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arXiv · 2402.07626

Stochastic Gradient Flow Dynamics of Test Risk and its Exact Solution for Weak Features

Rodrigo Veiga·Anastasia Remizova·Nicolas Macris
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Abstract

We investigate the test risk of continuous-time stochastic gradient flow dynamics in learning theory. Using a path integral formulation we provide, in the regime of a small learning rate, a general formula for computing the difference between test risk curves of pure gradient and stochastic gradient flows. We apply the general theory to a simple model of weak features, which displays the double descent phenomenon, and explicitly compute the corrections brought about by the added stochastic term in the dynamics, as a function of time and model parameters. The analytical results are compared to simulations of discrete-time stochastic gradient descent and show good agreement.

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BibTeXRIS

Rodrigo Veiga, Anastasia Remizova, Nicolas Macris. 2024-02-12. Stochastic Gradient Flow Dynamics of Test Risk and its Exact Solution for Weak Features. https://arxiv.org/abs/2402.07626

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