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Generative adversarial networks (GANs) are notoriously difficult to train andthe reasons underlying their (non-)convergence behaviors are still notcompletely understood. By first considering a simple yet representative GANexample, we mathematically analyze its local convergence behavior in anon-asymptotic way. Furthermore, the analysis is extended to general GANs undercertain assumptions. We find that in order to ensure a good convergence rate,two factors of the Jacobian in the GAN training dynamics should besimultaneously avoided, which are (i) the Phase Factor, i.e., the Jacobian hascomplex eigenvalues with a large imaginary-to-real ratio, and (ii) theConditioning Factor, i.e., the Jacobian is ill-conditioned. Previous methods ofregularizing the Jacobian can only alleviate one of these two factors, whilemaking the other more severe. Thus we propose a new JAcobian REgularization(JARE) for GANs, which simultaneously addresses both factors by construction.Finally, we conduct experiments that confirm our theoretical analysis anddemonstrate the advantages of JARE over previous methods in stabilizing GANs.

Towards a Better Understanding and Regularization of GAN Training Dynamics