{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:EJ2HFSUXQ6FXVPXOXAEYQSPY3V","short_pith_number":"pith:EJ2HFSUX","schema_version":"1.0","canonical_sha256":"227472ca97878b7abeeeb8098849f8dd768897e1bcfca8a9986678115ec76a4f","source":{"kind":"arxiv","id":"2005.11879","version":3},"attestation_state":"computed","paper":{"title":"Spectra of the Conjugate Kernel and Neural Tangent Kernel for linear-width neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Zhichao Wang, Zhou Fan","submitted_at":"2020-05-25T01:11:49Z","abstract_excerpt":"We study the eigenvalue distributions of the Conjugate Kernel and Neural Tangent Kernel associated to multi-layer feedforward neural networks. In an asymptotic regime where network width is increasing linearly in sample size, under random initialization of the weights, and for input samples satisfying a notion of approximate pairwise orthogonality, we show that the eigenvalue distributions of the CK and NTK converge to deterministic limits. The limit for the CK is described by iterating the Marcenko-Pastur map across the hidden layers. The limit for the NTK is equivalent to that of a linear co"},"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":"2005.11879","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-05-25T01:11:49Z","cross_cats_sorted":["cs.LG","math.PR","math.ST","stat.TH"],"title_canon_sha256":"18856b5bc403453403fabdc6cb8075f0df0b9e9dc01dc7f3d0b5a8747f26a7db","abstract_canon_sha256":"838b2c6151bfe56dd18b81a7abd92a2af4c3623dd4bfab22a5a937f158d6a317"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:41:54.329970Z","signature_b64":"fKkBWH3AFlUDVjKtIRu8etFVzThLoK1hI6YTMGwU4fH+LACv1gaHEGO6c/DTh2dE8e/ALy7M1h+VHa5umUROBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"227472ca97878b7abeeeb8098849f8dd768897e1bcfca8a9986678115ec76a4f","last_reissued_at":"2026-07-05T01:41:54.329465Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:41:54.329465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectra of the Conjugate Kernel and Neural Tangent Kernel for linear-width neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Zhichao Wang, Zhou Fan","submitted_at":"2020-05-25T01:11:49Z","abstract_excerpt":"We study the eigenvalue distributions of the Conjugate Kernel and Neural Tangent Kernel associated to multi-layer feedforward neural networks. In an asymptotic regime where network width is increasing linearly in sample size, under random initialization of the weights, and for input samples satisfying a notion of approximate pairwise orthogonality, we show that the eigenvalue distributions of the CK and NTK converge to deterministic limits. The limit for the CK is described by iterating the Marcenko-Pastur map across the hidden layers. The limit for the NTK is equivalent to that of a linear co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.11879","kind":"arxiv","version":3},"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/2005.11879/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":"2005.11879","created_at":"2026-07-05T01:41:54.329522+00:00"},{"alias_kind":"arxiv_version","alias_value":"2005.11879v3","created_at":"2026-07-05T01:41:54.329522+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.11879","created_at":"2026-07-05T01:41:54.329522+00:00"},{"alias_kind":"pith_short_12","alias_value":"EJ2HFSUXQ6FX","created_at":"2026-07-05T01:41:54.329522+00:00"},{"alias_kind":"pith_short_16","alias_value":"EJ2HFSUXQ6FXVPXO","created_at":"2026-07-05T01:41:54.329522+00:00"},{"alias_kind":"pith_short_8","alias_value":"EJ2HFSUX","created_at":"2026-07-05T01:41:54.329522+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EJ2HFSUXQ6FXVPXOXAEYQSPY3V","json":"https://pith.science/pith/EJ2HFSUXQ6FXVPXOXAEYQSPY3V.json","graph_json":"https://pith.science/api/pith-number/EJ2HFSUXQ6FXVPXOXAEYQSPY3V/graph.json","events_json":"https://pith.science/api/pith-number/EJ2HFSUXQ6FXVPXOXAEYQSPY3V/events.json","paper":"https://pith.science/paper/EJ2HFSUX"},"agent_actions":{"view_html":"https://pith.science/pith/EJ2HFSUXQ6FXVPXOXAEYQSPY3V","download_json":"https://pith.science/pith/EJ2HFSUXQ6FXVPXOXAEYQSPY3V.json","view_paper":"https://pith.science/paper/EJ2HFSUX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2005.11879&json=true","fetch_graph":"https://pith.science/api/pith-number/EJ2HFSUXQ6FXVPXOXAEYQSPY3V/graph.json","fetch_events":"https://pith.science/api/pith-number/EJ2HFSUXQ6FXVPXOXAEYQSPY3V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EJ2HFSUXQ6FXVPXOXAEYQSPY3V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EJ2HFSUXQ6FXVPXOXAEYQSPY3V/action/storage_attestation","attest_author":"https://pith.science/pith/EJ2HFSUXQ6FXVPXOXAEYQSPY3V/action/author_attestation","sign_citation":"https://pith.science/pith/EJ2HFSUXQ6FXVPXOXAEYQSPY3V/action/citation_signature","submit_replication":"https://pith.science/pith/EJ2HFSUXQ6FXVPXOXAEYQSPY3V/action/replication_record"}},"created_at":"2026-07-05T01:41:54.329522+00:00","updated_at":"2026-07-05T01:41:54.329522+00:00"}