{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:XAH2FOR5CYVVKPQ5DUWZLTXDG4","short_pith_number":"pith:XAH2FOR5","schema_version":"1.0","canonical_sha256":"b80fa2ba3d162b553e1d1d2d95cee337196ae67ff21f36cb3def275a2bcdb3d9","source":{"kind":"arxiv","id":"2405.05818","version":2},"attestation_state":"computed","paper":{"title":"Fine-grained Analysis and Faster Algorithms for Iteratively Solving Linear Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA","math.OC"],"primary_cat":"cs.DS","authors_text":"Daniel LeJeune, Deanna Needell, Elizaveta Rebrova, Micha{\\l} Derezi\\'nski","submitted_at":"2024-05-09T14:56:49Z","abstract_excerpt":"Despite being a key bottleneck in many machine learning tasks, the cost of solving large linear systems has proven challenging to quantify due to problem-dependent quantities such as condition numbers. To tackle this, we consider a fine-grained notion of complexity for solving linear systems, which is motivated by applications where the data exhibits low-dimensional structure, including spiked covariance models and kernel machines, and when the linear system is explicitly regularized, such as ridge regression. Concretely, let $\\kappa_\\ell$ be the ratio between the $\\ell$th largest and the smal"},"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":"2405.05818","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-05-09T14:56:49Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.OC"],"title_canon_sha256":"59515f7c9130128cefa92ba2ea33cf765b2c5b5ed178c70f7d852e3c74dcda48","abstract_canon_sha256":"ceb3201e872f77632c1daf748f07d665d4e6d79f3baacd0b46b97dccc6cea229"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:22:30.475942Z","signature_b64":"a2ARE1aE0ujJYEOpjA3qLIgta/jKCja2untfB0OG+bp0FANssaBx3qEaS7ThhITOHOUjZ/4Eio00gd1rjiARBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b80fa2ba3d162b553e1d1d2d95cee337196ae67ff21f36cb3def275a2bcdb3d9","last_reissued_at":"2026-07-05T11:22:30.475367Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:22:30.475367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fine-grained Analysis and Faster Algorithms for Iteratively Solving Linear Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA","math.OC"],"primary_cat":"cs.DS","authors_text":"Daniel LeJeune, Deanna Needell, Elizaveta Rebrova, Micha{\\l} Derezi\\'nski","submitted_at":"2024-05-09T14:56:49Z","abstract_excerpt":"Despite being a key bottleneck in many machine learning tasks, the cost of solving large linear systems has proven challenging to quantify due to problem-dependent quantities such as condition numbers. To tackle this, we consider a fine-grained notion of complexity for solving linear systems, which is motivated by applications where the data exhibits low-dimensional structure, including spiked covariance models and kernel machines, and when the linear system is explicitly regularized, such as ridge regression. Concretely, let $\\kappa_\\ell$ be the ratio between the $\\ell$th largest and the smal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.05818","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/2405.05818/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":"2405.05818","created_at":"2026-07-05T11:22:30.475427+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.05818v2","created_at":"2026-07-05T11:22:30.475427+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.05818","created_at":"2026-07-05T11:22:30.475427+00:00"},{"alias_kind":"pith_short_12","alias_value":"XAH2FOR5CYVV","created_at":"2026-07-05T11:22:30.475427+00:00"},{"alias_kind":"pith_short_16","alias_value":"XAH2FOR5CYVVKPQ5","created_at":"2026-07-05T11:22:30.475427+00:00"},{"alias_kind":"pith_short_8","alias_value":"XAH2FOR5","created_at":"2026-07-05T11:22:30.475427+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.21022","citing_title":"A Sketch-and-Project Analysis of Subsampled Natural Gradient Algorithms","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XAH2FOR5CYVVKPQ5DUWZLTXDG4","json":"https://pith.science/pith/XAH2FOR5CYVVKPQ5DUWZLTXDG4.json","graph_json":"https://pith.science/api/pith-number/XAH2FOR5CYVVKPQ5DUWZLTXDG4/graph.json","events_json":"https://pith.science/api/pith-number/XAH2FOR5CYVVKPQ5DUWZLTXDG4/events.json","paper":"https://pith.science/paper/XAH2FOR5"},"agent_actions":{"view_html":"https://pith.science/pith/XAH2FOR5CYVVKPQ5DUWZLTXDG4","download_json":"https://pith.science/pith/XAH2FOR5CYVVKPQ5DUWZLTXDG4.json","view_paper":"https://pith.science/paper/XAH2FOR5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.05818&json=true","fetch_graph":"https://pith.science/api/pith-number/XAH2FOR5CYVVKPQ5DUWZLTXDG4/graph.json","fetch_events":"https://pith.science/api/pith-number/XAH2FOR5CYVVKPQ5DUWZLTXDG4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XAH2FOR5CYVVKPQ5DUWZLTXDG4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XAH2FOR5CYVVKPQ5DUWZLTXDG4/action/storage_attestation","attest_author":"https://pith.science/pith/XAH2FOR5CYVVKPQ5DUWZLTXDG4/action/author_attestation","sign_citation":"https://pith.science/pith/XAH2FOR5CYVVKPQ5DUWZLTXDG4/action/citation_signature","submit_replication":"https://pith.science/pith/XAH2FOR5CYVVKPQ5DUWZLTXDG4/action/replication_record"}},"created_at":"2026-07-05T11:22:30.475427+00:00","updated_at":"2026-07-05T11:22:30.475427+00:00"}