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arXiv · 2607.06290

Quantitative Gaussian-Process limits of Tensor Programs

Andrea Agazzi·Eloy Mosig García·Dario Trevisan
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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.

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Andrea Agazzi, Eloy Mosig García, Dario Trevisan. 2026-07-07. Quantitative Gaussian-Process limits of Tensor Programs. https://arxiv.org/abs/2607.06290

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