  Recent work (Pennington et al, 2017) suggests that controlling the entire
distribution of Jacobian singular values is an important design consideration
in deep learning. Motivated by this, we study the distribution of singular
values of the Jacobian of the generator in Generative Adversarial Networks
(GANs). We find that this Jacobian generally becomes ill-conditioned at the
beginning of training. Moreover, we find that the average (with z from p(z))
conditioning of the generator is highly predictive of two other ad-hoc metrics
for measuring the 'quality' of trained GANs: the Inception Score and the
Frechet Inception Distance (FID). We test the hypothesis that this relationship
is causal by proposing a 'regularization' technique (called Jacobian Clamping)
that softly penalizes the condition number of the generator Jacobian. Jacobian
Clamping improves the mean Inception Score and the mean FID for GANs trained on
several datasets. It also greatly reduces inter-run variance of the
aforementioned scores, addressing (at least partially) one of the main
criticisms of GANs.
