  Generative adversarial networks (GANs) provide state-of-the-art results in
image generation. However, despite being so powerful, they still remain very
challenging to train. This is in particular caused by their highly non-convex
optimization space leading to a number of instabilities. Among them, mode
collapse stands out as one of the most daunting ones. This undesirable event
occurs when the model can only fit a few modes of the data distribution, while
ignoring the majority of them. In this work, we combat mode collapse using
second-order gradient information. To do so, we analyse the loss surface
through its Hessian eigenvalues, and show that mode collapse is related to the
convergence towards sharp minima. In particular, we observe how the eigenvalues
of the $G$ are directly correlated with the occurrence of mode collapse.
Finally, motivated by these findings, we design a new optimization algorithm
called nudged-Adam (NuGAN) that uses spectral information to overcome mode
collapse, leading to empirically more stable convergence properties.
