Quantitative Gaussian-Process limits of Tensor Programs
Machine Learning
2026-07-07 v1 Probability
Machine Learning
Abstract
We study the infinite-width Gaussian-process limit of random neural networks through the lens of tensor programs, and we provide a quantitative convergence theory in Wasserstein distance. Our main result gives explicit finite-width error bounds, of order inverse square-root of the widths between finite-network executions and their Gaussian-process limits. The framework is architecture-agnostic and covers feed-forward models together with weight-sharing schemes relevant for recurrent and transformer-type architectures.
Cite
@article{arxiv.2607.06290,
title = {Quantitative Gaussian-Process limits of Tensor Programs},
author = {Andrea Agazzi and Eloy Mosig García and Dario Trevisan},
journal= {arXiv preprint arXiv:2607.06290},
year = {2026}
}