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arXiv · 2307.15744

How regularization affects the geometry of loss functions

Nathaniel Bottman·Y. Cooper·Antonio Lerario
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Abstract

What neural networks learn depends fundamentally on the geometry of the underlying loss function. We study how different regularizers affect the geometry of this function. One of the most basic geometric properties of a smooth function is whether it is Morse or not. For nonlinear deep neural networks, the unregularized loss function $L$ is typically not Morse. We consider several different regularizers, including weight decay, and study for which regularizers the regularized function $L_\epsilon$ becomes Morse.

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Nathaniel Bottman, Y. Cooper, Antonio Lerario. 2023-07-28. How regularization affects the geometry of loss functions. https://arxiv.org/abs/2307.15744

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