{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:SWZ74JCEYVZHDESMV5TSWR3DKY","short_pith_number":"pith:SWZ74JCE","schema_version":"1.0","canonical_sha256":"95b3fe2444c57271924caf672b47635605fb423ce5b6058f74e39a7084918111","source":{"kind":"arxiv","id":"1706.00241","version":1},"attestation_state":"computed","paper":{"title":"Krylov Subspace Recycling for Fast Iterative Least-Squares in Machine Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","stat.ML"],"primary_cat":"cs.LG","authors_text":"Filip de Roos, Philipp Hennig","submitted_at":"2017-06-01T10:17:12Z","abstract_excerpt":"Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time approximations, such as spectral and inducing-point methods, have been suggested and are now in wide use. These are low-rank approximations that choose the low-rank space a priori and do not refine it over time. While this allows linear cost in the data-set size, it also causes a finite, uncorrected approximation error. Authors from numerical linear algebra have e"},"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":"1706.00241","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-06-01T10:17:12Z","cross_cats_sorted":["math.NA","stat.ML"],"title_canon_sha256":"c76b9fd5a02c1e848a2e5b2ec2635ee8daca8ce3af7107035c413e7f402d566f","abstract_canon_sha256":"1b87efe37776597cbb11fd2f388a05efb030d0a55aa4ad14b51526996c5456c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:14.646363Z","signature_b64":"FMSCWP10hqq4Tqm2fD2tDRE3bQ14+aUXotKf/XCF7kPar64Gvn8kPUDBB1gB9hxjbVhvR4yQZM56xEDLGdGqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95b3fe2444c57271924caf672b47635605fb423ce5b6058f74e39a7084918111","last_reissued_at":"2026-05-18T00:43:14.645672Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:14.645672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Krylov Subspace Recycling for Fast Iterative Least-Squares in Machine Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","stat.ML"],"primary_cat":"cs.LG","authors_text":"Filip de Roos, Philipp Hennig","submitted_at":"2017-06-01T10:17:12Z","abstract_excerpt":"Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time approximations, such as spectral and inducing-point methods, have been suggested and are now in wide use. These are low-rank approximations that choose the low-rank space a priori and do not refine it over time. While this allows linear cost in the data-set size, it also causes a finite, uncorrected approximation error. Authors from numerical linear algebra have e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00241","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":""},"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":"1706.00241","created_at":"2026-05-18T00:43:14.645788+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.00241v1","created_at":"2026-05-18T00:43:14.645788+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00241","created_at":"2026-05-18T00:43:14.645788+00:00"},{"alias_kind":"pith_short_12","alias_value":"SWZ74JCEYVZH","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"SWZ74JCEYVZHDESM","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"SWZ74JCE","created_at":"2026-05-18T12:31:43.269735+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.02964","citing_title":"Contributed Discussion of \"A Bayesian Conjugate Gradient Method\"","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SWZ74JCEYVZHDESMV5TSWR3DKY","json":"https://pith.science/pith/SWZ74JCEYVZHDESMV5TSWR3DKY.json","graph_json":"https://pith.science/api/pith-number/SWZ74JCEYVZHDESMV5TSWR3DKY/graph.json","events_json":"https://pith.science/api/pith-number/SWZ74JCEYVZHDESMV5TSWR3DKY/events.json","paper":"https://pith.science/paper/SWZ74JCE"},"agent_actions":{"view_html":"https://pith.science/pith/SWZ74JCEYVZHDESMV5TSWR3DKY","download_json":"https://pith.science/pith/SWZ74JCEYVZHDESMV5TSWR3DKY.json","view_paper":"https://pith.science/paper/SWZ74JCE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.00241&json=true","fetch_graph":"https://pith.science/api/pith-number/SWZ74JCEYVZHDESMV5TSWR3DKY/graph.json","fetch_events":"https://pith.science/api/pith-number/SWZ74JCEYVZHDESMV5TSWR3DKY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SWZ74JCEYVZHDESMV5TSWR3DKY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SWZ74JCEYVZHDESMV5TSWR3DKY/action/storage_attestation","attest_author":"https://pith.science/pith/SWZ74JCEYVZHDESMV5TSWR3DKY/action/author_attestation","sign_citation":"https://pith.science/pith/SWZ74JCEYVZHDESMV5TSWR3DKY/action/citation_signature","submit_replication":"https://pith.science/pith/SWZ74JCEYVZHDESMV5TSWR3DKY/action/replication_record"}},"created_at":"2026-05-18T00:43:14.645788+00:00","updated_at":"2026-05-18T00:43:14.645788+00:00"}