{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:JPWGBK3DCLUAK4BFIMRGHTTTXZ","short_pith_number":"pith:JPWGBK3D","schema_version":"1.0","canonical_sha256":"4bec60ab6312e8057025432263ce73be76c4d12bf32498342cc029149b70e435","source":{"kind":"arxiv","id":"2201.10684","version":1},"attestation_state":"computed","paper":{"title":"Stochastic diagonal estimation: probabilistic bounds and an improved algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","math.PR"],"primary_cat":"cs.DS","authors_text":"Robert A. Baston, Yuji Nakatsukasa","submitted_at":"2022-01-26T00:05:12Z","abstract_excerpt":"We study the problem of estimating the diagonal of an implicitly given matrix $A$. For such a matrix we have access to an oracle that allows us to evaluate the matrix vector product $Av$. For random variable $v$ drawn from an appropriate distribution, this may be used to return an estimate of the diagonal of the matrix $A$. Whilst results exist for probabilistic guarantees relating to the error of estimates of the trace of $A$, no such results have yet been derived for the diagonal. We analyse the number of queries $s$ required to guarantee that with probability at least $1-\\delta$ the estimat"},"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":"2201.10684","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-01-26T00:05:12Z","cross_cats_sorted":["cs.NA","math.NA","math.PR"],"title_canon_sha256":"e0e449680c3b27c7411efc76790dac6b21a263f07e2f7bac54431ac8bc875a9a","abstract_canon_sha256":"598d8bedd842beff6b594a15a883a797fd084ee1df120242abac84fbee388803"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:51:48.612648Z","signature_b64":"AZ/u9rgNlpwzS8yDjt8azQkkQCsDZKX4z6rpI7RtVk3gFMsAQcS+lPTCmN26oG7I2MOFWnV5FFkDN5lw/+b0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bec60ab6312e8057025432263ce73be76c4d12bf32498342cc029149b70e435","last_reissued_at":"2026-07-05T03:51:48.612176Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:51:48.612176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic diagonal estimation: probabilistic bounds and an improved algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","math.PR"],"primary_cat":"cs.DS","authors_text":"Robert A. Baston, Yuji Nakatsukasa","submitted_at":"2022-01-26T00:05:12Z","abstract_excerpt":"We study the problem of estimating the diagonal of an implicitly given matrix $A$. For such a matrix we have access to an oracle that allows us to evaluate the matrix vector product $Av$. For random variable $v$ drawn from an appropriate distribution, this may be used to return an estimate of the diagonal of the matrix $A$. Whilst results exist for probabilistic guarantees relating to the error of estimates of the trace of $A$, no such results have yet been derived for the diagonal. We analyse the number of queries $s$ required to guarantee that with probability at least $1-\\delta$ the estimat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.10684","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/2201.10684/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":"2201.10684","created_at":"2026-07-05T03:51:48.612234+00:00"},{"alias_kind":"arxiv_version","alias_value":"2201.10684v1","created_at":"2026-07-05T03:51:48.612234+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.10684","created_at":"2026-07-05T03:51:48.612234+00:00"},{"alias_kind":"pith_short_12","alias_value":"JPWGBK3DCLUA","created_at":"2026-07-05T03:51:48.612234+00:00"},{"alias_kind":"pith_short_16","alias_value":"JPWGBK3DCLUAK4BF","created_at":"2026-07-05T03:51:48.612234+00:00"},{"alias_kind":"pith_short_8","alias_value":"JPWGBK3D","created_at":"2026-07-05T03:51:48.612234+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.01627","citing_title":"Importance-Guided Basis Selection for Low-Rank Decomposition of Large Language Models","ref_index":2,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JPWGBK3DCLUAK4BFIMRGHTTTXZ","json":"https://pith.science/pith/JPWGBK3DCLUAK4BFIMRGHTTTXZ.json","graph_json":"https://pith.science/api/pith-number/JPWGBK3DCLUAK4BFIMRGHTTTXZ/graph.json","events_json":"https://pith.science/api/pith-number/JPWGBK3DCLUAK4BFIMRGHTTTXZ/events.json","paper":"https://pith.science/paper/JPWGBK3D"},"agent_actions":{"view_html":"https://pith.science/pith/JPWGBK3DCLUAK4BFIMRGHTTTXZ","download_json":"https://pith.science/pith/JPWGBK3DCLUAK4BFIMRGHTTTXZ.json","view_paper":"https://pith.science/paper/JPWGBK3D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2201.10684&json=true","fetch_graph":"https://pith.science/api/pith-number/JPWGBK3DCLUAK4BFIMRGHTTTXZ/graph.json","fetch_events":"https://pith.science/api/pith-number/JPWGBK3DCLUAK4BFIMRGHTTTXZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JPWGBK3DCLUAK4BFIMRGHTTTXZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JPWGBK3DCLUAK4BFIMRGHTTTXZ/action/storage_attestation","attest_author":"https://pith.science/pith/JPWGBK3DCLUAK4BFIMRGHTTTXZ/action/author_attestation","sign_citation":"https://pith.science/pith/JPWGBK3DCLUAK4BFIMRGHTTTXZ/action/citation_signature","submit_replication":"https://pith.science/pith/JPWGBK3DCLUAK4BFIMRGHTTTXZ/action/replication_record"}},"created_at":"2026-07-05T03:51:48.612234+00:00","updated_at":"2026-07-05T03:51:48.612234+00:00"}