Manifold adversarial training for supervised and semi-supervised learning.

We propose a new regularization method for deep learning based on the manifold adversarial training (MAT). Unlike previous regularization and adversarial training methods, MAT further considers the local manifold of latent representations. Specifically, MAT manages to build an adversarial framework based on how the worst perturbation could affect the statistical manifold in the latent space rather than the output space. Particularly, a latent feature space with the Gaussian Mixture Model (GMM) is first derived in a deep neural network. We then define the smoothness by the largest variation of Gaussian mixtures when a local perturbation is given around the input data point. On one hand, the perturbations are added in the way that would rough the statistical manifold of the latent space the worst. On the other hand, the model is trained to promote the manifold smoothness the most in the latent space. Importantly, since the latent space is more informative than the output space, the proposed MAT can learn a more robust and compact data representation, leading to further performance improvement. The proposed MAT is important in that it can be considered as a superset of one recently-proposed discriminative feature learning approach called center loss. We conduct a series of experiments in both supervised and semi-supervised learning on four benchmark data sets, showing that the proposed MAT can achieve remarkable performance, much better than those of the state-of-the-art approaches. In addition, we present a series of visualization which could generate further understanding or explanation on adversarial examples.