Quantitative convergence of trained single layer neural networks to Gaussian processes

• URL: http://arxiv.org/abs/2509.24544v2
• Date: Thu, 23 Oct 2025 10:27:48 GMT
• Title: Quantitative convergence of trained single layer neural networks to Gaussian processes
• Authors: Eloy Mosig, Andrea Agazzi, Dario Trevisan,
• Abstract summary: We study the quantitative convergence of shallow neural networks trained via gradient descent to their associated Gaussian processes in the infinite-width limit.<n>We provide explicit upper bounds on the quadratic Wasserstein distance between the network output and its Gaussian approximation at any training time.<n>Our results quantify how architectural parameters, such as width and input dimension, influence convergence, and how training dynamics affect the approximation error.
• Score: 3.441021278275805
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we study the quantitative convergence of shallow neural networks trained via gradient descent to their associated Gaussian processes in the infinite-width limit. While previous work has established qualitative convergence under broad settings, precise, finite-width estimates remain limited, particularly during training. We provide explicit upper bounds on the quadratic Wasserstein distance between the network output and its Gaussian approximation at any training time $t \ge 0$, demonstrating polynomial decay with network width. Our results quantify how architectural parameters, such as width and input dimension, influence convergence, and how training dynamics affect the approximation error.

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