On Measuring Excess Capacity in Neural Networks
This work addresses the issue of understanding and quantifying excess capacity in neural networks for researchers and practitioners, offering insights into compressibility via weight norms, though it is incremental as it builds on prior complexity bounds.
The paper tackles the problem of measuring excess capacity in deep neural networks for supervised classification, finding that there is substantial excess capacity per task and that capacity can be maintained at similar levels across tasks, with results based on empirical Rademacher complexity bounds and experiments on benchmark datasets.
We study the excess capacity of deep networks in the context of supervised classification. That is, given a capacity measure of the underlying hypothesis class - in our case, empirical Rademacher complexity - to what extent can we (a priori) constrain this class while retaining an empirical error on a par with the unconstrained regime? To assess excess capacity in modern architectures (such as residual networks), we extend and unify prior Rademacher complexity bounds to accommodate function composition and addition, as well as the structure of convolutions. The capacity-driving terms in our bounds are the Lipschitz constants of the layers and an (2, 1) group norm distance to the initializations of the convolution weights. Experiments on benchmark datasets of varying task difficulty indicate that (1) there is a substantial amount of excess capacity per task, and (2) capacity can be kept at a surprisingly similar level across tasks. Overall, this suggests a notion of compressibility with respect to weight norms, complementary to classic compression via weight pruning. Source code is available at https://github.com/rkwitt/excess_capacity.