Rethinking Gauss-Newton for learning over-parameterized models

• URL: http://arxiv.org/abs/2302.02904v3
• Date: Tue, 12 Dec 2023 08:40:56 GMT
• Title: Rethinking Gauss-Newton for learning over-parameterized models
• Authors: Michael Arbel and Romain Menegaux and Pierre Wolinski
• Abstract summary: 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.
• Score: 14.780386419851956
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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