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

• URL: http://arxiv.org/abs/2402.07626v2
• Date: Mon, 10 Jun 2024 10:25:14 GMT
• Title: Stochastic Gradient Flow Dynamics of Test Risk and its Exact Solution for Weak Features
• Authors: Rodrigo Veiga, Anastasia Remizova, Nicolas Macris,
• Abstract summary: We provide a formula for computing the difference between test risk curves of pure gradient and gradient flows. We explicitly compute the corrections brought about by the added term in the dynamics. The analytical results are compared to simulations of discrete-time gradient descent and show good agreement.
• Score: 8.645858565518155
• License: http://creativecommons.org/licenses/by/4.0/
• 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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