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Method /DatasetMNISTFashion
SSWAE14.91 ± 0.3243.94 ± 0.81
SWAE15.18 ± 0.3244.78 ± 1.07
WAE-MMD IMQ18.12 ± 0.6268.51 ± 2.76
WAE-MMDRBF20.09 ±1.4270.58 ± 1.75
SAE19.39 ± 0.5656.75 ±1.7
Circular GSWAE15.01 ± 0.2644.65 ± 1.2
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\\Big ) ^ { 2 } + \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } x _ { i } + \\frac { 1 } { 3 } + \\Big ( \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } x _ { i } \\Big ) ^ { 2 } - \\frac { 1 } { 4 } } } } \\\\ { { \\displaystyle { = \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } x _ { i } ^ { 2 } - \\Big ( \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } x _ { i } \\Big ) ^ { 2 } + \\frac { 1 } { n ^ { 2 } } \\sum _ { i = 1 } ^ { n } ( n + 1 - 2 i ) x _ { i } + \\frac { 1 } { 1 2 } . } } } \\end{array}" }, { "category_id": 14, "poly": [ 399, 1649, 1300, 1649, 1300, 1741, 399, 1741 ], "score": 0.93, "latex": "\\hat { \\alpha } _ { n } + \\hat { \\alpha } _ { n } ^ { 2 } = \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } x _ { i } - \\frac { 1 } { 2 } + \\left( \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } x _ { i } \\right) ^ { 2 } + \\frac { 1 } { 4 } - \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } x _ { i } = \\left( \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } x _ { i } \\right) ^ { 2 } - \\frac { 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Input: V a potential, K the number of iterations of SWVI, N the batch size,l the number of MCMC steps
Initialization: Choose qe a sampler
for k = 1 to K do
Sample （2）1~q0 Run (MCMC steps tarting from (29)=1 to get (2j)N=1
N
// Denote μ0 =N∑j=1δzg and j=∑=1 8
Compute J= SW²(μo, μe) Backpropagate through J w.r.t. 0
Perform a gradient step end for
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MethodEncoder outputs²
Supervised82.2681.43
Chen et al. [21]66.5559.09
Wang and Isola [104]60.5355.86
SW-SSL,λ= 1,L = 1062.6557.77
SW-SSL,λ= 1,L = 362.4657.64
SSW-SSL,入= 20,L=1064.8958.91
SSW-SSL,λ= 20,L = 363.7559.75
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MethodLuniform(zA) + Luniform(zB)Complexity
Chen et al. [21]2n TO(n²d)
Wang and Isola [104]∑zE{24,zB}logn(n-1)∑i>jexp(-t|i -zjll2) 2O(n2d)
SSW-SSL (Ours)1(SSW2(zA,v)+ SSW2(zB,v))O(Ln(d + log n))
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