Asymptotics of Wide Networks from Feynman Diagrams
This work addresses the theoretical understanding of wide network training for researchers in machine learning, offering incremental improvements through a novel analytical framework.
The authors tackled the problem of analyzing the asymptotic behavior of wide neural networks by adapting Feynman diagrams, a tool from physics, to derive improved bounds and new results on training dynamics under stochastic gradient descent, including closed-form expressions for higher-order terms that were empirically validated.
Understanding the asymptotic behavior of wide networks is of considerable interest. In this work, we present a general method for analyzing this large width behavior. The method is an adaptation of Feynman diagrams, a standard tool for computing multivariate Gaussian integrals. We apply our method to study training dynamics, improving existing bounds and deriving new results on wide network evolution during stochastic gradient descent. Going beyond the strict large width limit, we present closed-form expressions for higher-order terms governing wide network training, and test these predictions empirically.