Towards Principled Methods for Training Generative Adversarial Networks. Martin Arjovsky & Léon Bottou

Transcription

1 Towards Principled Methods for Training Generative Adversarial Networks Martin Arjovsky & Léon Bottou

2 Unsupervised learning - We have samples from an unknown distribution

3 Unsupervised learning - We have samples from an unknown distribution - We want to approximate it by a parametric distribution that s close to in some sense.

4 Unsupervised learning - We have samples from an unknown distribution - We want to approximate it by a parametric distribution that s close to in some sense. - Close how?

5 Maximum Likelihood - Maximum likelihood:

6 Maximum Likelihood - Maximum likelihood: - Assumptions: continuous with full support.

7 Maximum Likelihood - Maximum likelihood: - Assumptions: continuous with full support. - Problems: restricted capacity distributes mass. Modeling low dimensional distributions is impossible.

8 Kullback-Leibler Divergence - Closeness measured by KL divergence (equivalent to ML):

9 Kullback-Leibler Divergence - Closeness measured by KL divergence (equivalent to ML): - When integrand goes to infinity: high cost for mode dropping.

10 Kullback-Leibler Divergence - Closeness measured by KL divergence (equivalent to ML): - When integrand goes to infinity: high cost for mode dropping. - When integrand goes to 0: low cost for fake looking samples.

11 Generative Adversarial Networks (Goodfellow et al.) - Let be the dist of for some simple (e.g. Gaussian) r.v Z, passed through a complex function.

12 Generative Adversarial Networks (Goodfellow et al.) - Let be the dist of for some simple (e.g. Gaussian) r.v Z, passed through a complex function. - Discriminator maximizes and generator minimizes

13 Generative Adversarial Networks (Goodfellow et al.) - Let be the dist of for some simple (e.g. Gaussian) r.v Z, passed through a complex function. - Discriminator maximizes and generator minimizes

14 JSD seems maxed out..

15 Generative Adversarial Networks - Under optimal discriminator, minimizes - Problems: vanishing gradients very quickly when D s accuracy is high.

16 Discriminator is pretty good...

17 Vanishing gradients, original cost

18 Alternate update - Alternate update that has less vanishing gradients

19 Alternate update - Alternate update that has less vanishing gradients - Under optimality optimizes

20 Alternate update - Alternate update that has less vanishing gradients - Under optimality optimizes - Problems: JSD with the wrong sign, reverse KL has high mode dropping. Still unstable when D is good.

21 High variance updates

22 Problems of GANs (and divergences) - When and lie on low dimensional manifolds, there s always a perfect discriminator, that provides no usable gradients.

23 Manifold picture - Real - Generated

24 Problems of GANs (and divergences) - When and lie on low dimensional manifolds, there s always a perfect discriminator, that provides no usable gradients.

25 Problems of GANs (and divergences) - When and lie on low dimensional manifolds, there s always a perfect discriminator, that provides no usable gradients.

26 Problems of GANs (and divergences) - When and lie on low dimensional manifolds, there s always a perfect discriminator, that provides no usable gradients. - Under the same assumptions

27 A first step to a solution - Distributions are essentially disjoint

28 A first step to a solution - Distributions are essentially disjoint - Add noise during training to make them overlap!

29 A first step to a solution - Distributions are essentially disjoint - Add noise during training to make them overlap! - Matching noisy distributions amounts to matching the underlying ones.

30 Manifold picture - Real - Generated

31 Manifold picture with noise - Real - Generated

32 A first step to a solution We move our samples towards point in the data manifold, weighted by their probability and distance to our samples.

33 Theoretical guarantee

34 Theoretical guarantee - Wasserstein is well defined in the manifold setting.

35 Theoretical guarantee - Wasserstein is well defined in the manifold setting. - The noise method optimizes an upper bound of it.

36 Theoretical guarantee - Wasserstein is well defined in the manifold setting. - The noise method optimizes an upper bound of it. - We can reduce the first summand by annealing the noise, the second one by optimizing with noise.

37 Loads of work done since then! - Now we have more understanding of the relationship between Wasserstein, JSD and the rest: Weak vs strong.

38 Loads of work done since then! - Now we have more understanding of the relationship between Wasserstein, JSD and the rest: Weak vs strong. - Optimizing an approximation of Wasserstein directly is doable. (Arjovsky, Chintala & Bottou, 2017)

39 Loads of work done since then! - Now we have more understanding of the relationship between Wasserstein, JSD and the rest: Weak vs strong. - Optimizing an approximation of Wasserstein directly is doable. (Arjovsky, Chintala & Bottou, 2017) - Different ways to do this. (Gulrajani et al. 2017)

40 Loads of work done since then! - Now we have more understanding of the relationship between Wasserstein, JSD and the rest: Weak vs strong. - Optimizing an approximation of Wasserstein directly is doable. (Arjovsky, Chintala & Bottou, 2017) - Different ways to do this. (Gulrajani et al. 2017) - Time to scale up!

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