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arXiv · 2410.22069

Flavors of Margin: Implicit Bias of Steepest Descent in Homogeneous Neural Networks

Nikolaos Tsilivis·Eitan Gronich·Julia Kempe·Gal Vardi
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Abstract

We study the implicit bias of the general family of steepest descent algorithms with infinitesimal learning rate in deep homogeneous neural networks. We show that: (a) an algorithm-dependent geometric margin starts increasing once the networks reach perfect training accuracy, and (b) any limit point of the training trajectory corresponds to a KKT point of the corresponding margin-maximization problem. We experimentally zoom into the trajectories of neural networks optimized with various steepest descent algorithms, highlighting connections to the implicit bias of popular adaptive methods (Adam and Shampoo).

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BibTeXRIS

Nikolaos Tsilivis, Eitan Gronich, Julia Kempe, Gal Vardi. 2024-10-29. Flavors of Margin: Implicit Bias of Steepest Descent in Homogeneous Neural Networks. https://arxiv.org/abs/2410.22069

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