{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:63UGQOTZJSKVO2CAAAPLYU5E2L","short_pith_number":"pith:63UGQOTZ","schema_version":"1.0","canonical_sha256":"f6e8683a794c95576840001ebc53a4d2e6174d43791506fc0058557a99fa5040","source":{"kind":"arxiv","id":"1806.02958","version":2},"attestation_state":"computed","paper":{"title":"Efficient Full-Matrix Adaptive Regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Brian Bullins, Cyril Zhang, Elad Hazan, Karan Singh, Naman Agarwal, Xinyi Chen, Yi Zhang","submitted_at":"2018-06-08T03:31:05Z","abstract_excerpt":"Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how to modify full-matrix adaptive regularization in order to make it practical and effective. We also provide a novel theoretical analysis for adaptive regularization in non-convex optimization settings. The core of our algorithm, termed GGT, consists of the efficient computation of the inverse square root of a low-rank matrix. Our preliminary experiments show 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":"1806.02958","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-06-08T03:31:05Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"37c9411d8bef9f151996e7bb2d111c06183db5bb0d2cb000eea4e4fbc0b23a18","abstract_canon_sha256":"8c5215185e3d3054594ec7081d999750843b282080ac05b534a2645897f2fb8f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:52:32.232577Z","signature_b64":"dwGPZ803tnqp2W2bSHMX6/fjeT4YanX51MAj3jgrqXuXskuMyPKDIs1Ah7/fRcwimJrCoCanfDSvnKl7yFi1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6e8683a794c95576840001ebc53a4d2e6174d43791506fc0058557a99fa5040","last_reissued_at":"2026-07-05T01:52:32.232115Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:52:32.232115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficient Full-Matrix Adaptive Regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Brian Bullins, Cyril Zhang, Elad Hazan, Karan Singh, Naman Agarwal, Xinyi Chen, Yi Zhang","submitted_at":"2018-06-08T03:31:05Z","abstract_excerpt":"Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how to modify full-matrix adaptive regularization in order to make it practical and effective. We also provide a novel theoretical analysis for adaptive regularization in non-convex optimization settings. The core of our algorithm, termed GGT, consists of the efficient computation of the inverse square root of a low-rank matrix. Our preliminary experiments show i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02958","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/1806.02958/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":"1806.02958","created_at":"2026-07-05T01:52:32.232181+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.02958v2","created_at":"2026-07-05T01:52:32.232181+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02958","created_at":"2026-07-05T01:52:32.232181+00:00"},{"alias_kind":"pith_short_12","alias_value":"63UGQOTZJSKV","created_at":"2026-07-05T01:52:32.232181+00:00"},{"alias_kind":"pith_short_16","alias_value":"63UGQOTZJSKVO2CA","created_at":"2026-07-05T01:52:32.232181+00:00"},{"alias_kind":"pith_short_8","alias_value":"63UGQOTZ","created_at":"2026-07-05T01:52:32.232181+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2003.00295","citing_title":"Adaptive Federated Optimization","ref_index":41,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/63UGQOTZJSKVO2CAAAPLYU5E2L","json":"https://pith.science/pith/63UGQOTZJSKVO2CAAAPLYU5E2L.json","graph_json":"https://pith.science/api/pith-number/63UGQOTZJSKVO2CAAAPLYU5E2L/graph.json","events_json":"https://pith.science/api/pith-number/63UGQOTZJSKVO2CAAAPLYU5E2L/events.json","paper":"https://pith.science/paper/63UGQOTZ"},"agent_actions":{"view_html":"https://pith.science/pith/63UGQOTZJSKVO2CAAAPLYU5E2L","download_json":"https://pith.science/pith/63UGQOTZJSKVO2CAAAPLYU5E2L.json","view_paper":"https://pith.science/paper/63UGQOTZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.02958&json=true","fetch_graph":"https://pith.science/api/pith-number/63UGQOTZJSKVO2CAAAPLYU5E2L/graph.json","fetch_events":"https://pith.science/api/pith-number/63UGQOTZJSKVO2CAAAPLYU5E2L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/63UGQOTZJSKVO2CAAAPLYU5E2L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/63UGQOTZJSKVO2CAAAPLYU5E2L/action/storage_attestation","attest_author":"https://pith.science/pith/63UGQOTZJSKVO2CAAAPLYU5E2L/action/author_attestation","sign_citation":"https://pith.science/pith/63UGQOTZJSKVO2CAAAPLYU5E2L/action/citation_signature","submit_replication":"https://pith.science/pith/63UGQOTZJSKVO2CAAAPLYU5E2L/action/replication_record"}},"created_at":"2026-07-05T01:52:32.232181+00:00","updated_at":"2026-07-05T01:52:32.232181+00:00"}