Rethinking Gauss-Newton for learning over-parameterized models

TL;DR

This paper analyzes the convergence and implicit bias of Gauss-Newton optimization in over-parameterized neural networks, revealing a trade-off between convergence speed and generalization ability.

Contribution

It provides the first global convergence analysis of Gauss-Newton in the mean-field regime and explores its implicit bias through empirical studies.

Findings

GN converges faster than gradient descent due to better conditioning.

Under certain conditions, GN finds solutions with good generalization.

A trade-off exists between convergence speed and generalization in GN.

Abstract

This work studies the global convergence and implicit bias of Gauss Newton's (GN) when optimizing over-parameterized one-hidden layer networks in the mean-field regime. We first establish a global convergence result for GN in the continuous-time limit exhibiting a faster convergence rate compared to GD due to improved conditioning. We then perform an empirical study on a synthetic regression task to investigate the implicit bias of GN's method. While GN is consistently faster than GD in finding a global optimum, the learned model generalizes well on test data when starting from random initial weights with a small variance and using a small step size to slow down convergence. Specifically, our study shows that such a setting results in a hidden learning phenomenon, where the dynamics are able to recover features with good generalization properties despite the model having sub-optimal training and test performances due to an under-optimized linear layer. This study exhibits a trade-off between the convergence speed of GN and the generalization ability of the learned solution.