{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:TUXMEFA6DERV5ZN6XZEMLXT2KE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"51c31d139c09f2f35a56e847ddec6fd91c1cc553b9af8138c2b2e5862574c4b8","cross_cats_sorted":["cs.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-04-24T21:48:24Z","title_canon_sha256":"79297fc75b24044b6b2eaa3a5ce5e34ad9a987db006e1c7e96d4a1133498f240"},"schema_version":"1.0","source":{"id":"2304.12465","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.12465","created_at":"2026-08-12T01:24:10Z"},{"alias_kind":"arxiv_version","alias_value":"2304.12465v6","created_at":"2026-08-12T01:24:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.12465","created_at":"2026-08-12T01:24:10Z"},{"alias_kind":"pith_short_12","alias_value":"TUXMEFA6DERV","created_at":"2026-08-12T01:24:10Z"},{"alias_kind":"pith_short_16","alias_value":"TUXMEFA6DERV5ZN6","created_at":"2026-08-12T01:24:10Z"},{"alias_kind":"pith_short_8","alias_value":"TUXMEFA6","created_at":"2026-08-12T01:24:10Z"}],"graph_snapshots":[{"event_id":"sha256:c26fb3003d2db9e988367bfee69c6020160067a8c160ad0aa1e74dfd5feae8dd","target":"graph","created_at":"2026-08-12T01:24:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2304.12465/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate preconditioned conjugate gradient methods for kernel ridge regression (KRR) problems with a moderate to large number of data points ($10^4 \\leq N \\leq 10^7$). We develop and analyze two randomized preconditioners with complementary guarantees. For full-data KRR, RPCholesky preconditioning requires $O(N^2)$ arithmetic operations to achieve fixed accuracy under sufficiently rapid eigenvalue decay of the kernel matrix. For restricted KRR with $k\\ll N$ centers, KRILL preconditioning requires $O((N+k^2)k\\log k)$ operations with no eigenvalue-decay assumption. Experiments on benchmark","authors_text":"Ethan N. Epperly, Joel A. Tropp, Mateo D\\'iaz, Robert J. Webber, Zachary Frangella","cross_cats":["cs.NA","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-04-24T21:48:24Z","title":"Robust, randomized preconditioning for kernel ridge regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.12465","kind":"arxiv","version":6},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:918f1b211f57cd8d7e82cf3480c9ec48956ce7d43bbd7257a25d551f12c7f811","target":"record","created_at":"2026-08-12T01:24:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"51c31d139c09f2f35a56e847ddec6fd91c1cc553b9af8138c2b2e5862574c4b8","cross_cats_sorted":["cs.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-04-24T21:48:24Z","title_canon_sha256":"79297fc75b24044b6b2eaa3a5ce5e34ad9a987db006e1c7e96d4a1133498f240"},"schema_version":"1.0","source":{"id":"2304.12465","kind":"arxiv","version":6}},"canonical_sha256":"9d2ec2141e19235ee5bebe48c5de7a5110d5cb0f116456ba671d8862843476ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d2ec2141e19235ee5bebe48c5de7a5110d5cb0f116456ba671d8862843476ea","first_computed_at":"2026-08-12T01:24:10.554613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-12T01:24:10.554613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FpY4HwHkOl1/+67LhTa1lfV8dgdbXz+ETgRr7bMpGVdKdvqbiiP+9gbb1+BRmnRyutQikCcoIR9QYc4n0x0tDg==","signature_status":"signed_v1","signed_at":"2026-08-12T01:24:10.556243Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.12465","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:918f1b211f57cd8d7e82cf3480c9ec48956ce7d43bbd7257a25d551f12c7f811","sha256:c26fb3003d2db9e988367bfee69c6020160067a8c160ad0aa1e74dfd5feae8dd"],"state_sha256":"dd182637211381105ce3f26f7481c22fc221bd8d52893f439544eb40a48c756b"}