095,19289,1121],{"className":19290},[1156],[1095,19292,17785],{"className":19293},[1150,1151],[1095,19295,1230],{"className":19296},[1150],[1095,19298,1124],{"className":19299},[1150,1151],[1095,19301,4869],{"className":19302},[1163],[1095,19304],{"className":19305,"style":2264},[1383],[1095,19307,3733],{"className":19308},[1779],[1095,19310],{"className":19311,"style":2264},[1383],[1095,19313,19315,19318,19322,19325,19328,19331,19334,19337],{"className":19314},[1141],[1095,19316],{"className":19317,"style":1146},[1145],[1095,19319,19101],{"className":19320,"style":19321},[1150,1151],"margin-right:0.0813em;",[1095,19323,1121],{"className":19324},[1156],[1095,19326,17785],{"className":19327},[1150,1151],[1095,19329,1127],{"className":19330},[1163],[1095,19332],{"className":19333,"style":1542},[1383],[1095,19335,1463],{"className":19336},[1546],[1095,19338],{"className":19339,"style":1542},[1383],[1095,19341,19343,19346,19386,19389,19392,19395,19398,19401],{"className":19342},[1141],[1095,19344],{"className":19345,"style":1146},[1145],[1095,19347,19349,19352],{"className":19348},[1150],[1095,19350,2130],{"className":19351},[1150,1151],[1095,19353,19355],{"className":19354},[1570],[1095,19356,19358,19378],{"className":19357},[1574,1575],[1095,19359,19361,19375],{"className":19360},[1579],[1095,19362,19364],{"className":19363,"style":2210},[1583],[1095,19365,19366,19369],{"style":1647},[1095,19367],{"className":19368,"style":1592},[1591],[1095,19370,19372],{"className":19371},[1596,1597,1598,1599],[1095,19373,2608],{"className":19374,"style":2687},[1150,1151,1599],[1095,19376,1607],{"className":19377},[1606],[1095,19379,19381],{"className":19380},[1579],[1095,19382,19384],{"className":19383,"style":1666},[1583],[1095,19385],{},[1095,19387,1121],{"className":19388},[1156],[1095,19390,8480],{"className":19391},[1150,1151],[1095,19393,1349],{"className":19394},[1379],[1095,19396],{"className":19397,"style":1384},[1383],[1095,19399,19084],{"className":19400},[1150,1151],[1095,19402,1127],{"className":19403},[1163],[1091,19405,6157,19406,19460],{},[1095,19407,19409,19433],{"className":19408},[1098],[1095,19410,19412],{"className":19411},[1102],[1104,19413,19414],{"xmlns":1106},[1108,19415,19416,19430],{},[1111,19417,19418,19420,19422,19424,19426,19428],{},[1114,19419,19084],{},[1118,19421,1121],{"stretchy":1120},[1114,19423,17785],{},[1114,19425,1230],{"mathvariant":1229},[1114,19427,1124],{},[1118,19429,1127],{"stretchy":1120},[1129,19431,19432],{"encoding":1131},"Q(c|x)",[1095,19434,19436],{"className":19435,"ariaHidden":1137},[1136],[1095,19437,19439,19442,19445,19448,19451,19454,19457],{"className":19438},[1141],[1095,19440],{"className":19441,"style":1146},[1145],[1095,19443,19084],{"className":19444},[1150,1151],[1095,19446,1121],{"className":19447},[1156],[1095,19449,17785],{"className":19450},[1150,1151],[1095,19452,1230],{"className":19453},[1150],[1095,19455,1124],{"className":19456},[1150,1151],[1095,19458,1127],{"className":19459},[1163]," 是辅助网络，用于从生成样本预测隐编码。",[1091,19462,19463,19466],{},[1172,19464,19465],{},"InfoGAN 的价值","：无需标签即可自动发现数据中有意义的变化因子（如 MNIST 中的数字类型、倾斜角度、笔画粗细等）。",[1194,19468,19470],{"id":19469},"_45-gan-变体对比","4.5 GAN 变体对比",[1406,19472,19473,19492],{},[1409,19474,19475],{},[1412,19476,19477,19480,19483,19486,19489],{},[1415,19478,19479],{},"模型",[1415,19481,19482],{},"核心创新",[1415,19484,19485],{},"目标函数改进",[1415,19487,19488],{},"优势",[1415,19490,19491],{},"局限",[1428,19493,19494,19513,19532,19662],{},[1412,19495,19496,19501,19504,19507,19510],{},[1433,19497,19498],{},[1172,19499,19500],{},"DCGAN",[1433,19502,19503],{},"卷积架构设计原则",[1433,19505,19506],{},"无（原始 GAN 目标）",[1433,19508,19509],{},"训练更稳定，图像质量提升",[1433,19511,19512],{},"仍有模式崩塌",[1412,19514,19515,19520,19523,19526,19529],{},[1433,19516,19517],{},[1172,19518,19519],{},"WGAN",[1433,19521,19522],{},"Wasserstein 距离替代 JS 散度",[1433,19524,19525],{},"Critic + weight clipping",[1433,19527,19528],{},"梯度有意义，损失可监控",[1433,19530,19531],{},"weight clipping 限制网络容量",[1412,19533,19534,19539,19542,19656,19659],{},[1433,19535,19536],{},[1172,19537,19538],{},"CGAN",[1433,19540,19541],{},"条件信息引导生成",[1433,19543,19544,6744,19600],{},[1095,19545,19547,19570],{"className":19546},[1098],[1095,19548,19550],{"className":19549},[1102],[1104,19551,19552],{"xmlns":1106},[1108,19553,19554,19568],{},[1111,19555,19556,19558,19560,19562,19564,19566],{},[1114,19557,8480],{},[1118,19559,1121],{"stretchy":1120},[1114,19561,1352],{},[1118,19563,1349],{"separator":1137},[1114,19565,1226],{},[1118,19567,1127],{"stretchy":1120},[1129,19569,18499],{"encoding":1131},[1095,19571,19573],{"className":19572,"ariaHidden":1137},[1136],[1095,19574,19576,19579,19582,19585,19588,19591,19594,19597],{"className":19575},[1141],[1095,19577],{"className":19578,"style":1146},[1145],[1095,19580,8480],{"className":19581},[1150,1151],[1095,19583,1121],{"className":19584},[1156],[1095,19586,1352],{"className":19587,"style":1388},[1150,1151],[1095,19589,1349],{"className":19590},[1379],[1095,19592],{"className":19593,"style":1384},[1383],[1095,19595,1226],{"className":19596,"style":1256},[1150,1151],[1095,19598,1127],{"className":19599},[1163],[1095,19601,19603,19626],{"className":19602},[1098],[1095,19604,19606],{"className":19605},[1102],[1104,19607,19608],{"xmlns":1106},[1108,19609,19610,19624],{},[1111,19611,19612,19614,19616,19618,19620,19622],{},[1114,19613,3738],{},[1118,19615,1121],{"stretchy":1120},[1114,19617,1124],{},[1118,19619,1349],{"separator":1137},[1114,19621,1226],{},[1118,19623,1127],{"stretchy":1120},[1129,19625,18560],{"encoding":1131},[1095,19627,19629],{"className":19628,"ariaHidden":1137},[1136],[1095,19630,19632,19635,19638,19641,19644,19647,19650,19653],{"className":19631},[1141],[1095,19633],{"className":19634,"style":1146},[1145],[1095,19636,3738],{"className":19637,"style":1936},[1150,1151],[1095,19639,1121],{"className":19640},[1156],[1095,19642,1124],{"className":19643},[1150,1151],[1095,19645,1349],{"className":19646},[1379],[1095,19648],{"className":19649,"style":1384},[1383],[1095,19651,1226],{"className":19652,"style":1256},[1150,1151],[1095,19654,1127],{"className":19655},[1163],[1433,19657,19658],{},"可控生成",[1433,19660,19661],{},"需要标签数据",[1412,19663,19664,19669,19672,19675,19678],{},[1433,19665,19666],{},[1172,19667,19668],{},"InfoGAN",[1433,19670,19671],{},"最大化互信息学习解耦表示",[1433,19673,19674],{},"增加互信息正则项",[1433,19676,19677],{},"无监督发现语义因子",[1433,19679,19680],{},"训练复杂度增加",[1830,19682],{},[1189,19684,19686],{"id":19685},"五vae-与-gan-对比","五、VAE 与 GAN 对比",[1406,19688,19689,19702],{},[1409,19690,19691],{},[1412,19692,19693,19696,19699],{},[1415,19694,19695],{},"维度",[1415,19697,19698],{},"VAE",[1415,19700,19701],{},"GAN",[1428,19703,19704,19717,19730,19743,19756,19769,19782,19795,19808],{},[1412,19705,19706,19711,19714],{},[1433,19707,19708],{},[1172,19709,19710],{},"密度建模",[1433,19712,19713],{},"显式（近似）：最大化 ELBO",[1433,19715,19716],{},"隐式：不直接建模密度",[1412,19718,19719,19724,19727],{},[1433,19720,19721],{},[1172,19722,19723],{},"训练方式",[1433,19725,19726],{},"最大似然（变分推断）",[1433,19728,19729],{},"对抗博弈（minimax）",[1412,19731,19732,19737,19740],{},[1433,19733,19734],{},[1172,19735,19736],{},"生成质量",[1433,19738,19739],{},"倾向模糊（均值回归效应）",[1433,19741,19742],{},"图像锐利、细节丰富",[1412,19744,19745,19750,19753],{},[1433,19746,19747],{},[1172,19748,19749],{},"多样性",[1433,19751,19752],{},"覆盖性好（mode covering）",[1433,19754,19755],{},"易模式崩塌（mode dropping）",[1412,19757,19758,19763,19766],{},[1433,19759,19760],{},[1172,19761,19762],{},"隐空间",[1433,19764,19765],{},"结构化、连续、可插值",[1433,19767,19768],{},"不保证连续性",[1412,19770,19771,19776,19779],{},[1433,19772,19773],{},[1172,19774,19775],{},"训练稳定性",[1433,19777,19778],{},"稳定（标准 SGD 优化）",[1433,19780,19781],{},"不稳定（需精心调参）",[1412,19783,19784,19789,19792],{},[1433,19785,19786],{},[1172,19787,19788],{},"评估",[1433,19790,19791],{},"可计算 ELBO 作为指标",[1433,19793,19794],{},"缺乏内在评估指标",[1412,19796,19797,19802,19805],{},[1433,19798,19799],{},[1172,19800,19801],{},"数学基础",[1433,19803,19804],{},"变分推断、贝叶斯框架",[1433,19806,19807],{},"博弈论、对偶理论",[1412,19809,19810,19815,19818],{},[1433,19811,19812],{},[1172,19813,19814],{},"典型应用",[1433,19816,19817],{},"表示学习、异常检测、插值",[1433,19819,19820],{},"高质量图像生成、超分辨率",[1830,19822],{},[1189,19824,19826],{"id":19825},"六gan-应用","六、GAN 应用",[1194,19828,19830],{"id":19829},"_61-图像超分辨率srgan","6.1 图像超分辨率（SRGAN）",[1091,19832,19833],{},"SRGAN 使用对抗训练将低分辨率图像恢复为高分辨率图像。损失函数包含：",[1166,19835,19836,20135],{},[1169,19837,19838,19841,19842],{},[1172,19839,19840],{},"内容损失","：基于 VGG 特征的感知损失 ",[1095,19843,19845,19920],{"className":19844},[1098],[1095,19846,19848],{"className":19847},[1102],[1104,19849,19850],{"xmlns":1106},[1108,19851,19852,19917],{},[1111,19853,19854,19866,19868,19870,19873,19875,19885,19887,19889,19891,19893,19895,19897,19907,19909,19911],{},[1465,19855,19856,19858],{},[1114,19857,2130],{"mathvariant":2129},[1111,19859,19860,19862,19864],{},[1114,19861,6804],{},[1114,19863,8480],{},[1114,19865,8480],{},[1118,19867,1463],{},[1114,19869,2143],{"mathvariant":1229},[1114,19871,19872],{},"F",[1118,19874,1121],{"stretchy":1120},[2171,19876,19877,19879],{},[1114,19878,2608],{},[1111,19880,19881,19883],{},[1114,19882,19101],{},[1114,19884,14837],{},[1118,19886,1127],{"stretchy":1120},[1118,19888,1510],{},[1114,19890,19872],{},[1118,19892,1121],{"stretchy":1120},[1114,19894,8480],{},[1118,19896,1121],{"stretchy":1120},[2171,19898,19899,19901],{},[1114,19900,2608],{},[1111,19902,19903,19905],{},[1114,19904,2130],{},[1114,19906,14837],{},[1118,19908,1127],{"stretchy":1120},[1118,19910,1127],{"stretchy":1120},[2171,19912,19913,19915],{},[1114,19914,2143],{"mathvariant":1229},[1490,19916,2177],{},[1129,19918,19919],{"encoding":1131},"\\mathcal{L}_{VGG} = \\|F(I^{HR}) - F(G(I^{LR}))\\|^2",[1095,19921,19923,19985,20050],{"className":19922,"ariaHidden":1137},[1136],[1095,19924,19926,19929,19976,19979,19982],{"className":19925},[1141],[1095,19927],{"className":19928,"style":2190},[1145],[1095,19930,19932,19935],{"className":19931},[1150],[1095,19933,2130],{"className":19934},[1150,2197],[1095,19936,19938],{"className":19937},[1570],[1095,19939,19941,19968],{"className":19940},[1574,1575],[1095,19942,19944,19965],{"className":19943},[1579],[1095,19945,19947],{"className":19946,"style":2210},[1583],[1095,19948,19949,19952],{"style":1647},[1095,19950],{"className":19951,"style":1592},[1591],[1095,19953,19955],{"className":19954},[1596,1597,1598,1599],[1095,19956,19958,19961],{"className":19957},[1150,1599],[1095,19959,6804],{"className":19960,"style":2264},[1150,1151,1599],[1095,19962,19964],{"className":19963},[1150,1151,1599],"GG",[1095,19966,1607],{"className":19967},[1606],[1095,19969,19971],{"className":19970},[1579],[1095,19972,19974],{"className":19973,"style":1666},[1583],[1095,19975],{},[1095,19977],{"className":19978,"style":1542},[1383],[1095,19980,1463],{"className":19981},[1546],[1095,19983],{"className":19984,"style":1542},[1383],[1095,19986,19988,19992,19995,19998,20001,20038,20041,20044,20047],{"className":19987},[1141],[1095,19989],{"className":19990,"style":19991},[1145],"height:1.0913em;vertical-align:-0.25em;",[1095,19993,2143],{"className":19994},[1150],[1095,19996,19872],{"className":19997,"style":1152},[1150,1151],[1095,19999,1121],{"className":20000},[1156],[1095,20002,20004,20007],{"className":20003},[1150],[1095,20005,2608],{"className":20006,"style":2687},[1150,1151],[1095,20008,20010],{"className":20009},[1570],[1095,20011,20013],{"className":20012},[1574],[1095,20014,20016],{"className":20015},[1579],[1095,20017,20020],{"className":20018,"style":20019},[1583],"height:0.8413em;",[1095,20021,20022,20025],{"style":2392},[1095,20023],{"className":20024,"style":1592},[1591],[1095,20026,20028],{"className":20027},[1596,1597,1598,1599],[1095,20029,20031,20034],{"className":20030},[1150,1599],[1095,20032,19101],{"className":20033,"style":19321},[1150,1151,1599],[1095,20035,14837],{"className":20036,"style":20037},[1150,1151,1599],"margin-right:0.0077em;",[1095,20039,1127],{"className":20040},[1163],[1095,20042],{"className":20043,"style":2264},[1383],[1095,20045,1510],{"className":20046},[1779],[1095,20048],{"className":20049,"style":2264},[1383],[1095,20051,20053,20056,20059,20062,20065,20068,20103,20106],{"className":20052},[1141],[1095,20054],{"className":20055,"style":19991},[1145],[1095,20057,19872],{"className":20058,"style":1152},[1150,1151],[1095,20060,1121],{"className":20061},[1156],[1095,20063,8480],{"className":20064},[1150,1151],[1095,20066,1121],{"className":20067},[1156],[1095,20069,20071,20074],{"className":20070},[1150],[1095,20072,2608],{"className":20073,"style":2687},[1150,1151],[1095,20075,20077],{"className":20076},[1570],[1095,20078,20080],{"className":20079},[1574],[1095,20081,20083],{"className":20082},[1579],[1095,20084,20086],{"className":20085,"style":20019},[1583],[1095,20087,20088,20091],{"style":2392},[1095,20089],{"className":20090,"style":1592},[1591],[1095,20092,20094],{"className":20093},[1596,1597,1598,1599],[1095,20095,20097,20100],{"className":20096},[1150,1599],[1095,20098,2130],{"className":20099},[1150,1151,1599],[1095,20101,14837],{"className":20102,"style":20037},[1150,1151,1599],[1095,20104,2370],{"className":20105},[1163],[1095,20107,20109,20112],{"className":20108},[1150],[1095,20110,2143],{"className":20111},[1150],[1095,20113,20115],{"className":20114},[1570],[1095,20116,20118],{"className":20117},[1574],[1095,20119,20121],{"className":20120},[1579],[1095,20122,20124],{"className":20123,"style":2389},[1583],[1095,20125,20126,20129],{"style":2392},[1095,20127],{"className":20128,"style":1592},[1591],[1095,20130,20132],{"className":20131},[1596,1597,1598,1599],[1095,20133,2177],{"className":20134},[1150,1599],[1169,20136,20137,20140],{},[1172,20138,20139],{},"对抗损失","：使超分结果在判别器看来像真实高清图",[1194,20142,20144],{"id":20143},"_62-图像修复image-inpainting","6.2 图像修复（Image Inpainting）",[1091,20146,20147],{},"利用 GAN 填补图像中缺失或损坏的区域。生成器学习根据周围上下文信息合理补全内容，判别器确保补全部分与原图风格一致。",[1194,20149,20151],{"id":20150},"_63-风格迁移cyclegan","6.3 风格迁移（CycleGAN）",[1091,20153,20154,20155,20158],{},"CycleGAN 实现",[1172,20156,20157],{},"无配对","的图像到图像翻译（如照片到油画、马到斑马）。核心创新：",[1166,20160,20161,20314,20647],{},[1169,20162,20163,20164,20240,20241],{},"两对生成器-判别器：",[1095,20165,20167,20192],{"className":20166},[1098],[1095,20168,20170],{"className":20169},[1102],[1104,20171,20172],{"xmlns":1106},[1108,20173,20174,20189],{},[1111,20175,20176,20178,20181,20184,20186],{},[1114,20177,8480],{},[1118,20179,20180],{},":",[1114,20182,20183],{},"X",[1118,20185,14926],{},[1114,20187,20188],{},"Y",[1129,20190,20191],{"encoding":1131},"G: X \\to Y",[1095,20193,20195,20213,20231],{"className":20194,"ariaHidden":1137},[1136],[1095,20196,20198,20201,20204,20207,20210],{"className":20197},[1141],[1095,20199],{"className":20200,"style":5154},[1145],[1095,20202,8480],{"className":20203},[1150,1151],[1095,20205],{"className":20206,"style":1542},[1383],[1095,20208,20180],{"className":20209},[1546],[1095,20211],{"className":20212,"style":1542},[1383],[1095,20214,20216,20219,20222,20225,20228],{"className":20215},[1141],[1095,20217],{"className":20218,"style":5154},[1145],[1095,20220,20183],{"className":20221,"style":2687},[1150,1151],[1095,20223],{"className":20224,"style":1542},[1383],[1095,20226,14926],{"className":20227},[1546],[1095,20229],{"className":20230,"style":1542},[1383],[1095,20232,20234,20237],{"className":20233},[1141],[1095,20235],{"className":20236,"style":5154},[1145],[1095,20238,20188],{"className":20239,"style":2264},[1150,1151],"，",[1095,20242,20244,20266],{"className":20243},[1098],[1095,20245,20247],{"className":20246},[1102],[1104,20248,20249],{"xmlns":1106},[1108,20250,20251,20263],{},[1111,20252,20253,20255,20257,20259,20261],{},[1114,20254,19872],{},[1118,20256,20180],{},[1114,20258,20188],{},[1118,20260,14926],{},[1114,20262,20183],{},[1129,20264,20265],{"encoding":1131},"F: Y \\to X",[1095,20267,20269,20287,20305],{"className":20268,"ariaHidden":1137},[1136],[1095,20270,20272,20275,20278,20281,20284],{"className":20271},[1141],[1095,20273],{"className":20274,"style":5154},[1145],[1095,20276,19872],{"className":20277,"style":1152},[1150,1151],[1095,20279],{"className":20280,"style":1542},[1383],[1095,20282,20180],{"className":20283},[1546],[1095,20285],{"className":20286,"style":1542},[1383],[1095,20288,20290,20293,20296,20299,20302],{"className":20289},[1141],[1095,20291],{"className":20292,"style":5154},[1145],[1095,20294,20188],{"className":20295,"style":2264},[1150,1151],[1095,20297],{"className":20298,"style":1542},[1383],[1095,20300,14926],{"className":20301},[1546],[1095,20303],{"className":20304,"style":1542},[1383],[1095,20306,20308,20311],{"className":20307},[1141],[1095,20309],{"className":20310,"style":5154},[1145],[1095,20312,20183],{"className":20313,"style":2687},[1150,1151],[1169,20315,20316,4359,20319],{},[1172,20317,20318],{},"循环一致性损失",[1095,20320,20322,20402],{"className":20321},[1098],[1095,20323,20325],{"className":20324},[1102],[1104,20326,20327],{"xmlns":1106},[1108,20328,20329,20399],{},[1111,20330,20331,20343,20345,20347,20349,20351,20353,20355,20357,20359,20361,20363,20365,20371,20373,20375,20377,20379,20381,20383,20385,20387,20389,20391,20393],{},[1465,20332,20333,20335],{},[1114,20334,2130],{"mathvariant":2129},[1111,20336,20337,20339,20341],{},[1114,20338,17785],{},[1114,20340,1226],{},[1114,20342,17785],{},[1118,20344,1463],{},[1114,20346,2143],{"mathvariant":1229},[1114,20348,19872],{},[1118,20350,1121],{"stretchy":1120},[1114,20352,8480],{},[1118,20354,1121],{"stretchy":1120},[1114,20356,1124],{},[1118,20358,1127],{"stretchy":1120},[1118,20360,1127],{"stretchy":1120},[1118,20362,1510],{},[1114,20364,1124],{},[1465,20366,20367,20369],{},[1114,20368,2143],{"mathvariant":1229},[1490,20370,1492],{},[1118,20372,3733],{},[1114,20374,2143],{"mathvariant":1229},[1114,20376,8480],{},[1118,20378,1121],{"stretchy":1120},[1114,20380,19872],{},[1118,20382,1121],{"stretchy":1120},[1114,20384,1226],{},[1118,20386,1127],{"stretchy":1120},[1118,20388,1127],{"stretchy":1120},[1118,20390,1510],{},[1114,20392,1226],{},[1465,20394,20395,20397],{},[1114,20396,2143],{"mathvariant":1229},[1490,20398,1492],{},[1129,20400,20401],{"encoding":1131},"\\mathcal{L}_{cyc} = \\|F(G(x)) - x\\|_1 + \\|G(F(y)) - 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64",[1095,20687,20689,20707],{"className":20688,"ariaHidden":1137},[1136],[1095,20690,20692,20695,20698,20701,20704],{"className":20691},[1141],[1095,20693],{"className":20694,"style":15120},[1145],[1095,20696,15018],{"className":20697},[1150],[1095,20699],{"className":20700,"style":2264},[1383],[1095,20702,14939],{"className":20703},[1779],[1095,20705],{"className":20706,"style":2264},[1383],[1095,20708,20710,20713],{"className":20709},[1141],[1095,20711],{"className":20712,"style":12299},[1145],[1095,20714,15018],{"className":20715},[1150],"）",[1169,20718,20719,20722,20723,20716],{},[1172,20720,20721],{},"Stage-II","：在草图基础上细化生成高分辨率图像（",[1095,20724,20726,20744],{"className":20725},[1098],[1095,20727,20729],{"className":20728},[1102],[1104,20730,20731],{"xmlns":1106},[1108,20732,20733,20741],{},[1111,20734,20735,20737,20739],{},[1490,20736,14987],{},[1118,20738,14939],{},[1490,20740,14987],{},[1129,20742,20743],{"encoding":1131},"256 \\times 256",[1095,20745,20747,20765],{"className":20746,"ariaHidden":1137},[1136],[1095,20748,20750,20753,20756,20759,20762],{"className":20749},[1141],[1095,20751],{"className":20752,"style":15120},[1145],[1095,20754,14987],{"className":20755},[1150],[1095,20757],{"className":20758,"style":2264},[1383],[1095,20760,14939],{"className":20761},[1779],[1095,20763],{"className":20764,"style":2264},[1383],[1095,20766,20768,20771],{"className":20767},[1141],[1095,20769],{"className":20770,"style":12299},[1145],[1095,20772,14987],{"className":20773},[1150],[1830,20775],{},[1189,20777,20779],{"id":20778},"七相关公式","七、相关公式",[1406,20781,20782,20792],{},[1409,20783,20784],{},[1412,20785,20786,20789],{},[1415,20787,20788],{},"公式名称",[1415,20790,20791],{},"表达式",[1428,20793,20794,21170,21339,21828,22196,22589,22966],{},[1412,20795,20796,20799],{},[1433,20797,20798],{},"VAE 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p(x) \\geq \\mathbb{E}_{q(z \\mid x)}[\\log p(x \\mid z)] - D_{KL}(q(z \\mid x) \\parallel 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