{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:N6UPRU2ULILVL2CFI7ZGQVRGN6","short_pith_number":"pith:N6UPRU2U","canonical_record":{"source":{"id":"2104.12031","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-04-24T22:24:14Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.OC","stat.ME"],"title_canon_sha256":"7425b226948b413cdd369984b75275ad9a591389a83b76383a01d095918cd9c0","abstract_canon_sha256":"c415f336f5f588f6ac6a6db0e51e42950869e9749cf6f8b6079ff9713e4aa1bd"},"schema_version":"1.0"},"canonical_sha256":"6fa8f8d3545a1755e84547f26856266fb40bf17991118670c1a74f846739aa00","source":{"kind":"arxiv","id":"2104.12031","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.12031","created_at":"2026-07-05T06:28:50Z"},{"alias_kind":"arxiv_version","alias_value":"2104.12031v4","created_at":"2026-07-05T06:28:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.12031","created_at":"2026-07-05T06:28:50Z"},{"alias_kind":"pith_short_12","alias_value":"N6UPRU2ULILV","created_at":"2026-07-05T06:28:50Z"},{"alias_kind":"pith_short_16","alias_value":"N6UPRU2ULILVL2CF","created_at":"2026-07-05T06:28:50Z"},{"alias_kind":"pith_short_8","alias_value":"N6UPRU2U","created_at":"2026-07-05T06:28:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:N6UPRU2ULILVL2CFI7ZGQVRGN6","target":"record","payload":{"canonical_record":{"source":{"id":"2104.12031","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-04-24T22:24:14Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.OC","stat.ME"],"title_canon_sha256":"7425b226948b413cdd369984b75275ad9a591389a83b76383a01d095918cd9c0","abstract_canon_sha256":"c415f336f5f588f6ac6a6db0e51e42950869e9749cf6f8b6079ff9713e4aa1bd"},"schema_version":"1.0"},"canonical_sha256":"6fa8f8d3545a1755e84547f26856266fb40bf17991118670c1a74f846739aa00","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:28:50.764622Z","signature_b64":"TPkS5kutjV1rtoTBME9+rTUx0W2AzSRpFTichd6aL+LnQP6tWvB7F61/H7rPDFr4h+Nyk79RTO0hA919ErO0CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fa8f8d3545a1755e84547f26856266fb40bf17991118670c1a74f846739aa00","last_reissued_at":"2026-07-05T06:28:50.764040Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:28:50.764040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.12031","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:28:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wiHOCKLCXDIFL4N4pLD3dvBm+JxqqoyT0PZdiEV2htik98cYnpNyIpnzvLBdwoDT6YuM3v2bO+vnJRZ0B55UDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T14:20:28.067692Z"},"content_sha256":"0b1633ab2a6f73dc1c40fb67261ccb7013feafea6c985e2b61de24c2c60f0769","schema_version":"1.0","event_id":"sha256:0b1633ab2a6f73dc1c40fb67261ccb7013feafea6c985e2b61de24c2c60f0769"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:N6UPRU2ULILVL2CFI7ZGQVRGN6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA","math.OC","stat.ME"],"primary_cat":"stat.ML","authors_text":"Anru R. Zhang, Yuetian Luo","submitted_at":"2021-04-24T22:24:14Z","abstract_excerpt":"In this paper, we consider the estimation of a low Tucker rank tensor from a number of noisy linear measurements. The general problem covers many specific examples arising from applications, including tensor regression, tensor completion, and tensor PCA/SVD. We consider an efficient Riemannian Gauss-Newton (RGN) method for low Tucker rank tensor estimation. Different from the generic (super)linear convergence guarantee of RGN in the literature, we prove the first local quadratic convergence guarantee of RGN for low-rank tensor estimation in the noisy setting under some regularity conditions an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.12031","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/2104.12031/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:28:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RymGsGgihXO8hYulPdcUWR0bctD5g4crhec2C6wPJydkIN/nEwmVzBNmIi5NjbYXk9yvmPsWQ3vvXMSGAfN5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T14:20:28.068537Z"},"content_sha256":"6795296b355db53f45568e315ae69c554f4081882967c71228f08c9163467f3d","schema_version":"1.0","event_id":"sha256:6795296b355db53f45568e315ae69c554f4081882967c71228f08c9163467f3d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N6UPRU2ULILVL2CFI7ZGQVRGN6/bundle.json","state_url":"https://pith.science/pith/N6UPRU2ULILVL2CFI7ZGQVRGN6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N6UPRU2ULILVL2CFI7ZGQVRGN6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-10T14:20:28Z","links":{"resolver":"https://pith.science/pith/N6UPRU2ULILVL2CFI7ZGQVRGN6","bundle":"https://pith.science/pith/N6UPRU2ULILVL2CFI7ZGQVRGN6/bundle.json","state":"https://pith.science/pith/N6UPRU2ULILVL2CFI7ZGQVRGN6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N6UPRU2ULILVL2CFI7ZGQVRGN6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:N6UPRU2ULILVL2CFI7ZGQVRGN6","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":"c415f336f5f588f6ac6a6db0e51e42950869e9749cf6f8b6079ff9713e4aa1bd","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.OC","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-04-24T22:24:14Z","title_canon_sha256":"7425b226948b413cdd369984b75275ad9a591389a83b76383a01d095918cd9c0"},"schema_version":"1.0","source":{"id":"2104.12031","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.12031","created_at":"2026-07-05T06:28:50Z"},{"alias_kind":"arxiv_version","alias_value":"2104.12031v4","created_at":"2026-07-05T06:28:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.12031","created_at":"2026-07-05T06:28:50Z"},{"alias_kind":"pith_short_12","alias_value":"N6UPRU2ULILV","created_at":"2026-07-05T06:28:50Z"},{"alias_kind":"pith_short_16","alias_value":"N6UPRU2ULILVL2CF","created_at":"2026-07-05T06:28:50Z"},{"alias_kind":"pith_short_8","alias_value":"N6UPRU2U","created_at":"2026-07-05T06:28:50Z"}],"graph_snapshots":[{"event_id":"sha256:6795296b355db53f45568e315ae69c554f4081882967c71228f08c9163467f3d","target":"graph","created_at":"2026-07-05T06:28:50Z","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/2104.12031/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we consider the estimation of a low Tucker rank tensor from a number of noisy linear measurements. The general problem covers many specific examples arising from applications, including tensor regression, tensor completion, and tensor PCA/SVD. We consider an efficient Riemannian Gauss-Newton (RGN) method for low Tucker rank tensor estimation. Different from the generic (super)linear convergence guarantee of RGN in the literature, we prove the first local quadratic convergence guarantee of RGN for low-rank tensor estimation in the noisy setting under some regularity conditions an","authors_text":"Anru R. Zhang, Yuetian Luo","cross_cats":["cs.LG","cs.NA","math.NA","math.OC","stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-04-24T22:24:14Z","title":"Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.12031","kind":"arxiv","version":4},"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":"sha256:0b1633ab2a6f73dc1c40fb67261ccb7013feafea6c985e2b61de24c2c60f0769","target":"record","created_at":"2026-07-05T06:28:50Z","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":"c415f336f5f588f6ac6a6db0e51e42950869e9749cf6f8b6079ff9713e4aa1bd","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.OC","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-04-24T22:24:14Z","title_canon_sha256":"7425b226948b413cdd369984b75275ad9a591389a83b76383a01d095918cd9c0"},"schema_version":"1.0","source":{"id":"2104.12031","kind":"arxiv","version":4}},"canonical_sha256":"6fa8f8d3545a1755e84547f26856266fb40bf17991118670c1a74f846739aa00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fa8f8d3545a1755e84547f26856266fb40bf17991118670c1a74f846739aa00","first_computed_at":"2026-07-05T06:28:50.764040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:28:50.764040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TPkS5kutjV1rtoTBME9+rTUx0W2AzSRpFTichd6aL+LnQP6tWvB7F61/H7rPDFr4h+Nyk79RTO0hA919ErO0CA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:28:50.764622Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.12031","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b1633ab2a6f73dc1c40fb67261ccb7013feafea6c985e2b61de24c2c60f0769","sha256:6795296b355db53f45568e315ae69c554f4081882967c71228f08c9163467f3d"],"state_sha256":"eb48e796f6c9151d92da75c7e0f9f381670313ae79eadd3b1d163e159a7a894d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TB6+mT7X1TiP2430quJFfXS1qZ5/1B6/BPTYShQQpD56YJ29pjgyT5t8XYQJZ6diXZdh+dKc1XTCYAcCIAPIAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T14:20:28.073869Z","bundle_sha256":"719d2bab85c2c37f0ef945c372b36605018293b1c9ffa85c01b6252f5dc6fe3d"}}