{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:PUOCU4VGUZXI4KBW2MZD3PVTZL","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":"37b875e944ef271060d0da9636b69bcca758522bc59439a2e65520a2907bac8c","cross_cats_sorted":["cs.LG","math.OC","stat.ME","stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2022-06-17T13:15:27Z","title_canon_sha256":"e070153ea57aeffdc2ab820e80b7aa125d2fe08947aa1c309fe1d582d7003cba"},"schema_version":"1.0","source":{"id":"2206.08756","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.08756","created_at":"2026-07-05T07:33:47Z"},{"alias_kind":"arxiv_version","alias_value":"2206.08756v3","created_at":"2026-07-05T07:33:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.08756","created_at":"2026-07-05T07:33:47Z"},{"alias_kind":"pith_short_12","alias_value":"PUOCU4VGUZXI","created_at":"2026-07-05T07:33:47Z"},{"alias_kind":"pith_short_16","alias_value":"PUOCU4VGUZXI4KBW","created_at":"2026-07-05T07:33:47Z"},{"alias_kind":"pith_short_8","alias_value":"PUOCU4VG","created_at":"2026-07-05T07:33:47Z"}],"graph_snapshots":[{"event_id":"sha256:141be28f291b7d9add5cb3181529165eb5a5458bc070e55c810d2fcb97331bb0","target":"graph","created_at":"2026-07-05T07:33:47Z","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/2206.08756/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Anru R. Zhang, Yuetian Luo","cross_cats":["cs.LG","math.OC","stat.ME","stat.ML","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2022-06-17T13:15:27Z","title":"Tensor-on-Tensor Regression: Riemannian Optimization, Over-parameterization, Statistical-computational Gap, and Their Interplay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.08756","kind":"arxiv","version":3},"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:c8284f798556eb7831b8d45a949353dd9b2540859b4d35b6ca814653b8cd774f","target":"record","created_at":"2026-07-05T07:33:47Z","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":"37b875e944ef271060d0da9636b69bcca758522bc59439a2e65520a2907bac8c","cross_cats_sorted":["cs.LG","math.OC","stat.ME","stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2022-06-17T13:15:27Z","title_canon_sha256":"e070153ea57aeffdc2ab820e80b7aa125d2fe08947aa1c309fe1d582d7003cba"},"schema_version":"1.0","source":{"id":"2206.08756","kind":"arxiv","version":3}},"canonical_sha256":"7d1c2a72a6a66e8e2836d3323dbeb3cac15cf467d479cc91c1cba9762744631e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d1c2a72a6a66e8e2836d3323dbeb3cac15cf467d479cc91c1cba9762744631e","first_computed_at":"2026-07-05T07:33:47.325279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:33:47.325279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8iYnCFEhxSvU58NxAO4ErwieRrKt7IM7dcpygzxOzW18BYt4fo/hlCzBrc7mnaoZnNPiZPQwRapo5kqH+Y+3CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:33:47.325741Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.08756","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8284f798556eb7831b8d45a949353dd9b2540859b4d35b6ca814653b8cd774f","sha256:141be28f291b7d9add5cb3181529165eb5a5458bc070e55c810d2fcb97331bb0"],"state_sha256":"cd726f6391fe14f9a211574e70ec5d320574cf8e15f086b793416de42fea58d0"}