{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ACUFIXYOK2F2OWJK33N6LBF4HY","short_pith_number":"pith:ACUFIXYO","schema_version":"1.0","canonical_sha256":"00a8545f0e568ba7592adedbe584bc3e0b4522bbaa5861a8268b67999053582a","source":{"kind":"arxiv","id":"1912.01198","version":3},"attestation_state":"computed","paper":{"title":"Towards Understanding the Spectral Bias of Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Ding-Xuan Zhou, Quanquan Gu, Yuan Cao, Yue Wu, Zhiying Fang","submitted_at":"2019-12-03T05:34:30Z","abstract_excerpt":"An intriguing phenomenon observed during training neural networks is the spectral bias, which states that neural networks are biased towards learning less complex functions. The priority of learning functions with low complexity might be at the core of explaining generalization ability of neural network, and certain efforts have been made to provide theoretical explanation for spectral bias. However, there is still no satisfying theoretical result justifying the underlying mechanism of spectral bias. In this paper, we give a comprehensive and rigorous explanation for spectral bias and relate i"},"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":"1912.01198","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-12-03T05:34:30Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"527c74abd2e7020d73685c7e8b3826b76ff5b25da8a34e1eecc5068f520157b6","abstract_canon_sha256":"7584b3bdba78d5cc609ddae74f7d70ae5a376f74e8cd43d82685d3069b08195c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:40:17.174721Z","signature_b64":"rAsB8LxGa2+wIhkKT3wj2R0X9uwrIOcdtQ5EkW3iQ/dXyr1eOnAYACMsLGy8hrrRkgThS+EA4dKGN22e2qY3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00a8545f0e568ba7592adedbe584bc3e0b4522bbaa5861a8268b67999053582a","last_reissued_at":"2026-07-05T01:40:17.174340Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:40:17.174340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards Understanding the Spectral Bias of Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Ding-Xuan Zhou, Quanquan Gu, Yuan Cao, Yue Wu, Zhiying Fang","submitted_at":"2019-12-03T05:34:30Z","abstract_excerpt":"An intriguing phenomenon observed during training neural networks is the spectral bias, which states that neural networks are biased towards learning less complex functions. The priority of learning functions with low complexity might be at the core of explaining generalization ability of neural network, and certain efforts have been made to provide theoretical explanation for spectral bias. However, there is still no satisfying theoretical result justifying the underlying mechanism of spectral bias. In this paper, we give a comprehensive and rigorous explanation for spectral bias and relate i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.01198","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/1912.01198/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":"1912.01198","created_at":"2026-07-05T01:40:17.174415+00:00"},{"alias_kind":"arxiv_version","alias_value":"1912.01198v3","created_at":"2026-07-05T01:40:17.174415+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.01198","created_at":"2026-07-05T01:40:17.174415+00:00"},{"alias_kind":"pith_short_12","alias_value":"ACUFIXYOK2F2","created_at":"2026-07-05T01:40:17.174415+00:00"},{"alias_kind":"pith_short_16","alias_value":"ACUFIXYOK2F2OWJK","created_at":"2026-07-05T01:40:17.174415+00:00"},{"alias_kind":"pith_short_8","alias_value":"ACUFIXYO","created_at":"2026-07-05T01:40:17.174415+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":10,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06949","citing_title":"SpiS-GAN: Spiral-Modulated Handwriting Synthesis with Star Operation","ref_index":58,"is_internal_anchor":true},{"citing_arxiv_id":"2607.01694","citing_title":"Frequency Shift Physics-Informed Extreme Learning Machine for Solving High-Frequency Partial Differential Equations","ref_index":21,"is_internal_anchor":false},{"citing_arxiv_id":"2606.10089","citing_title":"A Theory on Flow Matching with Neural Networks","ref_index":259,"is_internal_anchor":false},{"citing_arxiv_id":"2605.24278","citing_title":"Fourier Feature Pyramids for Physics-Informed Neural Networks","ref_index":3,"is_internal_anchor":false},{"citing_arxiv_id":"2605.14370","citing_title":"Deciphering Neural Reparameterized Full-Waveform Inversion with Neural Sensitivity Kernel and Wave Tangent Kernel","ref_index":89,"is_internal_anchor":false},{"citing_arxiv_id":"2603.24654","citing_title":"Spectral methods: crucial for machine learning, natural for quantum computers?","ref_index":92,"is_internal_anchor":false},{"citing_arxiv_id":"2401.01335","citing_title":"Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models","ref_index":240,"is_internal_anchor":false},{"citing_arxiv_id":"2605.12763","citing_title":"State-Space NTK Collapse Near Bifurcations","ref_index":121,"is_internal_anchor":false},{"citing_arxiv_id":"2605.08746","citing_title":"The Global Empirical NTK: Self-Referential Bias and Dimensionality of Gradient Descent Learning","ref_index":121,"is_internal_anchor":false},{"citing_arxiv_id":"2604.18686","citing_title":"Neural Spectral Bias and Conformal Correlators I: Introduction and Applications","ref_index":39,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ACUFIXYOK2F2OWJK33N6LBF4HY","json":"https://pith.science/pith/ACUFIXYOK2F2OWJK33N6LBF4HY.json","graph_json":"https://pith.science/api/pith-number/ACUFIXYOK2F2OWJK33N6LBF4HY/graph.json","events_json":"https://pith.science/api/pith-number/ACUFIXYOK2F2OWJK33N6LBF4HY/events.json","paper":"https://pith.science/paper/ACUFIXYO"},"agent_actions":{"view_html":"https://pith.science/pith/ACUFIXYOK2F2OWJK33N6LBF4HY","download_json":"https://pith.science/pith/ACUFIXYOK2F2OWJK33N6LBF4HY.json","view_paper":"https://pith.science/paper/ACUFIXYO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1912.01198&json=true","fetch_graph":"https://pith.science/api/pith-number/ACUFIXYOK2F2OWJK33N6LBF4HY/graph.json","fetch_events":"https://pith.science/api/pith-number/ACUFIXYOK2F2OWJK33N6LBF4HY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ACUFIXYOK2F2OWJK33N6LBF4HY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ACUFIXYOK2F2OWJK33N6LBF4HY/action/storage_attestation","attest_author":"https://pith.science/pith/ACUFIXYOK2F2OWJK33N6LBF4HY/action/author_attestation","sign_citation":"https://pith.science/pith/ACUFIXYOK2F2OWJK33N6LBF4HY/action/citation_signature","submit_replication":"https://pith.science/pith/ACUFIXYOK2F2OWJK33N6LBF4HY/action/replication_record"}},"created_at":"2026-07-05T01:40:17.174415+00:00","updated_at":"2026-07-05T01:40:17.174415+00:00"}