A Theoretical Explanation of Activation Sparsity through Flat Minima and Adversarial Robustness
This addresses the problem of high computation costs in deep learning for practitioners by theoretically explaining and improving activation sparsity, though it builds incrementally on prior empirical observations.
The paper provides a theoretical explanation for activation sparsity in neural networks by linking it to gradient sparsity and adversarial robustness through flat minima, applicable to standardly trained models like LayerNorm-ed MLPs and Transformers. Experiments on ImageNet-1k and C4 show 50% sparsity improvements with proposed plug-and-play modules, enabling potential computation cost reductions.
A recent empirical observation (Li et al., 2022b) of activation sparsity in MLP blocks offers an opportunity to drastically reduce computation costs for free. Although having attributed it to training dynamics, existing theoretical explanations of activation sparsity are restricted to shallow networks, small training steps and special training, despite its emergence in deep models standardly trained for a large number of steps. To fill these gaps, we propose the notion of gradient sparsity as one source of activation sparsity and a theoretical explanation based on it that sees sparsity a necessary step to adversarial robustness w.r.t. hidden features and parameters, which is approximately the flatness of minima for well-learned models. The theory applies to standardly trained LayerNorm-ed MLPs, and further to Transformers or other architectures trained with weight noises. Eliminating other sources of flatness except for sparsity, we discover the phenomenon that the ratio between the largest and smallest non-zero singular values of weight matrices is small. When discussing the emergence of this spectral concentration, we use random matrix theory (RMT) as a powerful tool to analyze stochastic gradient noises. Validational experiments are conducted to verify our gradient-sparsity-based explanation. We propose two plug-and-play modules for both training and finetuning for sparsity. Experiments on ImageNet-1k and C4 demonstrate their 50% sparsity improvements, indicating further potential cost reduction in both training and inference.