{"paper":{"title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"A. Vezzani, L. Giambagli, P. Baglioni, P. Rotondo, R. Burioni, R. Pacelli","submitted_at":"2024-12-20T14:01:16Z","abstract_excerpt":"Finite-width one hidden layer networks with multiple neurons in the readout layer display non-trivial output-output correlations that vanish in the lazy-training infinite-width limit. In this manuscript we leverage recent progress in the proportional limit of Bayesian deep learning (that is the limit where the size of the training set $P$ and the width of the hidden layers $N$ are taken to infinity keeping their ratio $\\alpha = P/N$ finite) to rationalize this empirical evidence. In particular, we show that output-output correlations in finite fully-connected networks are taken into account by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15911","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/2412.15911/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"}