{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EL2Z4IJPJWEW2PXT2ITT67WU2K","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":"479edf8b1e86e81cfb369add6c109f712674f49df8269b206f9d104aab174dc4","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-20T22:05:49Z","title_canon_sha256":"fde1844f4b9342a250f0547f19a1d8972a6c492e17ace9e9edfe4c2db3194249"},"schema_version":"1.0","source":{"id":"1709.07093","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.07093","created_at":"2026-05-18T00:34:36Z"},{"alias_kind":"arxiv_version","alias_value":"1709.07093v1","created_at":"2026-05-18T00:34:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.07093","created_at":"2026-05-18T00:34:36Z"},{"alias_kind":"pith_short_12","alias_value":"EL2Z4IJPJWEW","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EL2Z4IJPJWEW2PXT","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EL2Z4IJP","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:a1301ea3b423b26196fa908f055f28a57084839d64b68f12f799a3907c4b442b","target":"graph","created_at":"2026-05-18T00:34:36Z","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"},"paper":{"abstract_excerpt":"We study the least squares regression problem \\begin{align*} \\min_{\\Theta \\in \\mathcal{S}_{\\odot D,R}} \\|A\\Theta-b\\|_2, \\end{align*} where $\\mathcal{S}_{\\odot D,R}$ is the set of $\\Theta$ for which $\\Theta = \\sum_{r=1}^{R} \\theta_1^{(r)} \\circ \\cdots \\circ \\theta_D^{(r)}$ for vectors $\\theta_d^{(r)} \\in \\mathbb{R}^{p_d}$ for all $r \\in [R]$ and $d \\in [D]$, and $\\circ$ denotes the outer product of vectors. That is, $\\Theta$ is a low-dimensional, low-rank tensor. This is motivated by the fact that the number of parameters in $\\Theta$ is only $R \\cdot \\sum_{d=1}^D p_d$, which is significantly sm","authors_text":"David P. Woodruff, Jarvis Haupt, Xingguo Li","cross_cats":["cs.DS","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-20T22:05:49Z","title":"Near Optimal Sketching of Low-Rank Tensor Regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07093","kind":"arxiv","version":1},"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:cd710174b775fdccd14c3067882348ef1774de2b33922dcfda98033bc9027b8f","target":"record","created_at":"2026-05-18T00:34:36Z","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":"479edf8b1e86e81cfb369add6c109f712674f49df8269b206f9d104aab174dc4","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-20T22:05:49Z","title_canon_sha256":"fde1844f4b9342a250f0547f19a1d8972a6c492e17ace9e9edfe4c2db3194249"},"schema_version":"1.0","source":{"id":"1709.07093","kind":"arxiv","version":1}},"canonical_sha256":"22f59e212f4d896d3ef3d2273f7ed4d2828ffca7a9af0198d2629eb094204cff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22f59e212f4d896d3ef3d2273f7ed4d2828ffca7a9af0198d2629eb094204cff","first_computed_at":"2026-05-18T00:34:36.593525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:36.593525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3yElQeEt2PFkGgelF8l3+/bZD7tSwShQcpEtk1l+Iv8Hsfmx6tlz/HlFgikjDM7ZvaKxZbz3z7k5AMS2pZ6+Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:36.594170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.07093","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd710174b775fdccd14c3067882348ef1774de2b33922dcfda98033bc9027b8f","sha256:a1301ea3b423b26196fa908f055f28a57084839d64b68f12f799a3907c4b442b"],"state_sha256":"7e86d020a71b86a63b2cf594f2d12cdc474d1b569d06206f08cf6eeba0bfc84e"}