Twin Auxiliary Classifiers GAN (TAC-GAN) Mingming Gong* Yanwu Xu* - - PowerPoint PPT Presentation

SLIDE 1

Mingming Gong* Yanwu Xu* Chunyuan Li Kun Zhang Kayhan Batmanghelich

Twin Auxiliary Classifiers GAN (TAC-GAN)

SLIDE 2

Generative adversarial networks(GAN)

2

Generator (G)

Noise ( )

z

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Real/Fake

Discriminator (D)

Minimax game between G and D

SLIDE 3

Conditional GAN(CGAN)

3

Noise ( )

z

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Real Cat vs/Fake Cat Input Label ( Cat ) Generator (G)

Discriminator (D)

Minimax game between G and D

SLIDE 4

Auxiliary Classifier Conditional GAN(AC-GAN)

4

Generator (G) Noise ( )

z

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Real vs/Fake Discriminator (D) Input Label ( Cat ) Classifier (C) Output Label ( Cat )

Minimax game between G and D Auxiliary classifier C

SLIDE 5

Apple Fish Tree Motorcycle Mountain

Low diversity Tends toward mode collapse

Issues with AC-GAN

5

CIFAR100 Imagenet1000

SLIDE 6

6

1D Mixture of Gaussian

True Distribution Estimated Distribution by AC-GAN

(PX)

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(QX)

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SLIDE 7

AC-GAN: Density Matching Point of View

7

data distribution estimated distribution

P

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Q

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XY

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joint

SLIDE 8

AC-GAN: Density Matching Point of View

8

data estimated

P

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Q

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XY

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joint

X

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data

Y |X

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conditional

Y

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label

SLIDE 9

AC-GAN: Density Matching Point of View

9

JSD(PX, QX)

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data estimated

P

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Q

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XY

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joint

X

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data

Y |X

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conditional

Y

<latexit sha1_base64="hetRNmVqKWZen/S491Dadp4Pp4=">AB6HicbVBNS8NAEJ34WetX1aOXxSJ4KokKeix68diC/ZA2lM120q7dbMLuRihv8CLB0W8+pO8+W/ctjlo64OBx3szMwLEsG1cd1vZ2V1bX1js7BV3N7Z3dsvHRw2dZwqhg0Wi1i1A6pRcIkNw43AdqKQRoHAVjC6nfqtJ1Sax/LejBP0IzqQPOSMGivVH3qlsltxZyDLxMtJGXLUeqWvbj9maYTSMEG17nhuYvyMKsOZwEmxm2pMKBvRAXYslTRC7WezQyfk1Cp9EsbKljRkpv6eyGik9TgKbGdEzVAvelPxP6+TmvDaz7hMUoOSzReFqSAmJtOvSZ8rZEaMLaFMcXsrYUOqKDM2m6INwVt8eZk0zyveRcWrX5arN3kcBTiGEzgD6gCndQgwYwQHiGV3hzHp0X5935mLeuOPnMEfyB8/kDuDmM4A=</latexit>

label

SLIDE 10

AC-GAN: Density Matching Point of View

10

JSD(PX, QX)

<latexit sha1_base64="Uybl/pSQlqgqAzbvu9tJlkjaRA=">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</latexit>

data estimated

P

<latexit sha1_base64="s/exqeaXa47KUfqvjKRaIZRa+aU=">AB6HicdVDLSgMxFL3js9ZX1aWbYBFcDTNT+3BXdOyBfuAdpBMmljM5khyQhl6Be4caGIWz/JnX9j+hBU9EDgcM65N4TJwp7Tgf1srq2vrGZm4rv72zu7dfODhsqziVhLZIzGPZDbCinAna0kxz2k0kxVHAaScYX838zj2VisXiRk8S6kd4KFjICNZGajZuC0XHdmqVUq2CHNtzneqFZ0jZK5c8F7m2M0cRljD59/4gJmlEhSYcK9VznUT7GZaEU6n+X6qaILJGA9pz1CBI6r8bL7oFJ0aZYDCWJonNJqr3ycyHCk1iQKTjLAeqd/eTPzL6U6rPkZE0mqSCLj8KUIx2j2dVowCQlmk8MwUQysysiIywx0abvCnh61L0P2l7tluy3eZ5sX65rCMHx3ACZ+BCFepwDQ1oAQEKD/AEz9ad9Wi9WK+L6Iq1nDmCH7DePgEQVo0d</latexit>

Q

<latexit sha1_base64="x4BK2VgOpXHSkC8FBu7BJjsRKFs=">AB6HicdVDJSgNBEO2JW4xb1KOXxiB4GnqSIcst6MVjAmaBZAg9nUrSpmehu0cIQ7AiwdFvPpJ3vwbO4ugog8KHu9VUVXPjwVXmpAPK7OxubW9k93N7e0fHB7lj0/aKkokgxaLRCS7PlUgeAgtzbWAbiyBr6Aj+9Xvide5CKR+GtnsXgBXQc8hFnVBup2RzkC8QulhzXJZjYbpmQSs0QUquWykXs2GSJAlqjMci/94cRSwINRNUqZ5DYu2lVGrOBMxz/URBTNmUjqFnaEgDUF6PHSOL4wyxKNImgo1XqrfJ1IaKDULfNMZUD1Rv72F+JfXS/So6qU8jBMNIVstGiUC6wgvsZDLoFpMTOEMsnNrZhNqKRMm2xyJoSvT/H/pF20nZLtN1C/WodRxadoXN0iRxUQXV0gxqohRgC9ICe0LN1Zz1aL9brqjVjrWdO0Q9Yb58OCo0c</latexit>

XY

<latexit sha1_base64="EBy45Qk2sUIZo/T8IjVOh4eaNzg=">AB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU0GPRi8cq9kPaUDbTbt0swm7E6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvSKQw6LrfTmFldW19o7hZ2tre2d0r7x80TZxqxhslrFuB9RwKRvoEDJ24nmNAokbwWjm6nfeuLaiFg94DjhfkQHSoSCUbTSfuxV64VXcGsky8nFQgR71X/ur2Y5ZGXCGT1JiO5yboZ1SjYJPSt3U8ISyER3wjqWKRtz42ezSCTmxSp+EsbalkMzU3xMZjYwZR4HtjCgOzaI3Ff/zOimGV34mVJIiV2y+KEwlwZhM3yZ9oTlDObaEMi3srYQNqaYMbTglG4K3+PIyaZ5VvfOqd3dRqV3ncRThCI7hFDy4hBrcQh0awCEZ3iFN2fkvDjvzse8teDkM4fwB87nD2LkjUI=</latexit>

joint

X

<latexit sha1_base64="8qOjKVUOV3WtxLlf9fJ/ZGLVadQ=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU0GPRi8cW7Ae0oWy2k3btZhN2N0IJ/QVePCji1Z/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4bua3n1BpHsHM0nQj+hQ8pAzaqzU6PTLFbfqzkFWiZeTCuSo98tfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeGNn3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ipXVS9y6rXuKrUbvM4inACp3AOHlxDe6hDk1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDtrWM3w=</latexit>

data

Y |X

<latexit sha1_base64="dAdtkaf8MKyPz11odEQxhtSVUts=">AAAB6nicbVBNS8NAEJ34WetX1aOXxSJ4KokKeix68VjRfkgbyma7aZduNmF3IpTYn+DFgyJe/UXe/Ddu2xy09cHA470ZZuYFiRQGXffbWVpeWV1bL2wUN7e2d3ZLe/sNE6ea8TqLZaxbATVcCsXrKFDyVqI5jQLJm8HweuI3H7k2Ilb3OEq4H9G+EqFgFK109/DU6pbKbsWdgiwSLydlyFHrlr46vZilEVfIJDWm7bkJ+hnVKJjk42InNTyhbEj7vG2pohE3fjY9dUyOrdIjYaxtKSRT9fdERiNjRlFgOyOKAzPvTcT/vHaK4aWfCZWkyBWbLQpTSTAmk79JT2jOUI4soUwLeythA6opQ5tO0Ybgzb+8SBqnFe+s4t2el6tXeRwFOIQjOAEPLqAKN1CDOjDowzO8wpsjnRfn3fmYtS45+cwB/IHz+QNEn43I</latexit>

conditional

Y

<latexit sha1_base64="hetRNmVqKWZen/S491Dadp4Pp4=">AB6HicbVBNS8NAEJ34WetX1aOXxSJ4KokKeix68diC/ZA2lM120q7dbMLuRihv8CLB0W8+pO8+W/ctjlo64OBx3szMwLEsG1cd1vZ2V1bX1js7BV3N7Z3dsvHRw2dZwqhg0Wi1i1A6pRcIkNw43AdqKQRoHAVjC6nfqtJ1Sax/LejBP0IzqQPOSMGivVH3qlsltxZyDLxMtJGXLUeqWvbj9maYTSMEG17nhuYvyMKsOZwEmxm2pMKBvRAXYslTRC7WezQyfk1Cp9EsbKljRkpv6eyGik9TgKbGdEzVAvelPxP6+TmvDaz7hMUoOSzReFqSAmJtOvSZ8rZEaMLaFMcXsrYUOqKDM2m6INwVt8eZk0zyveRcWrX5arN3kcBTiGEzgD6gCndQgwYwQHiGV3hzHp0X5935mLeuOPnMEfyB8/kDuDmM4A=</latexit>

label

SLIDE 11

JSD(PX, QX)

<latexit sha1_base64="Uybl/pSQlqgqAzbvu9tJlkjaRA=">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</latexit>

AC-GAN: Density Matching Point of View

H(PY |X, Qc

Y |X)

< l a t e x i t s h a 1 _ b a s e 6 4 = "

• N

5 z t 4 O Y p a 8 L l a 5 s c 3 Z N w v s c r 8 = " > A A A B / 3 i c b Z D L S s N A F I Z P v N Z 6 i w p u 3 A S L U E F K

• I

u i 2 6 6 b M F e p I 1 h M p 2 2 Q y e T M D M R S p q F r + L G h S J u f Q 1 3 v

• 3

T N g t t / W H g 4 z / n c M 7 8 f s S

• V

L b 9 b S w t r 6 y u r e c 2 8 p t b 2 z u 7 5 t 5 + Q 4 a x w K S O Q x a K l

• 8

k Y Z S T u q K K k V Y k C A p 8 R p r + 8 H Z S b z 4 S I W n I 7 9 Q

• I

m 6 A + p z 2 K E Z K W 5 5 5 W C l W v e R + 3 E r P a g 8 J T m d 8 6 p k F u 2 R P Z S 2 C k E B M l U 9 8 6 v T D X E c E K 4 w Q 1 K 2 H T t S b

• K

E

• p

i R N N + J J Y k Q H q I + a W v k K C D S T a b 3 p 9 a J d r p W L x T 6 c W V N 3 d 8 T C Q q k H A W + 7 g y Q G s j 5 2 s T 8 r 9 a O V e / a T S i P Y k U 4 n i 3 q x c x S

• T

U J w + p S Q b B i I w I C 6 p v t f A A C Y S V j i y v Q 3 D m v 7 w I j f O S c 1 F y a p e F 8 k W R w 6 O 4 B i K 4 M A V l K E C V a g D h j E 8 w y u 8 G U / G i / F u f M x a l 4 x s 5 g D + y P j 8 A W D I l b E = < / l a t e x i t >

KL(PY |X||Qc

Y |X)

<latexit sha1_base64="q+9q9r2rM83dmAd67Vg+GWYFgJo=">ACAXicbVDLSsNAFJ3UV62vqBvBzWAR6qYkKuiy6EbQRQv2IW0Mk+mkHTqZhJmJUNK48VfcuFDErX/hzr9x2mahrQcunDnXube40WMSmVZ30ZuYXFpeSW/Wlhb39jcMrd3GjKMBSZ1HLJQtDwkCaOc1BVjLQiQVDgMdL0Bpdjv/lAhKQhv1XDiDgB6nHqU4yUlxz7/qmVHWTu1ErHY1q9wlOp48j1yxaZWsCOE/sjBRBhqprfnW6IY4DwhVmSMq2bUXKSZBQFDOSFjqxJBHCA9QjbU05Coh0kskFKTzUShf6odDFZyovycSFEg5DzdGSDVl7PeWPzPa8fKP3cSyqNYEY6nH/kxgyqE4zhglwqCFRtqgrCgeleI+0grHRoBR2CPXvyPGkcl+2Tsl07LVYusjyYB8cgBKwRmogCtQBXWAwSN4Bq/gzXgyXox342PamjOymV3wB8bnD2yTluA=</latexit>

H(PY |X)

<latexit sha1_base64="xfLRd+RaFRpAGy2Y+7Ncg/XTa/k=">AB8XicdVDLTgJBEOz1ifhCPXqZSEzwQnYRFG5ELxwxkYcCIbPDABNmZzczsyZk5S+8eNAYr/6N/GWVgTNVpJ5Wq7nR3uQFnStv2h7W0vLK6tp7aSG9ube/sZvb2m8oPJaEN4nNftl2sKGeCNjTnLYDSbHnctpyJ5ex37qjUjFfXOtpQHseHgk2ZARrI93WcvV+dHPfnp30M1k7XymXKqUzZOftOWJSrJTsAnISJQsJ6v3Me3fgk9CjQhOleo4dqB7EZaEU5n6W6oaIDJBI9ox1CBPap60fziGTo2ygANfWlKaDRXv09E2FNq6rm08N6rH57sfiX1wn1sNyLmAhCTQVZLBqGHGkfxe+jAZOUaD41BPJzK2IjLHERJuQ0iaEr0/R/6RZyDuneqmK1eJHGk4BCOIAcOnEMValCHBhAQ8ABP8Gwp69F6sV4XrUtWMnMAP2C9fQIYapCM</latexit>

11

data estimated

P

<latexit sha1_base64="s/exqeaXa47KUfqvjKRaIZRa+aU=">AB6HicdVDLSgMxFL3js9ZX1aWbYBFcDTNT+3BXdOyBfuAdpBMmljM5khyQhl6Be4caGIWz/JnX9j+hBU9EDgcM65N4TJwp7Tgf1srq2vrGZm4rv72zu7dfODhsqziVhLZIzGPZDbCinAna0kxz2k0kxVHAaScYX838zj2VisXiRk8S6kd4KFjICNZGajZuC0XHdmqVUq2CHNtzneqFZ0jZK5c8F7m2M0cRljD59/4gJmlEhSYcK9VznUT7GZaEU6n+X6qaILJGA9pz1CBI6r8bL7oFJ0aZYDCWJonNJqr3ycyHCk1iQKTjLAeqd/eTPzL6U6rPkZE0mqSCLj8KUIx2j2dVowCQlmk8MwUQysysiIywx0abvCnh61L0P2l7tluy3eZ5sX65rCMHx3ACZ+BCFepwDQ1oAQEKD/AEz9ad9Wi9WK+L6Iq1nDmCH7DePgEQVo0d</latexit>

Q

<latexit sha1_base64="x4BK2VgOpXHSkC8FBu7BJjsRKFs=">AB6HicdVDJSgNBEO2JW4xb1KOXxiB4GnqSIcst6MVjAmaBZAg9nUrSpmehu0cIQ7AiwdFvPpJ3vwbO4ugog8KHu9VUVXPjwVXmpAPK7OxubW9k93N7e0fHB7lj0/aKkokgxaLRCS7PlUgeAgtzbWAbiyBr6Aj+9Xvide5CKR+GtnsXgBXQc8hFnVBup2RzkC8QulhzXJZjYbpmQSs0QUquWykXs2GSJAlqjMci/94cRSwINRNUqZ5DYu2lVGrOBMxz/URBTNmUjqFnaEgDUF6PHSOL4wyxKNImgo1XqrfJ1IaKDULfNMZUD1Rv72F+JfXS/So6qU8jBMNIVstGiUC6wgvsZDLoFpMTOEMsnNrZhNqKRMm2xyJoSvT/H/pF20nZLtN1C/WodRxadoXN0iRxUQXV0gxqohRgC9ICe0LN1Zz1aL9brqjVjrWdO0Q9Yb58OCo0c</latexit>

XY

<latexit sha1_base64="EBy45Qk2sUIZo/T8IjVOh4eaNzg=">AB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU0GPRi8cq9kPaUDbTbt0swm7E6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvSKQw6LrfTmFldW19o7hZ2tre2d0r7x80TZxqxhslrFuB9RwKRvoEDJ24nmNAokbwWjm6nfeuLaiFg94DjhfkQHSoSCUbTSfuxV64VXcGsky8nFQgR71X/ur2Y5ZGXCGT1JiO5yboZ1SjYJPSt3U8ISyER3wjqWKRtz42ezSCTmxSp+EsbalkMzU3xMZjYwZR4HtjCgOzaI3Ff/zOimGV34mVJIiV2y+KEwlwZhM3yZ9oTlDObaEMi3srYQNqaYMbTglG4K3+PIyaZ5VvfOqd3dRqV3ncRThCI7hFDy4hBrcQh0awCEZ3iFN2fkvDjvzse8teDkM4fwB87nD2LkjUI=</latexit>

joint

X

<latexit sha1_base64="8qOjKVUOV3WtxLlf9fJ/ZGLVadQ=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU0GPRi8cW7Ae0oWy2k3btZhN2N0IJ/QVePCji1Z/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4bua3n1BpHsHM0nQj+hQ8pAzaqzU6PTLFbfqzkFWiZeTCuSo98tfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeGNn3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ipXVS9y6rXuKrUbvM4inACp3AOHlxDe6hDk1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDtrWM3w=</latexit>

data

Y |X

<latexit sha1_base64="dAdtkaf8MKyPz11odEQxhtSVUts=">AAAB6nicbVBNS8NAEJ34WetX1aOXxSJ4KokKeix68VjRfkgbyma7aZduNmF3IpTYn+DFgyJe/UXe/Ddu2xy09cHA470ZZuYFiRQGXffbWVpeWV1bL2wUN7e2d3ZLe/sNE6ea8TqLZaxbATVcCsXrKFDyVqI5jQLJm8HweuI3H7k2Ilb3OEq4H9G+EqFgFK109/DU6pbKbsWdgiwSLydlyFHrlr46vZilEVfIJDWm7bkJ+hnVKJjk42InNTyhbEj7vG2pohE3fjY9dUyOrdIjYaxtKSRT9fdERiNjRlFgOyOKAzPvTcT/vHaK4aWfCZWkyBWbLQpTSTAmk79JT2jOUI4soUwLeythA6opQ5tO0Ybgzb+8SBqnFe+s4t2el6tXeRwFOIQjOAEPLqAKN1CDOjDowzO8wpsjnRfn3fmYtS45+cwB/IHz+QNEn43I</latexit>

conditional

Y

<latexit sha1_base64="hetRNmVqKWZen/S491Dadp4Pp4=">AB6HicbVBNS8NAEJ34WetX1aOXxSJ4KokKeix68diC/ZA2lM120q7dbMLuRihv8CLB0W8+pO8+W/ctjlo64OBx3szMwLEsG1cd1vZ2V1bX1js7BV3N7Z3dsvHRw2dZwqhg0Wi1i1A6pRcIkNw43AdqKQRoHAVjC6nfqtJ1Sax/LejBP0IzqQPOSMGivVH3qlsltxZyDLxMtJGXLUeqWvbj9maYTSMEG17nhuYvyMKsOZwEmxm2pMKBvRAXYslTRC7WezQyfk1Cp9EsbKljRkpv6eyGik9TgKbGdEzVAvelPxP6+TmvDaz7hMUoOSzReFqSAmJtOvSZ8rZEaMLaFMcXsrYUOqKDM2m6INwVt8eZk0zyveRcWrX5arN3kcBTiGEzgD6gCndQgwYwQHiGV3hzHp0X5935mLeuOPnMEfyB8/kDuDmM4A=</latexit>

label

:Constant

≡

<latexit sha1_base64="1M5tmE0P5SuCbPt3zvwbytBZYMI=">AB/XicbVDLSsNAFJ34rPUVHzs3wSK4KokKuiy6cVnBPqAJZTK9aYdOJnEehRqCv+LGhSJu/Q93/o3TtAtPXDhcM69c+eMGVUKtf9tpaWV1bX1ksb5c2t7Z1de2+/KRMtCDRIwhLRDrERjk0FUM2qkAHIcMWuHwZuK3RiAkTfi9GqcQxLjPaUQJVkbq2od+8UYWMg15sODpqO8a1fcqlvAWSTejFTQDPWu/eX3EqJj4IowLGXHc1MVZFgoShjkZV9LSDEZ4j50DOU4BhlkxebcOTFKz4kSYorp1B/T2Q4lnIch6Yzxmog572J+J/X0Sq6CjLKU62Ak+miSDNHJc4kCqdHBRDFxoZgIqj5q0MGWGCiTGBlE4I3f/IiaZ5VvfOqd3dRqV3P4ihI3SMTpGHLlEN3aI6aiCHtEzekVv1pP1Yr1bH9PWJWs2c4D+wPr8AcDMlg8=</latexit>

SLIDE 12

AC-GAN: Density Matching Point of View

JSD(PX, QX)

<latexit sha1_base64="Uybl/pSQlqgqAzbvu9tJlkjaRA=">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</latexit>

12

H(PY |X, Qc

Y |X)

< l a t e x i t s h a 1 _ b a s e 6 4 = "

• N

5 z t 4 O Y p a 8 L l a 5 s c 3 Z N w v s c r 8 = " > A A A B / 3 i c b Z D L S s N A F I Z P v N Z 6 i w p u 3 A S L U E F K

• I

u i 2 6 6 b M F e p I 1 h M p 2 2 Q y e T M D M R S p q F r + L G h S J u f Q 1 3 v

• 3

T N g t t / W H g 4 z / n c M 7 8 f s S

• V

L b 9 b S w t r 6 y u r e c 2 8 p t b 2 z u 7 5 t 5 + Q 4 a x w K S O Q x a K l

• 8

k Y Z S T u q K K k V Y k C A p 8 R p r + 8 H Z S b z 4 S I W n I 7 9 Q

• I

m 6 A + p z 2 K E Z K W 5 5 5 W C l W v e R + 3 E r P a g 8 J T m d 8 6 p k F u 2 R P Z S 2 C k E B M l U 9 8 6 v T D X E c E K 4 w Q 1 K 2 H T t S b

• K

E

• p

i R N N + J J Y k Q H q I + a W v k K C D S T a b 3 p 9 a J d r p W L x T 6 c W V N 3 d 8 T C Q q k H A W + 7 g y Q G s j 5 2 s T 8 r 9 a O V e / a T S i P Y k U 4 n i 3 q x c x S

• T

U J w + p S Q b B i I w I C 6 p v t f A A C Y S V j i y v Q 3 D m v 7 w I j f O S c 1 F y a p e F 8 k W R w 6 O 4 B i K 4 M A V l K E C V a g D h j E 8 w y u 8 G U / G i / F u f M x a l 4 x s 5 g D + y P j 8 A W D I l b E = < / l a t e x i t >

KL(QY |X||Qc

Y |X)

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H(QY |X)

<latexit sha1_base64="GnTc+I3Ot7H0ODvYil+MgQpsBg=">AB8XicdVDLTsJAFJ3iC/GFunQzkZjgpmkRKOyIblhCIg+FhkyHASZMp83M1IRU/sKNC41x69+482+cAiZq9CQ3OTn3tx7jxcyKpVlfRiptfWNza30dmZnd2/IHt41JZBJDBp4YAFoushSRjlpKWoYqQbCoJ8j5GON71K/M4dEZIG/FrNQuL6aMzpiGKktHRbzcH8c19d34+yOYs1opF0oFaJmWXS46TkJKFbvqQNu0FsiBFRqD7Ht/GODIJ1xhqTs2Vao3BgJRTEj80w/kiREeIrGpKcpRz6Rbry4eA7PtDKEo0Do4gou1O8TMfKlnPme7vSRmsjfXiL+5fUiNaq4MeVhpAjHy0WjiEVwOR9OKSCYMVmiAsqL4V4gkSCsdUkaH8PUp/J+0C6Z9YdrNYq52uYojDU7AKcgDGzigBuqgAVoAw4ewBN4NqTxaLwYr8vWlLGaOQY/YLx9Aj1NkKY=</latexit>

data estimated

P

<latexit sha1_base64="s/exqeaXa47KUfqvjKRaIZRa+aU=">AB6HicdVDLSgMxFL3js9ZX1aWbYBFcDTNT+3BXdOyBfuAdpBMmljM5khyQhl6Be4caGIWz/JnX9j+hBU9EDgcM65N4TJwp7Tgf1srq2vrGZm4rv72zu7dfODhsqziVhLZIzGPZDbCinAna0kxz2k0kxVHAaScYX838zj2VisXiRk8S6kd4KFjICNZGajZuC0XHdmqVUq2CHNtzneqFZ0jZK5c8F7m2M0cRljD59/4gJmlEhSYcK9VznUT7GZaEU6n+X6qaILJGA9pz1CBI6r8bL7oFJ0aZYDCWJonNJqr3ycyHCk1iQKTjLAeqd/eTPzL6U6rPkZE0mqSCLj8KUIx2j2dVowCQlmk8MwUQysysiIywx0abvCnh61L0P2l7tluy3eZ5sX65rCMHx3ACZ+BCFepwDQ1oAQEKD/AEz9ad9Wi9WK+L6Iq1nDmCH7DePgEQVo0d</latexit>

Q

<latexit sha1_base64="x4BK2VgOpXHSkC8FBu7BJjsRKFs=">AB6HicdVDJSgNBEO2JW4xb1KOXxiB4GnqSIcst6MVjAmaBZAg9nUrSpmehu0cIQ7AiwdFvPpJ3vwbO4ugog8KHu9VUVXPjwVXmpAPK7OxubW9k93N7e0fHB7lj0/aKkokgxaLRCS7PlUgeAgtzbWAbiyBr6Aj+9Xvide5CKR+GtnsXgBXQc8hFnVBup2RzkC8QulhzXJZjYbpmQSs0QUquWykXs2GSJAlqjMci/94cRSwINRNUqZ5DYu2lVGrOBMxz/URBTNmUjqFnaEgDUF6PHSOL4wyxKNImgo1XqrfJ1IaKDULfNMZUD1Rv72F+JfXS/So6qU8jBMNIVstGiUC6wgvsZDLoFpMTOEMsnNrZhNqKRMm2xyJoSvT/H/pF20nZLtN1C/WodRxadoXN0iRxUQXV0gxqohRgC9ICe0LN1Zz1aL9brqjVjrWdO0Q9Yb58OCo0c</latexit>

XY

<latexit sha1_base64="EBy45Qk2sUIZo/T8IjVOh4eaNzg=">AB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU0GPRi8cq9kPaUDbTbt0swm7E6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvSKQw6LrfTmFldW19o7hZ2tre2d0r7x80TZxqxhslrFuB9RwKRvoEDJ24nmNAokbwWjm6nfeuLaiFg94DjhfkQHSoSCUbTSfuxV64VXcGsky8nFQgR71X/ur2Y5ZGXCGT1JiO5yboZ1SjYJPSt3U8ISyER3wjqWKRtz42ezSCTmxSp+EsbalkMzU3xMZjYwZR4HtjCgOzaI3Ff/zOimGV34mVJIiV2y+KEwlwZhM3yZ9oTlDObaEMi3srYQNqaYMbTglG4K3+PIyaZ5VvfOqd3dRqV3ncRThCI7hFDy4hBrcQh0awCEZ3iFN2fkvDjvzse8teDkM4fwB87nD2LkjUI=</latexit>

joint

X

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data

Y |X

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conditional

Y

<latexit sha1_base64="hetRNmVqKWZen/S491Dadp4Pp4=">AB6HicbVBNS8NAEJ34WetX1aOXxSJ4KokKeix68diC/ZA2lM120q7dbMLuRihv8CLB0W8+pO8+W/ctjlo64OBx3szMwLEsG1cd1vZ2V1bX1js7BV3N7Z3dsvHRw2dZwqhg0Wi1i1A6pRcIkNw43AdqKQRoHAVjC6nfqtJ1Sax/LejBP0IzqQPOSMGivVH3qlsltxZyDLxMtJGXLUeqWvbj9maYTSMEG17nhuYvyMKsOZwEmxm2pMKBvRAXYslTRC7WezQyfk1Cp9EsbKljRkpv6eyGik9TgKbGdEzVAvelPxP6+TmvDaz7hMUoOSzReFqSAmJtOvSZ8rZEaMLaFMcXsrYUOqKDM2m6INwVt8eZk0zyveRcWrX5arN3kcBTiGEzgD6gCndQgwYwQHiGV3hzHp0X5935mLeuOPnMEfyB8/kDuDmM4A=</latexit>

label

KL(PY |X||Qc

Y |X)

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H(PY |X)

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:Constant : NOT Constant

≡

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6⌘

< l a t e x i t s h a 1 _ b a s e 6 4 = " 9 w V w z 9 I s U C / z A m C q Y q q J k m p

• R

= " > A A A C A X i c b V D L S s N A F J 3 4 r P U V d S O 4 C R b B V U l U G X R j c s K 9 g F N K J P p T T t M h N n J

• U

S 6 s Z f c e N C E b f + h T v / x m m a h b Y e u H A 4 5 9 6 5 c + Y M K q 6 3 5 b S 8 s r q 2 v r p Y 3 y 5 t b 2 z q 6 9 t 9 9 U I p U E G k Q w I d s h V s A

• h

4 a m m k E 7 k Y D j k E E r H N 5 M / d Y I p K K C 3 + t x A k G M + 5 x G l G B t p K 5 9 6 O d v Z C F L Y Z L 5 X G g f H l I 6 m n T t i l t 1 c z i L x C t I B R W

• d

+ v v y d I G g P X h G G l O p 6 b 6 C D D U l P C Y F L 2 U w U J J k P c h 4 6 h H M e g g i z f P n F O j N J z I i F N c e 3 k 6 u + J D M d K j e P Q d M Z Y D 9 S 8 N x X / 8 z q p j q 6 C j P I k 1 c D J b F G U M k c L Z x q H 6 M S i G Z j Q z C R 1 P z V I Q M s M d E m t L I J w Z s / e Z E z 6 r e e d W 7 u 6 j U r

• s

4 S u g I H a N T 5 K F L V E O 3 q I 4 a i K B H 9 I x e Z v 1 Z L 1 Y 7 9 b H r H X J K m Y O B 9 Y n z 8 E X p f k < / l a t e x i t >

H(QY |X, Qc

Y |X)

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SLIDE 13

13

Conversion to a Min-Max Game

• If 𝑞(𝑍) is a uniform distribution, the following are equivalent:
• Maximizing 𝐼&(𝑍|𝑌)

Proposition:

SLIDE 14

14

Conversion to a Min-Max Game

• If 𝑞(𝑍) is a uniform distribution, the following are equivalent:
• Maximizing 𝐼&(𝑍|𝑌)
• Minimizing 𝐽&(𝑌, 𝑍)

Proposition:

SLIDE 15

15

Conversion to a Min-Max Game

• If 𝑞(𝑍) is a uniform distribution, the following are equivalent:
• Maximizing 𝐼&(𝑍|𝑌)
• Minimizing 𝐽&(𝑌, 𝑍)
• Minimizing 𝐾𝑇𝐸(𝑅/|012, 𝑅/|013, ⋯ , 𝑅/|015)

Proposition:

SLIDE 16

16

Conversion to a Min-Max Game

• If 𝑞(𝑍) is a uniform distribution, the following are equivalent:
• Maximizing 𝐼&(𝑍|𝑌)
• Minimizing 𝐽&(𝑌, 𝑍)
• Minimizing 𝐾𝑇𝐸(𝑅/|012, 𝑅/|013, ⋯ , 𝑅/|015)

Proposition: A Min-Max game can be introduced with a twin classifier!

SLIDE 17

17

Twin Classifier (CT) Output label Generator (G) Noise ( )

z

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Real vs/Fake Discriminator (D) Input Label ( Cat ) Classifier (C) Output Label ( Cat )

Twin Auxiliary Classifier Conditional GAN(TAC-GAN)

Minimax game between G and D Auxiliary classifier C Minimax game between G and CT

SLIDE 18

18

Back to 1D Mixture of Gaussian

Our Method True Distribution AC-GAN

SLIDE 19

19

TAC-GAN (Ours) AC-GAN

Bird Spider Dog

Better diversity

SLIDE 20

Poster #87

Comparison with Projection GAN! Quantitative results!

Twin Auxiliary Classifiers GAN (TAC-GAN)

20