{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:UM24OJY7KOGQFQP5ODY4O76THO","short_pith_number":"pith:UM24OJY7","schema_version":"1.0","canonical_sha256":"a335c7271f538d02c1fd70f1c77fd33b854a0b23c81a01f0c30aca2812883045","source":{"kind":"arxiv","id":"2501.18530","version":2},"attestation_state":"computed","paper":{"title":"Optimal generalisation and learning transition in extensive-width shallow 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":"2025-01-30T17:56:52Z","abstract_excerpt":"We consider a teacher-student model of supervised learning with a fully-trained two-layer neural network whose width $k$ and input dimension $d$ are large and proportional. We provide an effective theory for approximating the Bayes-optimal generalisation error of the network for any activation function in the regime of sample size $n$ scaling quadratically with the input dimension, i.e., around the interpolation threshold where the number of trainable parameters $kd+k$ and of data $n$ are comparable. Our analysis tackles generic weight distributions. We uncover a discontinuous phase transition"},"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":"2501.18530","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-01-30T17:56:52Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.IT","cs.LG","math.IT"],"title_canon_sha256":"79cee65dc493565966c7b1d3566acd8e33e32d6769d29ee7dd868a2ddfde0310","abstract_canon_sha256":"c6c64ac85d26aa615ea3fe9e7f6fc70b648cdd46fbd544daedafefe77f0a0938"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:42:42.827553Z","signature_b64":"Zd9lCfyU3toTLexlvva+0FT1v+t9LDCQtg67rhvxwlpAEw4JSeoINnl7e0r9eeZNSadYHtQaCvg/hLO3p335Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a335c7271f538d02c1fd70f1c77fd33b854a0b23c81a01f0c30aca2812883045","last_reissued_at":"2026-07-05T10:42:42.827033Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:42:42.827033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal generalisation and learning transition in extensive-width shallow 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":"2025-01-30T17:56:52Z","abstract_excerpt":"We consider a teacher-student model of supervised learning with a fully-trained two-layer neural network whose width $k$ and input dimension $d$ are large and proportional. We provide an effective theory for approximating the Bayes-optimal generalisation error of the network for any activation function in the regime of sample size $n$ scaling quadratically with the input dimension, i.e., around the interpolation threshold where the number of trainable parameters $kd+k$ and of data $n$ are comparable. Our analysis tackles generic weight distributions. We uncover a discontinuous phase transition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18530","kind":"arxiv","version":2},"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/2501.18530/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":"2501.18530","created_at":"2026-07-05T10:42:42.827092+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.18530v2","created_at":"2026-07-05T10:42:42.827092+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.18530","created_at":"2026-07-05T10:42:42.827092+00:00"},{"alias_kind":"pith_short_12","alias_value":"UM24OJY7KOGQ","created_at":"2026-07-05T10:42:42.827092+00:00"},{"alias_kind":"pith_short_16","alias_value":"UM24OJY7KOGQFQP5","created_at":"2026-07-05T10:42:42.827092+00:00"},{"alias_kind":"pith_short_8","alias_value":"UM24OJY7","created_at":"2026-07-05T10:42:42.827092+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2606.31110","citing_title":"Explaining Machine Learning and Memorization with Statistical Mechanics","ref_index":22,"is_internal_anchor":true},{"citing_arxiv_id":"2605.29684","citing_title":"Kernel Renormalization in Bayesian Deep Neural Networks: the Equivalent Wishart Ansatz in the Proportional Regime","ref_index":72,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UM24OJY7KOGQFQP5ODY4O76THO","json":"https://pith.science/pith/UM24OJY7KOGQFQP5ODY4O76THO.json","graph_json":"https://pith.science/api/pith-number/UM24OJY7KOGQFQP5ODY4O76THO/graph.json","events_json":"https://pith.science/api/pith-number/UM24OJY7KOGQFQP5ODY4O76THO/events.json","paper":"https://pith.science/paper/UM24OJY7"},"agent_actions":{"view_html":"https://pith.science/pith/UM24OJY7KOGQFQP5ODY4O76THO","download_json":"https://pith.science/pith/UM24OJY7KOGQFQP5ODY4O76THO.json","view_paper":"https://pith.science/paper/UM24OJY7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.18530&json=true","fetch_graph":"https://pith.science/api/pith-number/UM24OJY7KOGQFQP5ODY4O76THO/graph.json","fetch_events":"https://pith.science/api/pith-number/UM24OJY7KOGQFQP5ODY4O76THO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UM24OJY7KOGQFQP5ODY4O76THO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UM24OJY7KOGQFQP5ODY4O76THO/action/storage_attestation","attest_author":"https://pith.science/pith/UM24OJY7KOGQFQP5ODY4O76THO/action/author_attestation","sign_citation":"https://pith.science/pith/UM24OJY7KOGQFQP5ODY4O76THO/action/citation_signature","submit_replication":"https://pith.science/pith/UM24OJY7KOGQFQP5ODY4O76THO/action/replication_record"}},"created_at":"2026-07-05T10:42:42.827092+00:00","updated_at":"2026-07-05T10:42:42.827092+00:00"}