Recent work 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. We find that this Jacobian generally becomes ill-conditioned at the beginning of training. Moreover, we find that the average (across the latent space) 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. We then 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 score for nearly all datasets on which we tested it. It also greatly reduces inter-run variance of the aforementioned scores, addressing (at least partially) one of the main criticisms of GANs.

In this paper we introduce new methods for the improved training of generative adversarial networks (GANs) for image synthesis. We construct a variant of GANs employing label conditioning that results in $128\times 128$ resolution image samples exhibiting global coherence. We expand on previous work for image quality assessment to provide two new analyses for assessing the discriminability and diversity of samples from class-conditional image synthesis models. These analyses demonstrate that high resolution samples provide class information not present in low resolution samples. Across 1000 ImageNet classes, $128\times 128$ samples are more than twice as discriminable as artificially resized $32\times 32$ samples. In addition, 84.7\% of the classes have samples exhibiting diversity comparable to real ImageNet data.