{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:XZI6XNA3OSGVQ5DOPQD5PLLLSR","short_pith_number":"pith:XZI6XNA3","schema_version":"1.0","canonical_sha256":"be51ebb41b748d58746e7c07d7ad6b94487fae16549fd5133fe191bfc3be2eb5","source":{"kind":"arxiv","id":"2401.01599","version":4},"attestation_state":"computed","paper":{"title":"Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decay","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Qian Lin, Weiye Gan, Yicheng Li, Zuoqiang Shi","submitted_at":"2024-01-03T08:00:50Z","abstract_excerpt":"The generalization error curve of certain kernel regression method aims at determining the exact order of generalization error with various source condition, noise level and choice of the regularization parameter rather than the minimax rate. In this work, under mild assumptions, we rigorously provide a full characterization of the generalization error curves of the kernel gradient descent method (and a large class of analytic spectral algorithms) in kernel regression. Consequently, we could sharpen the near inconsistency of kernel interpolation and clarify the saturation effects of kernel reg"},"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":"2401.01599","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-01-03T08:00:50Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"d745f34b8705ac83b15d121735520b2af9195d5af25de39256d501209d44b26d","abstract_canon_sha256":"94c6751b554bd99b86646ac71b61e77f0ed7619eff0e9656c7b096c40de4890d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:08:25.981835Z","signature_b64":"t5tik+EOj3Y0988Kqiyof5ofnRR+ePpUtIb5PJo+JcNDpUynHl2swprVY6Kh3U/dBMw7EWT+Svz62Rzosy5dCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be51ebb41b748d58746e7c07d7ad6b94487fae16549fd5133fe191bfc3be2eb5","last_reissued_at":"2026-06-09T02:08:25.981265Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:08:25.981265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decay","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Qian Lin, Weiye Gan, Yicheng Li, Zuoqiang Shi","submitted_at":"2024-01-03T08:00:50Z","abstract_excerpt":"The generalization error curve of certain kernel regression method aims at determining the exact order of generalization error with various source condition, noise level and choice of the regularization parameter rather than the minimax rate. In this work, under mild assumptions, we rigorously provide a full characterization of the generalization error curves of the kernel gradient descent method (and a large class of analytic spectral algorithms) in kernel regression. Consequently, we could sharpen the near inconsistency of kernel interpolation and clarify the saturation effects of kernel reg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.01599","kind":"arxiv","version":4},"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/2401.01599/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":"2401.01599","created_at":"2026-06-09T02:08:25.981346+00:00"},{"alias_kind":"arxiv_version","alias_value":"2401.01599v4","created_at":"2026-06-09T02:08:25.981346+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.01599","created_at":"2026-06-09T02:08:25.981346+00:00"},{"alias_kind":"pith_short_12","alias_value":"XZI6XNA3OSGV","created_at":"2026-06-09T02:08:25.981346+00:00"},{"alias_kind":"pith_short_16","alias_value":"XZI6XNA3OSGVQ5DO","created_at":"2026-06-09T02:08:25.981346+00:00"},{"alias_kind":"pith_short_8","alias_value":"XZI6XNA3","created_at":"2026-06-09T02:08:25.981346+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":3,"sample":[{"citing_arxiv_id":"2512.14473","citing_title":"Sharp convergence rates for Spectral methods via the feature space decomposition method","ref_index":14,"is_internal_anchor":true},{"citing_arxiv_id":"2509.20294","citing_title":"Alignment-Sensitive Minimax Rates for Spectral Algorithms with Learned Kernels","ref_index":33,"is_internal_anchor":true},{"citing_arxiv_id":"2605.14524","citing_title":"Large Dimensional Kernel Ridge Regression: Extending to Product Kernels","ref_index":134,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XZI6XNA3OSGVQ5DOPQD5PLLLSR","json":"https://pith.science/pith/XZI6XNA3OSGVQ5DOPQD5PLLLSR.json","graph_json":"https://pith.science/api/pith-number/XZI6XNA3OSGVQ5DOPQD5PLLLSR/graph.json","events_json":"https://pith.science/api/pith-number/XZI6XNA3OSGVQ5DOPQD5PLLLSR/events.json","paper":"https://pith.science/paper/XZI6XNA3"},"agent_actions":{"view_html":"https://pith.science/pith/XZI6XNA3OSGVQ5DOPQD5PLLLSR","download_json":"https://pith.science/pith/XZI6XNA3OSGVQ5DOPQD5PLLLSR.json","view_paper":"https://pith.science/paper/XZI6XNA3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2401.01599&json=true","fetch_graph":"https://pith.science/api/pith-number/XZI6XNA3OSGVQ5DOPQD5PLLLSR/graph.json","fetch_events":"https://pith.science/api/pith-number/XZI6XNA3OSGVQ5DOPQD5PLLLSR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XZI6XNA3OSGVQ5DOPQD5PLLLSR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XZI6XNA3OSGVQ5DOPQD5PLLLSR/action/storage_attestation","attest_author":"https://pith.science/pith/XZI6XNA3OSGVQ5DOPQD5PLLLSR/action/author_attestation","sign_citation":"https://pith.science/pith/XZI6XNA3OSGVQ5DOPQD5PLLLSR/action/citation_signature","submit_replication":"https://pith.science/pith/XZI6XNA3OSGVQ5DOPQD5PLLLSR/action/replication_record"}},"created_at":"2026-06-09T02:08:25.981346+00:00","updated_at":"2026-06-09T02:08:25.981346+00:00"}