Exciting new work on the generalization bounds for neural networks (NN) given by Neyshabur et al. , Bartlett et al. depend on two parameter-depenedent quantities: the Lipschitz constant upper-bound and the stable rank (a softer version of the rank operator). This leads to an interesting question of whether controlling these quantities might improve the generalization behaviour of NNs. To this end, we propose stable rank normalization (SRN), a novel, optimal, and computationally efficient weight-normalization scheme which minimizes the stable rank of a linear operator. Surprisingly we find that SRN, inspite of being non-convex problem, can be shown to have a unique optimal solution. Moreover, we show that SRN allows control of the data-dependent empirical Lipschitz constant, which in contrast to the Lipschitz upper-bound, reflects the true behaviour of a model on a given dataset. We provide thorough analyses to show that SRN, when applied to the linear layers of a NN for classification, provides striking improvements-11.3% on the generalization gap compared to the standard NN along with significant reduction in memorization. When applied to the discriminator of GANs (called SRN-GAN) it improves Inception, FID, and Neural divergence scores on the CIFAR 10/100 and CelebA datasets, while learning mappings with low empirical Lipschitz constants.

本篇论文提出一种新的权重规范化方法，即稳定秩规范化（SRN），可用于神经网络分类器和GAN中的分类器（SRN-GAN）。在实验中显示，使用SRN可以显著提高分类器和GAN生成结果的性能，同时减少记忆。

神经网络和GAN中的稳定排名归一化以提高泛化能力