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arXiv · 2502.05074

Two-Point Deterministic Equivalence for Stochastic Gradient Dynamics in Linear Models

Alexander Atanasov·Blake Bordelon·Jacob A. Zavatone-Veth·Courtney Paquette·Cengiz Pehlevan
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Abstract

We derive a novel deterministic equivalence for the two-point function of a random matrix resolvent. Using this result, we give a unified derivation of the performance of a wide variety of high-dimensional linear models trained with stochastic gradient descent. This includes high-dimensional linear regression, kernel regression, and linear random feature models. Our results include previously known asymptotics as well as novel ones.

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Alexander Atanasov, Blake Bordelon, Jacob A. Zavatone-Veth, Courtney Paquette, Cengiz Pehlevan. 2025-02-07. Two-Point Deterministic Equivalence for Stochastic Gradient Dynamics in Linear Models. https://doi.org/10.4310/atmp.260412235902

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