Implicit regularization via soft ascent-descent

• URL: http://arxiv.org/abs/2310.10006v1
• Date: Mon, 16 Oct 2023 02:02:56 GMT
• Title: Implicit regularization via soft ascent-descent
• Authors: Matthew J. Holland and Kosuke Nakatani
• Abstract summary: We show how to achieve better off-sample generalization with minimal trial-and-error. We propose a softened, pointwise mechanism called SoftAD that downweights points on the borderline, limits the effects of outliers, and retains the ascent-descent effect. Our empirical tests range from simple binary classification on the plane to image classification using neural networks with millions of parameters.
• Score: 7.335712499936906
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: As models grow larger and more complex, achieving better off-sample generalization with minimal trial-and-error is critical to the reliability and economy of machine learning workflows. As a proxy for the well-studied heuristic of seeking "flat" local minima, gradient regularization is a natural avenue, and first-order approximations such as Flooding and sharpness-aware minimization (SAM) have received significant attention, but their performance depends critically on hyperparameters (flood threshold and neighborhood radius, respectively) that are non-trivial to specify in advance. In order to develop a procedure which is more resilient to misspecified hyperparameters, with the hard-threshold "ascent-descent" switching device used in Flooding as motivation, we propose a softened, pointwise mechanism called SoftAD that downweights points on the borderline, limits the effects of outliers, and retains the ascent-descent effect. We contrast formal stationarity guarantees with those for Flooding, and empirically demonstrate how SoftAD can realize classification accuracy competitive with SAM and Flooding while maintaining a much smaller loss generalization gap and model norm. Our empirical tests range from simple binary classification on the plane to image classification using neural networks with millions of parameters; the key trends are observed across all datasets and models studied, and suggest a potential new approach to implicit regularization.

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