Stochastic Modified Flows, Mean-Field Limits and Dynamics of Stochastic Gradient Descent

• URL: http://arxiv.org/abs/2302.07125v1
• Date: Tue, 14 Feb 2023 15:33:59 GMT
• Title: Stochastic Modified Flows, Mean-Field Limits and Dynamics of Stochastic Gradient Descent
• Authors: Benjamin Gess, Sebastian Kassing, Vitalii Konarovskyi
• Abstract summary: We propose new limiting dynamics for gradient descent in the small learning rate regime called modified flows. These SDEs are driven by a cylindrical Brownian motion and improve the so-called modified equations by having regular diffusion coefficients and by matching the multi-point statistics.
• Score: 1.2031796234206138
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows. These SDEs are driven by a cylindrical Brownian motion and improve the so-called stochastic modified equations by having regular diffusion coefficients and by matching the multi-point statistics. As a second contribution, we introduce distribution dependent stochastic modified flows which we prove to describe the fluctuating limiting dynamics of stochastic gradient descent in the small learning rate - infinite width scaling regime.

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