{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:PUOCU4VGUZXI4KBW2MZD3PVTZL","short_pith_number":"pith:PUOCU4VG","schema_version":"1.0","canonical_sha256":"7d1c2a72a6a66e8e2836d3323dbeb3cac15cf467d479cc91c1cba9762744631e","source":{"kind":"arxiv","id":"2206.08756","version":3},"attestation_state":"computed","paper":{"title":"Tensor-on-Tensor Regression: Riemannian Optimization, Over-parameterization, Statistical-computational Gap, and Their Interplay","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.OC","stat.ME","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Anru R. Zhang, Yuetian Luo","submitted_at":"2022-06-17T13:15:27Z","abstract_excerpt":"We study the tensor-on-tensor regression, where the goal is to connect tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without the prior knowledge of its intrinsic rank. We propose the Riemannian gradient descent (RGD) and Riemannian Gauss-Newton (RGN) methods and cope with the challenge of unknown rank by studying the effect of rank over-parameterization. We provide the first convergence guarantee for the general tensor-on-tensor regression by showing that RGD and RGN respectively converge linearly and quadratically to a statistically optimal estimate in b"},"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":"2206.08756","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2022-06-17T13:15:27Z","cross_cats_sorted":["cs.LG","math.OC","stat.ME","stat.ML","stat.TH"],"title_canon_sha256":"e070153ea57aeffdc2ab820e80b7aa125d2fe08947aa1c309fe1d582d7003cba","abstract_canon_sha256":"37b875e944ef271060d0da9636b69bcca758522bc59439a2e65520a2907bac8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:33:47.325741Z","signature_b64":"8iYnCFEhxSvU58NxAO4ErwieRrKt7IM7dcpygzxOzW18BYt4fo/hlCzBrc7mnaoZnNPiZPQwRapo5kqH+Y+3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d1c2a72a6a66e8e2836d3323dbeb3cac15cf467d479cc91c1cba9762744631e","last_reissued_at":"2026-07-05T07:33:47.325279Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:33:47.325279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tensor-on-Tensor Regression: Riemannian Optimization, Over-parameterization, Statistical-computational Gap, and Their Interplay","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.OC","stat.ME","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Anru R. Zhang, Yuetian Luo","submitted_at":"2022-06-17T13:15:27Z","abstract_excerpt":"We study the tensor-on-tensor regression, where the goal is to connect tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without the prior knowledge of its intrinsic rank. We propose the Riemannian gradient descent (RGD) and Riemannian Gauss-Newton (RGN) methods and cope with the challenge of unknown rank by studying the effect of rank over-parameterization. We provide the first convergence guarantee for the general tensor-on-tensor regression by showing that RGD and RGN respectively converge linearly and quadratically to a statistically optimal estimate in b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.08756","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/2206.08756/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":"2206.08756","created_at":"2026-07-05T07:33:47.325344+00:00"},{"alias_kind":"arxiv_version","alias_value":"2206.08756v3","created_at":"2026-07-05T07:33:47.325344+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.08756","created_at":"2026-07-05T07:33:47.325344+00:00"},{"alias_kind":"pith_short_12","alias_value":"PUOCU4VGUZXI","created_at":"2026-07-05T07:33:47.325344+00:00"},{"alias_kind":"pith_short_16","alias_value":"PUOCU4VGUZXI4KBW","created_at":"2026-07-05T07:33:47.325344+00:00"},{"alias_kind":"pith_short_8","alias_value":"PUOCU4VG","created_at":"2026-07-05T07:33:47.325344+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.16032","citing_title":"A Scalable Factorization Approach for High-Order Structured Tensor Recovery","ref_index":67,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PUOCU4VGUZXI4KBW2MZD3PVTZL","json":"https://pith.science/pith/PUOCU4VGUZXI4KBW2MZD3PVTZL.json","graph_json":"https://pith.science/api/pith-number/PUOCU4VGUZXI4KBW2MZD3PVTZL/graph.json","events_json":"https://pith.science/api/pith-number/PUOCU4VGUZXI4KBW2MZD3PVTZL/events.json","paper":"https://pith.science/paper/PUOCU4VG"},"agent_actions":{"view_html":"https://pith.science/pith/PUOCU4VGUZXI4KBW2MZD3PVTZL","download_json":"https://pith.science/pith/PUOCU4VGUZXI4KBW2MZD3PVTZL.json","view_paper":"https://pith.science/paper/PUOCU4VG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2206.08756&json=true","fetch_graph":"https://pith.science/api/pith-number/PUOCU4VGUZXI4KBW2MZD3PVTZL/graph.json","fetch_events":"https://pith.science/api/pith-number/PUOCU4VGUZXI4KBW2MZD3PVTZL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PUOCU4VGUZXI4KBW2MZD3PVTZL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PUOCU4VGUZXI4KBW2MZD3PVTZL/action/storage_attestation","attest_author":"https://pith.science/pith/PUOCU4VGUZXI4KBW2MZD3PVTZL/action/author_attestation","sign_citation":"https://pith.science/pith/PUOCU4VGUZXI4KBW2MZD3PVTZL/action/citation_signature","submit_replication":"https://pith.science/pith/PUOCU4VGUZXI4KBW2MZD3PVTZL/action/replication_record"}},"created_at":"2026-07-05T07:33:47.325344+00:00","updated_at":"2026-07-05T07:33:47.325344+00:00"}