[2509.24544] Quantitative convergence of trained single layer neural networks to Gaussian processes

Statistics > Machine Learning arXiv:2509.24544 (stat) [Submitted on 29 Sep 2025 (v1), last revised 5 Mar 2026 (this version, v3)] Title:Quantitative convergence of trained single layer neural networks to Gaussian processes Authors:Eloy Mosig, Andrea Agazzi, Dario Trevisan View a PDF of the paper titled Quantitative convergence of trained single layer neural networks to Gaussian processes, by Eloy Mosig and 2 other authors View PDF HTML (experimental) 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. Comments: Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG); Probability (math.PR) Cite as: arXiv:2509.24544 [stat.ML]   (or arXiv:2509.24544v3 [stat.ML] for this version)   https://doi.org/10.48550/arXiv.2509.24544 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Eloy Mosig [v...