2022/06/09 by Chengli Tan, Jiangshe Zhang, Tan, Chengli +4
Computer Science · Physics and Astronomy · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Applications #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2206.04359
openalex publication_date 2022/06/09 · openalex created_date 2023/02/11 · openalex updated_date 2026/07/28
One of the fundamental challenges in the deep learning community is to theoretically understand how well a deep neural network generalizes to unseen data. However, current approaches often yield generalization bounds that are either too loose to be informative of the true generalization error or only valid to the compressed nets. In this study, we present a simple yet non-vacuous generalization bound from the optimization perspective. We achieve this goal by leveraging that the hypothesis set accessed by stochastic gradient algorithms is essentially fractal-like and thus can derive a tighter bound over the algorithm-dependent Rademacher complexity. The main argument rests on modeling the discrete-time recursion process via a continuous-time stochastic differential equation driven by fractional Brownian motion. Numerical studies demonstrate that our approach is able to yield plausible generalization guarantees for modern neural networks such as ResNet and Vision Transformer, even when they are trained on a large-scale dataset (e.g. ImageNet-1K).