Rethinking Gauss-Newton for learning over-parameterized models

Michael Arbel, Romain Menegaux, Pierre Wolinski

Keywords: implicit bias, gauss newton

TL;DR: global convergence and generalization of gauss-newton methods for over-parameterized one-hidden layer networks

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.

Submission Number: 14789