Wasserstein Regularization for Generative and Discriminative Learning
Guido Montufar is an Assistant Professor of Mathematics and Statistics at the University of California, Los Angeles, USA, and Research Group Leader of the ERC project Deep Learning Theory at the Max Planck Institute for Mathematics in the Sciences, Germany. His research is on mathematical machine learning.
We propose regularization strategies for learning models that are robust to in-class variations of the input data. We use the Wasserstein-2 metric to capture semantically meaningful neighborhoods in the space of images. We define a Riemannian Wasserstein gradient penalty to be used in Wasserstein Generative Adversarial Networks, and derive an effective Tikhonov-type Wasserstein smoothness regularizer from an input-dependent data augmentation model. The regularizer is computed efficiently via convolutions with negligible computational cost. Experiments demonstrate improved robust generalization.