On implicit regularization: Morse functions and applications to matrix factorization

Mohamed Ali Belabbas

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arXiv · 2001.04264

On implicit regularization: Morse functions and applications to matrix factorization

Mohamed Ali Belabbas

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Abstract

In this paper, we revisit implicit regularization from the ground up using notions from dynamical systems and invariant subspaces of Morse functions. The key contributions are a new criterion for implicit regularization---a leading contender to explain the generalization power of deep models such as neural networks---and a general blueprint to study it. We apply these techniques to settle a conjecture on implicit regularization in matrix factorization.

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Mohamed Ali Belabbas. 2020-01-13. On implicit regularization: Morse functions and applications to matrix factorization. https://arxiv.org/abs/2001.04264

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