{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:VNSS4LR2COK722AQHZQN47F4FQ","short_pith_number":"pith:VNSS4LR2","schema_version":"1.0","canonical_sha256":"ab652e2e3a1395fd68103e60de7cbc2c12eb5939314e2a55f96425b35bdeafe7","source":{"kind":"arxiv","id":"2505.23046","version":1},"attestation_state":"computed","paper":{"title":"Revisit CP Tensor Decomposition: Statistical Optimality and Fast Convergence","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.NA","math.NA","math.ST","stat.ML","stat.TH"],"primary_cat":"stat.ME","authors_text":"Anru R. Zhang, Julien Chhor, Olga Klopp, Runshi Tang","submitted_at":"2025-05-29T03:42:03Z","abstract_excerpt":"Canonical Polyadic (CP) tensor decomposition is a fundamental technique for analyzing high-dimensional tensor data. While the Alternating Least Squares (ALS) algorithm is widely used for computing CP decomposition due to its simplicity and empirical success, its theoretical foundation, particularly regarding statistical optimality and convergence behavior, remain underdeveloped, especially in noisy, non-orthogonal, and higher-rank settings.\n  In this work, we revisit CP tensor decomposition from a statistical perspective and provide a comprehensive theoretical analysis of ALS under a signal-pl"},"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":"2505.23046","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ME","submitted_at":"2025-05-29T03:42:03Z","cross_cats_sorted":["cs.NA","math.NA","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"04632a4fac78f804e61635a0988259b7058e01437ed2ae740652bc57c947cd09","abstract_canon_sha256":"9758b340cb50492a14f08dcef8eb409d4c39cd4ee104c76ee17d679acaffbae2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:54.320409Z","signature_b64":"fb5yv7ydXrdWAWbpeVl5Fk+JT81kpl83Q7Wiwfeo+SUaSKOZyiIJZOa3cuxdVcgeMGDIIqYm26qZaylmeLTNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab652e2e3a1395fd68103e60de7cbc2c12eb5939314e2a55f96425b35bdeafe7","last_reissued_at":"2026-07-05T11:11:54.319805Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:54.319805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Revisit CP Tensor Decomposition: Statistical Optimality and Fast Convergence","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.NA","math.NA","math.ST","stat.ML","stat.TH"],"primary_cat":"stat.ME","authors_text":"Anru R. Zhang, Julien Chhor, Olga Klopp, Runshi Tang","submitted_at":"2025-05-29T03:42:03Z","abstract_excerpt":"Canonical Polyadic (CP) tensor decomposition is a fundamental technique for analyzing high-dimensional tensor data. While the Alternating Least Squares (ALS) algorithm is widely used for computing CP decomposition due to its simplicity and empirical success, its theoretical foundation, particularly regarding statistical optimality and convergence behavior, remain underdeveloped, especially in noisy, non-orthogonal, and higher-rank settings.\n  In this work, we revisit CP tensor decomposition from a statistical perspective and provide a comprehensive theoretical analysis of ALS under a signal-pl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.23046","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.23046/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":"2505.23046","created_at":"2026-07-05T11:11:54.319894+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.23046v1","created_at":"2026-07-05T11:11:54.319894+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.23046","created_at":"2026-07-05T11:11:54.319894+00:00"},{"alias_kind":"pith_short_12","alias_value":"VNSS4LR2COK7","created_at":"2026-07-05T11:11:54.319894+00:00"},{"alias_kind":"pith_short_16","alias_value":"VNSS4LR2COK722AQ","created_at":"2026-07-05T11:11:54.319894+00:00"},{"alias_kind":"pith_short_8","alias_value":"VNSS4LR2","created_at":"2026-07-05T11:11:54.319894+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.24858","citing_title":"Optimal Estimation of Discrete Multiview Distributions under Heteroskedastic Multinomial Sampling","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2509.05221","citing_title":"A functional tensor model for dynamic multilayer networks with common invariant subspaces and the RKHS estimation","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2603.26029","citing_title":"Detection Is Harder Than Estimation in Certain Regimes: Inference for Moment and Cumulant Tensors","ref_index":60,"is_internal_anchor":false},{"citing_arxiv_id":"2604.10208","citing_title":"Mild Over-Parameterization Benefits Asymmetric Tensor PCA","ref_index":5,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VNSS4LR2COK722AQHZQN47F4FQ","json":"https://pith.science/pith/VNSS4LR2COK722AQHZQN47F4FQ.json","graph_json":"https://pith.science/api/pith-number/VNSS4LR2COK722AQHZQN47F4FQ/graph.json","events_json":"https://pith.science/api/pith-number/VNSS4LR2COK722AQHZQN47F4FQ/events.json","paper":"https://pith.science/paper/VNSS4LR2"},"agent_actions":{"view_html":"https://pith.science/pith/VNSS4LR2COK722AQHZQN47F4FQ","download_json":"https://pith.science/pith/VNSS4LR2COK722AQHZQN47F4FQ.json","view_paper":"https://pith.science/paper/VNSS4LR2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.23046&json=true","fetch_graph":"https://pith.science/api/pith-number/VNSS4LR2COK722AQHZQN47F4FQ/graph.json","fetch_events":"https://pith.science/api/pith-number/VNSS4LR2COK722AQHZQN47F4FQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VNSS4LR2COK722AQHZQN47F4FQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VNSS4LR2COK722AQHZQN47F4FQ/action/storage_attestation","attest_author":"https://pith.science/pith/VNSS4LR2COK722AQHZQN47F4FQ/action/author_attestation","sign_citation":"https://pith.science/pith/VNSS4LR2COK722AQHZQN47F4FQ/action/citation_signature","submit_replication":"https://pith.science/pith/VNSS4LR2COK722AQHZQN47F4FQ/action/replication_record"}},"created_at":"2026-07-05T11:11:54.319894+00:00","updated_at":"2026-07-05T11:11:54.319894+00:00"}