{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:OPTC2BICIGALT4QYHVJFRUOVGQ","short_pith_number":"pith:OPTC2BIC","schema_version":"1.0","canonical_sha256":"73e62d05024180b9f2183d5258d1d534146b7a5d34233d4b6368482430c04d12","source":{"kind":"arxiv","id":"1812.07956","version":5},"attestation_state":"computed","paper":{"title":"On Lazy Training in Differentiable Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Edouard Oyallon, Francis Bach (LIENS, Lenaic Chizat (CNRS, SIERRA), UP11)","submitted_at":"2018-12-19T14:11:20Z","abstract_excerpt":"In a series of recent theoretical works, it was shown that strongly over-parameterized neural networks trained with gradient-based methods could converge exponentially fast to zero training loss, with their parameters hardly varying. In this work, we show that this \"lazy training\" phenomenon is not specific to over-parameterized neural networks, and is due to a choice of scaling, often implicit, that makes the model behave as its linearization around the initialization, thus yielding a model equivalent to learning with positive-definite kernels. Through a theoretical analysis, we exhibit vario"},"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":"1812.07956","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-19T14:11:20Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"8cf7743ae5c607cfb47fd0de6ddac740a0295aea2d9b1067bb688039d2716f96","abstract_canon_sha256":"5631fc36adf438c6e93921d42412f1eb8727438d646610bccf4f761b6bd5a54a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:30:00.141899Z","signature_b64":"VsE1XR0CMpE0b2vMDoEjj2JTs27AkZbT/X/fVITvAPOn2A8UQGjeqJxiK2fArhb7zY9hJY5yPz78AxIcCb8sDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73e62d05024180b9f2183d5258d1d534146b7a5d34233d4b6368482430c04d12","last_reissued_at":"2026-07-05T00:30:00.141488Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:30:00.141488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Lazy Training in Differentiable Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Edouard Oyallon, Francis Bach (LIENS, Lenaic Chizat (CNRS, SIERRA), UP11)","submitted_at":"2018-12-19T14:11:20Z","abstract_excerpt":"In a series of recent theoretical works, it was shown that strongly over-parameterized neural networks trained with gradient-based methods could converge exponentially fast to zero training loss, with their parameters hardly varying. In this work, we show that this \"lazy training\" phenomenon is not specific to over-parameterized neural networks, and is due to a choice of scaling, often implicit, that makes the model behave as its linearization around the initialization, thus yielding a model equivalent to learning with positive-definite kernels. Through a theoretical analysis, we exhibit vario"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07956","kind":"arxiv","version":5},"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/1812.07956/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":"1812.07956","created_at":"2026-07-05T00:30:00.141561+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.07956v5","created_at":"2026-07-05T00:30:00.141561+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.07956","created_at":"2026-07-05T00:30:00.141561+00:00"},{"alias_kind":"pith_short_12","alias_value":"OPTC2BICIGAL","created_at":"2026-07-05T00:30:00.141561+00:00"},{"alias_kind":"pith_short_16","alias_value":"OPTC2BICIGALT4QY","created_at":"2026-07-05T00:30:00.141561+00:00"},{"alias_kind":"pith_short_8","alias_value":"OPTC2BIC","created_at":"2026-07-05T00:30:00.141561+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.22019","citing_title":"Channel Location Constrains the Auditability of Subliminal Learning","ref_index":16,"is_internal_anchor":false},{"citing_arxiv_id":"2605.01288","citing_title":"A Theory of Saddle Escape in Deep Nonlinear Networks","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"1906.08899","citing_title":"Limitations of Lazy Training of Two-layers Neural Networks","ref_index":10,"is_internal_anchor":false},{"citing_arxiv_id":"2502.10600","citing_title":"Weighted quantization using MMD: From mean field to mean shift via gradient flows","ref_index":20,"is_internal_anchor":false},{"citing_arxiv_id":"2605.01288","citing_title":"A Theory of Saddle Escape in Deep Nonlinear Networks","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2605.01288","citing_title":"A Theory of Saddle Escape in Deep Nonlinear Networks","ref_index":14,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OPTC2BICIGALT4QYHVJFRUOVGQ","json":"https://pith.science/pith/OPTC2BICIGALT4QYHVJFRUOVGQ.json","graph_json":"https://pith.science/api/pith-number/OPTC2BICIGALT4QYHVJFRUOVGQ/graph.json","events_json":"https://pith.science/api/pith-number/OPTC2BICIGALT4QYHVJFRUOVGQ/events.json","paper":"https://pith.science/paper/OPTC2BIC"},"agent_actions":{"view_html":"https://pith.science/pith/OPTC2BICIGALT4QYHVJFRUOVGQ","download_json":"https://pith.science/pith/OPTC2BICIGALT4QYHVJFRUOVGQ.json","view_paper":"https://pith.science/paper/OPTC2BIC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.07956&json=true","fetch_graph":"https://pith.science/api/pith-number/OPTC2BICIGALT4QYHVJFRUOVGQ/graph.json","fetch_events":"https://pith.science/api/pith-number/OPTC2BICIGALT4QYHVJFRUOVGQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OPTC2BICIGALT4QYHVJFRUOVGQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OPTC2BICIGALT4QYHVJFRUOVGQ/action/storage_attestation","attest_author":"https://pith.science/pith/OPTC2BICIGALT4QYHVJFRUOVGQ/action/author_attestation","sign_citation":"https://pith.science/pith/OPTC2BICIGALT4QYHVJFRUOVGQ/action/citation_signature","submit_replication":"https://pith.science/pith/OPTC2BICIGALT4QYHVJFRUOVGQ/action/replication_record"}},"created_at":"2026-07-05T00:30:00.141561+00:00","updated_at":"2026-07-05T00:30:00.141561+00:00"}