{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:N5DEMEH2IXEIL2CDUAQ7RLOKEH","short_pith_number":"pith:N5DEMEH2","schema_version":"1.0","canonical_sha256":"6f464610fa45c885e843a021f8adca21c1d09af9115e0fb138632faebdb8eadc","source":{"kind":"arxiv","id":"2512.14473","version":3},"attestation_state":"computed","paper":{"title":"Sharp convergence rates for Spectral methods via the feature space decomposition method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Guillaume Lecu\\'e, Zhifan Li, Zong Shang","submitted_at":"2025-12-16T15:01:51Z","abstract_excerpt":"In this paper, we apply the Feature Space Decomposition (FSD) method developed in [LS24, GLS25, LSSW26, ALSS26] to obtain, under fairly general conditions, matching upper and lower bounds for the population excess risk of spectral methods in linear regression under the squared loss, for every covariance and every signal. This result enables us, for a given linear regression problem, to define a pre-order on the set of spectral methods according to their convergence rates, thereby characterizing which spectral algorithm is superior for that specific problem. Furthermore, this allows us to gener"},"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":"2512.14473","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-12-16T15:01:51Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"c08a1ca7718621a7a088e77cd78dd247f85e603bd22532acc2559378334322f0","abstract_canon_sha256":"dc2f3b1495326cac6b276b427f2acdc23b34f63fd0c09797948200b12316f362"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:38.047718Z","signature_b64":"IpigZiCQaf+wF+GtjVwaXrH3Hqoj4JSJgryE38Y5XVW2nVS1C4FO8TN1jqo9IHjmN7wftib0KmW7FsFLtJpgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f464610fa45c885e843a021f8adca21c1d09af9115e0fb138632faebdb8eadc","last_reissued_at":"2026-05-20T00:01:38.046897Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:38.046897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp convergence rates for Spectral methods via the feature space decomposition method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Guillaume Lecu\\'e, Zhifan Li, Zong Shang","submitted_at":"2025-12-16T15:01:51Z","abstract_excerpt":"In this paper, we apply the Feature Space Decomposition (FSD) method developed in [LS24, GLS25, LSSW26, ALSS26] to obtain, under fairly general conditions, matching upper and lower bounds for the population excess risk of spectral methods in linear regression under the squared loss, for every covariance and every signal. This result enables us, for a given linear regression problem, to define a pre-order on the set of spectral methods according to their convergence rates, thereby characterizing which spectral algorithm is superior for that specific problem. Furthermore, this allows us to gener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.14473","kind":"arxiv","version":3},"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/2512.14473/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":"2512.14473","created_at":"2026-05-20T00:01:38.047013+00:00"},{"alias_kind":"arxiv_version","alias_value":"2512.14473v3","created_at":"2026-05-20T00:01:38.047013+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.14473","created_at":"2026-05-20T00:01:38.047013+00:00"},{"alias_kind":"pith_short_12","alias_value":"N5DEMEH2IXEI","created_at":"2026-05-20T00:01:38.047013+00:00"},{"alias_kind":"pith_short_16","alias_value":"N5DEMEH2IXEIL2CD","created_at":"2026-05-20T00:01:38.047013+00:00"},{"alias_kind":"pith_short_8","alias_value":"N5DEMEH2","created_at":"2026-05-20T00:01:38.047013+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/N5DEMEH2IXEIL2CDUAQ7RLOKEH","json":"https://pith.science/pith/N5DEMEH2IXEIL2CDUAQ7RLOKEH.json","graph_json":"https://pith.science/api/pith-number/N5DEMEH2IXEIL2CDUAQ7RLOKEH/graph.json","events_json":"https://pith.science/api/pith-number/N5DEMEH2IXEIL2CDUAQ7RLOKEH/events.json","paper":"https://pith.science/paper/N5DEMEH2"},"agent_actions":{"view_html":"https://pith.science/pith/N5DEMEH2IXEIL2CDUAQ7RLOKEH","download_json":"https://pith.science/pith/N5DEMEH2IXEIL2CDUAQ7RLOKEH.json","view_paper":"https://pith.science/paper/N5DEMEH2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2512.14473&json=true","fetch_graph":"https://pith.science/api/pith-number/N5DEMEH2IXEIL2CDUAQ7RLOKEH/graph.json","fetch_events":"https://pith.science/api/pith-number/N5DEMEH2IXEIL2CDUAQ7RLOKEH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N5DEMEH2IXEIL2CDUAQ7RLOKEH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N5DEMEH2IXEIL2CDUAQ7RLOKEH/action/storage_attestation","attest_author":"https://pith.science/pith/N5DEMEH2IXEIL2CDUAQ7RLOKEH/action/author_attestation","sign_citation":"https://pith.science/pith/N5DEMEH2IXEIL2CDUAQ7RLOKEH/action/citation_signature","submit_replication":"https://pith.science/pith/N5DEMEH2IXEIL2CDUAQ7RLOKEH/action/replication_record"}},"created_at":"2026-05-20T00:01:38.047013+00:00","updated_at":"2026-05-20T00:01:38.047013+00:00"}