{"ID":6023585,"CreatedAt":"2026-07-08T01:00:23.257252134Z","UpdatedAt":"2026-07-10T13:53:55.553307773Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.06290","arxiv_id":"2607.06290","title":"Quantitative Gaussian-Process limits of Tensor Programs","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.","short_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 executio...","url_abs":"https://arxiv.org/abs/2607.06290","url_pdf":"https://arxiv.org/pdf/2607.06290v1","authors":"[\"Andrea Agazzi\",\"Eloy Mosig García\",\"Dario Trevisan\"]","published":"2026-07-07T13:59:56Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.PR\",\"stat.ML\"]","methods":"[\"Transformer\"]","has_code":false}