Convergence of Stochastic Gradient Langevin Dynamics in the Lazy Training Regime

• URL: http://arxiv.org/abs/2510.21245v1
• Date: Fri, 24 Oct 2025 08:28:53 GMT
• Title: Convergence of Stochastic Gradient Langevin Dynamics in the Lazy Training Regime
• Authors: Noah Oberweis, Semih Cayci,
• Abstract summary: Continuoustime models provide insights into the training dynamics of optimization algorithms in deep learning.<n>We establish a non-asymptotic convergence analysis of gradient Langevin dynamics (SGLD)<n>We show that, under regularity conditions on the Hessian of the loss function, SGLD with multiplicative and state-dependent noise yields a non-degenerate kernel throughout the training process with high probability.
• Score: 4.297070083645049
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Continuous-time models provide important insights into the training dynamics of optimization algorithms in deep learning. In this work, we establish a non-asymptotic convergence analysis of stochastic gradient Langevin dynamics (SGLD), which is an It\^o stochastic differential equation (SDE) approximation of stochastic gradient descent in continuous time, in the lazy training regime. We show that, under regularity conditions on the Hessian of the loss function, SGLD with multiplicative and state-dependent noise (i) yields a non-degenerate kernel throughout the training process with high probability, and (ii) achieves exponential convergence to the empirical risk minimizer in expectation, and we establish finite-time and finite-width bounds on the optimality gap. We corroborate our theoretical findings with numerical examples in the regression setting.

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