{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:62IZ776N2TEZDZC2H5B3MFZCXM","short_pith_number":"pith:62IZ776N","schema_version":"1.0","canonical_sha256":"f6919fffcdd4c991e45a3f43b61722bb29e5e331dd5ab76e6773a1fa393c837d","source":{"kind":"arxiv","id":"2402.07114","version":1},"attestation_state":"computed","paper":{"title":"Towards Quantifying the Preconditioning Effect of Adam","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Inderjit S. Dhillon, Naman Agarwal, Rudrajit Das, Sujay Sanghavi","submitted_at":"2024-02-11T06:21:18Z","abstract_excerpt":"There is a notable dearth of results characterizing the preconditioning effect of Adam and showing how it may alleviate the curse of ill-conditioning -- an issue plaguing gradient descent (GD). In this work, we perform a detailed analysis of Adam's preconditioning effect for quadratic functions and quantify to what extent Adam can mitigate the dependence on the condition number of the Hessian. Our key finding is that Adam can suffer less from the condition number but at the expense of suffering a dimension-dependent quantity. Specifically, for a $d$-dimensional quadratic with a diagonal Hessia"},"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":"2402.07114","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-11T06:21:18Z","cross_cats_sorted":["cs.NA","math.NA","math.OC","stat.ML"],"title_canon_sha256":"89c7fa99f593934fcfb3504448d38885c63df74bb615e375c9f1e3b2a614ccd3","abstract_canon_sha256":"a9961ebf077f8c1c8a285e39cceeba773865517cf68fe32a439380af7ca2b19c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:44:46.767098Z","signature_b64":"jU9NMspWbMMprq+Si4s4UggT8tOOI5H7MqBx2zsg81NEqI7F/od/xpZMNBr8LZhhWGtWXi8ALEYI8Q50mPYrCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6919fffcdd4c991e45a3f43b61722bb29e5e331dd5ab76e6773a1fa393c837d","last_reissued_at":"2026-07-05T07:44:46.766667Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:44:46.766667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards Quantifying the Preconditioning Effect of Adam","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Inderjit S. Dhillon, Naman Agarwal, Rudrajit Das, Sujay Sanghavi","submitted_at":"2024-02-11T06:21:18Z","abstract_excerpt":"There is a notable dearth of results characterizing the preconditioning effect of Adam and showing how it may alleviate the curse of ill-conditioning -- an issue plaguing gradient descent (GD). In this work, we perform a detailed analysis of Adam's preconditioning effect for quadratic functions and quantify to what extent Adam can mitigate the dependence on the condition number of the Hessian. Our key finding is that Adam can suffer less from the condition number but at the expense of suffering a dimension-dependent quantity. Specifically, for a $d$-dimensional quadratic with a diagonal Hessia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.07114","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/2402.07114/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":"2402.07114","created_at":"2026-07-05T07:44:46.766725+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.07114v1","created_at":"2026-07-05T07:44:46.766725+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.07114","created_at":"2026-07-05T07:44:46.766725+00:00"},{"alias_kind":"pith_short_12","alias_value":"62IZ776N2TEZ","created_at":"2026-07-05T07:44:46.766725+00:00"},{"alias_kind":"pith_short_16","alias_value":"62IZ776N2TEZDZC2","created_at":"2026-07-05T07:44:46.766725+00:00"},{"alias_kind":"pith_short_8","alias_value":"62IZ776N","created_at":"2026-07-05T07:44:46.766725+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.09658","citing_title":"Muon Learns More Robust and Transferable Features than Adam","ref_index":68,"is_internal_anchor":false},{"citing_arxiv_id":"2605.00650","citing_title":"AdaMeZO: Adam-style Zeroth-Order Optimizer for LLM Fine-tuning Without Maintaining the Moments","ref_index":16,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/62IZ776N2TEZDZC2H5B3MFZCXM","json":"https://pith.science/pith/62IZ776N2TEZDZC2H5B3MFZCXM.json","graph_json":"https://pith.science/api/pith-number/62IZ776N2TEZDZC2H5B3MFZCXM/graph.json","events_json":"https://pith.science/api/pith-number/62IZ776N2TEZDZC2H5B3MFZCXM/events.json","paper":"https://pith.science/paper/62IZ776N"},"agent_actions":{"view_html":"https://pith.science/pith/62IZ776N2TEZDZC2H5B3MFZCXM","download_json":"https://pith.science/pith/62IZ776N2TEZDZC2H5B3MFZCXM.json","view_paper":"https://pith.science/paper/62IZ776N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.07114&json=true","fetch_graph":"https://pith.science/api/pith-number/62IZ776N2TEZDZC2H5B3MFZCXM/graph.json","fetch_events":"https://pith.science/api/pith-number/62IZ776N2TEZDZC2H5B3MFZCXM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/62IZ776N2TEZDZC2H5B3MFZCXM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/62IZ776N2TEZDZC2H5B3MFZCXM/action/storage_attestation","attest_author":"https://pith.science/pith/62IZ776N2TEZDZC2H5B3MFZCXM/action/author_attestation","sign_citation":"https://pith.science/pith/62IZ776N2TEZDZC2H5B3MFZCXM/action/citation_signature","submit_replication":"https://pith.science/pith/62IZ776N2TEZDZC2H5B3MFZCXM/action/replication_record"}},"created_at":"2026-07-05T07:44:46.766725+00:00","updated_at":"2026-07-05T07:44:46.766725+00:00"}