Ultra-fast feature learning for the training of two-layer neural networks in the two-timescale regime

• URL: http://arxiv.org/abs/2504.18208v2
• Date: Mon, 21 Jul 2025 14:02:53 GMT
• Title: Ultra-fast feature learning for the training of two-layer neural networks in the two-timescale regime
• Authors: Raphaël Barboni, Gabriel Peyré, François-Xavier Vialard,
• Abstract summary: We study the convergence of methods for the training of mean-field-hidden-layer neural networks.<n>We show that a strategy enables provable convergence rates for the sampling of a teacher feature distribution.
• Score: 26.47265060394168
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the convergence of gradient methods for the training of mean-field single-hidden-layer neural networks with square loss. For this high-dimensional and non-convex optimization problem, most known convergence results are either qualitative or rely on a neural tangent kernel analysis where nonlinear representations of the data are fixed. Using that this problem belongs to the class of separable nonlinear least squares problems, we consider here a Variable Projection (VarPro) or two-timescale learning algorithm, thereby eliminating the linear variables and reducing the learning problem to the training of nonlinear features. In a teacher-student scenario, we show such a strategy enables provable convergence rates for the sampling of a teacher feature distribution. Precisely, in the limit where the regularization strength vanishes, we show that the dynamic of the feature distribution corresponds to a weighted ultra-fast diffusion equation. Recent results on the asymptotic behavior of such PDEs then give quantitative guarantees for the convergence of the learned feature distribution.

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