{"paper":{"title":"Quantitative Gaussian-Process limits of Tensor Programs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR","stat.ML"],"primary_cat":"cs.LG","authors_text":"Andrea Agazzi, Dario Trevisan, Eloy Mosig Garc\\'ia","submitted_at":"2026-07-07T13:59:56Z","abstract_excerpt":"We study the infinite-width Gaussian-process limit of random neural networks\n  through the lens of tensor programs, and we provide a quantitative convergence\n  theory in Wasserstein distance.\n  Our main result gives explicit finite-width error bounds, of order inverse square-root of the widths\n  between finite-network executions and their\n  Gaussian-process limits. The framework is architecture-agnostic and covers feed-forward models together\n  with weight-sharing schemes relevant for recurrent and transformer-type\n  architectures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06290","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.06290/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}