{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:XCNB3NNMGQRBWLOGZFQTQYME2R","short_pith_number":"pith:XCNB3NNM","schema_version":"1.0","canonical_sha256":"b89a1db5ac34221b2dc6c961386184d455dd480e8da6e56ad24da95631a9c3d3","source":{"kind":"arxiv","id":"2505.24849","version":1},"attestation_state":"computed","paper":{"title":"Statistical mechanics of extensive-width Bayesian neural networks near interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","cs.IT","cs.LG","math.IT"],"primary_cat":"stat.ML","authors_text":"Francesco Camilli, Jean Barbier, Mauro Pastore, Minh-Toan Nguyen, Rudy Skerk","submitted_at":"2025-05-30T17:46:59Z","abstract_excerpt":"For three decades statistical mechanics has been providing a framework to analyse neural networks. However, the theoretically tractable models, e.g., perceptrons, random features models and kernel machines, or multi-index models and committee machines with few neurons, remained simple compared to those used in applications. In this paper we help reducing the gap between practical networks and their theoretical understanding through a statistical physics analysis of the supervised learning of a two-layer fully connected network with generic weight distribution and activation function, whose hid"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2505.24849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-05-30T17:46:59Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.IT","cs.LG","math.IT"],"title_canon_sha256":"3d4b2e1b6fb0b0e83232c927932a94d245112ed3a93fe44d6066983f2e7bd394","abstract_canon_sha256":"30e4f6aebd999ad8ba1639239c8c755a635263fca4e9a972b3b3657fc9487cb9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:12:57.776305Z","signature_b64":"Hv/usFfHmCpcEDPrLJ0/AwWUckF1bogKXCnYGG7TO/pLTlWhK0HHnY8KD0qPWXQLzDh2QExeUYFcwW7z18FhAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b89a1db5ac34221b2dc6c961386184d455dd480e8da6e56ad24da95631a9c3d3","last_reissued_at":"2026-07-05T11:12:57.775751Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:12:57.775751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Statistical mechanics of extensive-width Bayesian neural networks near interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","cs.IT","cs.LG","math.IT"],"primary_cat":"stat.ML","authors_text":"Francesco Camilli, Jean Barbier, Mauro Pastore, Minh-Toan Nguyen, Rudy Skerk","submitted_at":"2025-05-30T17:46:59Z","abstract_excerpt":"For three decades statistical mechanics has been providing a framework to analyse neural networks. However, the theoretically tractable models, e.g., perceptrons, random features models and kernel machines, or multi-index models and committee machines with few neurons, remained simple compared to those used in applications. In this paper we help reducing the gap between practical networks and their theoretical understanding through a statistical physics analysis of the supervised learning of a two-layer fully connected network with generic weight distribution and activation function, whose hid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24849","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/2505.24849/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2505.24849","created_at":"2026-07-05T11:12:57.775816+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.24849v1","created_at":"2026-07-05T11:12:57.775816+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24849","created_at":"2026-07-05T11:12:57.775816+00:00"},{"alias_kind":"pith_short_12","alias_value":"XCNB3NNMGQRB","created_at":"2026-07-05T11:12:57.775816+00:00"},{"alias_kind":"pith_short_16","alias_value":"XCNB3NNMGQRBWLOG","created_at":"2026-07-05T11:12:57.775816+00:00"},{"alias_kind":"pith_short_8","alias_value":"XCNB3NNM","created_at":"2026-07-05T11:12:57.775816+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.20989","citing_title":"Microscopic and collective signatures of feature learning in neural networks","ref_index":53,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XCNB3NNMGQRBWLOGZFQTQYME2R","json":"https://pith.science/pith/XCNB3NNMGQRBWLOGZFQTQYME2R.json","graph_json":"https://pith.science/api/pith-number/XCNB3NNMGQRBWLOGZFQTQYME2R/graph.json","events_json":"https://pith.science/api/pith-number/XCNB3NNMGQRBWLOGZFQTQYME2R/events.json","paper":"https://pith.science/paper/XCNB3NNM"},"agent_actions":{"view_html":"https://pith.science/pith/XCNB3NNMGQRBWLOGZFQTQYME2R","download_json":"https://pith.science/pith/XCNB3NNMGQRBWLOGZFQTQYME2R.json","view_paper":"https://pith.science/paper/XCNB3NNM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.24849&json=true","fetch_graph":"https://pith.science/api/pith-number/XCNB3NNMGQRBWLOGZFQTQYME2R/graph.json","fetch_events":"https://pith.science/api/pith-number/XCNB3NNMGQRBWLOGZFQTQYME2R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XCNB3NNMGQRBWLOGZFQTQYME2R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XCNB3NNMGQRBWLOGZFQTQYME2R/action/storage_attestation","attest_author":"https://pith.science/pith/XCNB3NNMGQRBWLOGZFQTQYME2R/action/author_attestation","sign_citation":"https://pith.science/pith/XCNB3NNMGQRBWLOGZFQTQYME2R/action/citation_signature","submit_replication":"https://pith.science/pith/XCNB3NNMGQRBWLOGZFQTQYME2R/action/replication_record"}},"created_at":"2026-07-05T11:12:57.775816+00:00","updated_at":"2026-07-05T11:12:57.775816+00:00"}