# Implicit Manifold Learning on Generative Adversarial Networks

This paper raises an implicit manifold learning perspective in Generative Adversarial Networks (GANs), by studying how the support of the learned distribution, modelled as a submanifold $\mathcal{M}_{\theta}$, perfectly match with $\mathcal{M}_{r}$, the support of the real data distribution. We show that optimizing Jensen-Shannon divergence forces $\mathcal{M}_{\theta}$ to perfectly match with $\mathcal{M}_{r}$, while optimizing Wasserstein distance does not. On the other hand, by comparing the gradients of the Jensen-Shannon divergence and the Wasserstein distances ($W_1$ and $W_2^2$) in their primal forms, we conjecture that Wasserstein $W_2^2$ may enjoy desirable properties such as reduced mode collapse. It is therefore interesting to design new distances that inherit the best from both distances.

@Conference{LuiIML,

Title = {Implicit Manifold Learning on Generative Adversarial Networks},

Author = {Kry Yik Chau Lui and Yanshuai Cao and Maxime Gazeau and Kelvin Shuangjian Zhang},

Year = {2017},

Abstract = {This paper raises an implicit manifold learning perspective in Generative Adversarial Networks (GANs), by studying how the support of the learned distribution, modelled as a submanifold $\mathcal{M}_{\theta}$, perfectly match with $\mathcal{M}_{r}$, the support of the real data distribution. We show that optimizing Jensen-Shannon divergence forces $\mathcal{M}_{\theta}$ to perfectly match with $\mathcal{M}_{r}$, while optimizing Wasserstein distance does not. On the other hand, by comparing the gradients of the Jensen-Shannon divergence and the Wasserstein distances ($W_1$ and $W_2^2$) in their primal forms, we conjecture that Wasserstein $W_2^2$ may enjoy desirable properties such as reduced mode collapse. It is therefore interesting to design new distances that inherit the best from both distances.},

Journal = {International Conference on Machine Learning (Workshop on Implicit Models)},

Url = {https://arxiv.org/abs/1710.11260}

}