Asymptotics of Wide Networks from Feynman Diagrams

TL;DR

This paper introduces a Feynman diagram-based method to analyze the asymptotic behavior of wide neural networks, providing new theoretical insights and empirical validations of training dynamics beyond the large width limit.

Contribution

It adapts Feynman diagrams for analyzing wide networks, deriving higher-order terms and improving bounds on training dynamics during stochastic gradient descent.

Findings

Improved bounds on training dynamics of wide networks.

Closed-form expressions for higher-order terms.

Empirical validation of theoretical predictions.

Abstract

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.