Adversarially Learned Inference

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1 Institut des algorithmes d apprentissage de Montréal Adversarially Learned Inference Aaron Courville CIFAR Fellow Université de Montréal Joint work with: Vincent Dumoulin, Ishmael Belghazi, Olivier Mastropietro, Ben Poole, Alex Lamb, Martin Arjovsky Université de Sherbrooke, Feb. 2017

2 Two papers, one model ALI: Vincent Dumoulin, Ishmael Belghazi, Olivier Mastropietro Ben Poole, Alex Lamb, Martin Arjovsky (2016) ADVERSARIALLY LEARNED INFERENCE, arxiv: BiGAN: Donahue, Krähenbühl and Darrell (2016), ADVERSARIAL FEATURE LEARNING, arxiv:

3 Deep directed generative models Latent variables inference z z 2 x 2 z G G? x x 3 z 1 x 1 x Observed variables

4 Latent variable-based generative modeling VAE-based techniques Trained to maximize a variational lower bound on log-likelihood of x. Introduce approximate posterior q(z x) (encoder) and train it together with the generative model (decoder) tends to produce blurred samples.

5 vanilla VAE: blurry samples Labelled Faces in the Wild (LFW) ImageNet (small)

6 PixelVAE: not so bad! LSUN bedroom scenes ImageNet (small)

7 Latent variable-based generative modeling VAE-based techniques GAN-based techniques Trained to maximize a variational lower bound on log-likelihood of x. Discriminative network is trained to distinguish between the data and generative network samples. Introduce approximate posterior q(z x) (encoder) and train it together with the generative model (decoder) Generator is trained to produce samples that fool the generator. tends to produce blurred samples. Sample quality exceeds that of VAE. Lacks an efficient mechanism for inference.

8 GANs side-steps need for inference z ~ p(z) x ~ q(x) Data D(x) Discriminator Generator G(z) x ~ p(x z)

9 GAN samples MNIST CIFAR-10

10 memorization with SGD and a small learning rate. DCGAN samples (Radford, Metz and Chintala; 2016) LSUN bedroom scenes

11 Under review as a conference paper at ICLR 2016 DCGAN samples Z-space interpolations LSUN bedroom scenes (Radford, Metz and Chintala; 2016)

12 Cartoon of the Image manifold x2 x1

13 Image manifold: VAE - vs - GAN x2 x2 VAE x1 GAN x1

14 Deep directed generative models GANs have no inference mechanism Latent variables z z 2 x 2 z G G? x x 3 z 1 x 1 x Observed variables

15 Adversarially learned inference: Main idea Cast the learning of both an inference model (encoder) and a generative model (decoder) in a GAN-like adversarial framework. Discriminator is trained to discriminate between joint samples (x, z) from: - Encoder distribution q(x, z) = q(x) q(z x), or Data distribution Prior distribution - Decoder distribution p(x, z) = p(z) p(x z). Generator learns conditionals q(z x) and p(x z) to fool the discriminator.

16 ALI: model diagram z ~ q(z x) z ~ p(z) Gz(x) Encoder D(x, z) Decoder Gx(z) x ~ q(x) x ~ p(x z)

17 ALI: objective function min G max V (D, G) =E q(x)[log(d(x,g z (x)))] + E [log(1 D(G p(z) x (z), z))] D ZZ = q(x)q(z x) log(d(x, z))dxdz ZZ + p(z)p(x z) log(1 D(x, z))dxdz

18 ALI: implementation details Alternative generator objective function: maximize V 0 (D, G) =E q(x) [log(1 D(x,G z (x)))] + E p(z) [log(d(g x (z), z))]

19 Theoretical properties In analogy with GAN, under an ideal discriminator, the generator minimizes the Jensen-Shannon divergence between p(x, z) and q(x, z).

20 BiGAN: Encoder & Decoder are Inverses Donahue, Krähenbühl and Darrell (2016), ADVERSARIAL FEATURE LEARNING: - In the case of a deterministic encoder & decoder, in order to fool an ideal discriminator, the encoder and decoder must invert each other.

21 BiGAN: Encoder & Decoder are Inverses Donahue, Krähenbühl and Darrell (2016) Intuition: Discriminator input pair (x, z) must satisfy at least one of the following two properties: (a) (b) x supp (p data (x)) G z (x) =z z supp (p prior (z)) G x (z) =x If only one of these properties is satisfied, a perfect discriminator can infer the source of (x, z) with certainty. Therefore, in order to fool an ideal discriminator, the encoder G z (x) and decoder G x (z) (x, z) must satisfy both (a) and (b) at

22 Toy Example Learning the Identity function: Encoder: X ~ N(0,1) Decoder: Z ~ N(0,1) Zihang Dai

23 SVHN Samples Data Recon Reconstructions

24 CIFAR-10 Samples Data Recon Reconstructions

25 Recon Samples Data CelebA Reconstructions

26 Recon Samples Data Tiny ImageNet Reconstructions

27 Interpolating in latent space

28 Interpolating in latent space Tom White CelebA - 128x128 Smile vector:

29 Conditional generation min G max D V (D, G) =E q(x) p(y)[log(d(x,g z (x, y), y))]+e p(z) p(y) [log(1 D(G x (z, y), z, y))] ALI can be extended to incorporate feature labels to perform conditional generation - Encoder: (x,y) -> z - Decoder (z,y) -> x - Discriminator (x,y,z) -> 0/1

30 Conditional generation: CelebA black hair blond, bangs blond, balding open smile, black, wavy hair glasses

Semi-supervised experiments Table 1: SVHN test set missclassification rate Model Misclassification rate. VAE (M1 + M2) (Kingma et al., 2014) 36.02 SWWAE with dropout (Zhao et al., 2015) 23.

50 ALI (ours, no feature matching) 7.42 ± 0.65 Table 2: CIFAR10 test set missclassification rate for semi-supervised learning using different numbers of trained labeled examples.

31 Semi-supervised experiments Table 1: SVHN test set missclassification rate Model Misclassification rate. VAE (M1 + M2) (Kingma et al., 2014) SWWAE with dropout (Zhao et al., 2015) DCGAN + L2-SVM (Radford et al., 2015) SDGM (Maaløe et al., 2016) GAN (feature matching) (Salimans et al., 2016) 8.11 ± 1.3 ALI (ours, L2-SVM) ± 0.50 ALI (ours, no feature matching) 7.42 ± 0.65 Table 2: CIFAR10 test set missclassification rate for semi-supervised learning using different numbers of trained labeled examples. For ALI, error bars correspond to 3 times the standard deviation. Number of labeled examples Model Misclassification rate Ladder network (Rasmus et al., 2015) CatGAN (Springenberg, 2015) GAN (feature matching) (Salimans et al., 2016) ± ± ± ± 1.82 ALI (ours, no feature matching) ± ± ± ± 1.49

32 Alternative Inference Alternative inference mechanisms: Mechanisms (a) ALI (ours) (b) Learn encoder via z reconstruction (c) Post hoc encoder learning (ALI-style) (d) Variational Autoencoder (VAE)

33 Hierarchical ALI: model diagram z2 ~ q(z2 z1) z2 ~ p(z2) z1 ~ q(z1 x) D(x, z1, z2) Gz1(x) Encoder Gz2(z1) Gz1(z2) z1 ~ p(z1 z2) Decoder Gx(z1) x ~ q(x) x ~ p(x z1)

34 Hierarchical ALI: model diagram Input: x~p(x) Sample: x~p(x z 1 ) Decoder D(z 2 ;ψ) z 1 ~p(z 1 z 2 ) z 1 ~q(z 1 x) Encoder E(x; φ) Code: z 2 ~q(z 2 x) Prior: z 2 ~p(z) Discriminator D(x, z 1, z 2 ; θ)

35 Hierarchical ALI: SVHN Model samples Data Recon Data Recon Reconstructions given z1, z2 Reconstructions given z2

36 Reconstructions given z1, z2 Recon Data Recon Model samples Data Hierarchical ALI: CelebA Reconstructions given z2

37 Hierarchical ALI: CIFAR-10 Model samples Data Recon Data Recon Reconstructions given z1, z2 Reconstructions given z2

38 Recon Reconstructions given z1, z2 Data Recon Data Hierarchical ALI: ImageNet-128X128 Reconstructions given z2

39 Hierarchical ALI: ImageNet-128X128 Model samples

40 Acknowledgements Co-authors Vincent Dumoulin Ishmael Belghazi Ben Poole Alex Lamb HALI contributors ALI Animation Martin Arjovsky Olivier Mastropietro Sai Rajeshwar Negar Rostamzadeh Zihang Dai

Bidirectional GAN. Adversarially Learned Inference (ICLR 2017) Adversarial Feature Learning (ICLR 2017)

Bidirectional GAN. Adversarially Learned Inference (ICLR 2017) Adversarial Feature Learning (ICLR 2017) Bidirectional GAN Adversarially Learned Inference (ICLR 2017) V. Dumoulin 1, I. Belghazi 1, B. Poole 2, O. Mastropietro 1, A. Lamb 1, M. Arjovsky 3 and A. Courville 1 1 Universite de Montreal & 2 Stanford