{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KYXXA2XOVLISDS7JOQG42SGXZK","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":"4134f1aa0ae60b9cfba9723b6ada8847ff359b339b8e032ca9694829f0a45c55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-06-17T20:08:04Z","title_canon_sha256":"7ac374d6429542988deb7b57c6b991c7ca21641cfa0b4898365a856bb9669ce2"},"schema_version":"1.0","source":{"id":"1406.4519","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4519","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4519v1","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4519","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"pith_short_12","alias_value":"KYXXA2XOVLIS","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KYXXA2XOVLISDS7J","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KYXXA2XO","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:8b2793554c1eb4d544101533fb231210e21de63f0a64964485f4c5484b6def9d","target":"graph","created_at":"2026-05-18T02:49:31Z","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 present a technique for significantly speeding up Alternating Least Squares (ALS) and Gradient Descent (GD), two widely used algorithms for tensor factorization. By exploiting properties of the Khatri-Rao product, we show how to efficiently address a computationally challenging sub-step of both algorithms. Our algorithm, DFacTo, only requires two sparse matrix-vector products and is easy to parallelize. DFacTo is not only scalable but also on average 4 to 10 times faster than competing algorithms on a variety of datasets. For instance, DFacTo only takes 480 seconds on 4 machines to perform ","authors_text":"Joon Hee Choi, S. V. N. Vishwanathan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-06-17T20:08:04Z","title":"DFacTo: Distributed Factorization of Tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4519","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":"sha256:6819127c7fbc807be155620f80902e17e154729a779812a6a8f3821816225ebe","target":"record","created_at":"2026-05-18T02:49:31Z","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":"4134f1aa0ae60b9cfba9723b6ada8847ff359b339b8e032ca9694829f0a45c55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-06-17T20:08:04Z","title_canon_sha256":"7ac374d6429542988deb7b57c6b991c7ca21641cfa0b4898365a856bb9669ce2"},"schema_version":"1.0","source":{"id":"1406.4519","kind":"arxiv","version":1}},"canonical_sha256":"562f706aeeaad121cbe9740dcd48d7caab91f27d43af351f4bcf5b0e5cccc9ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"562f706aeeaad121cbe9740dcd48d7caab91f27d43af351f4bcf5b0e5cccc9ca","first_computed_at":"2026-05-18T02:49:31.305733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:31.305733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"snOBgf86ajvN8wTO2WdlSeSgpuhIzWRGADTcdyzvJpLSy0xlvFEs/4ueRoybvngxPivLeILAIwBBPhBcIVnvCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:31.306147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.4519","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6819127c7fbc807be155620f80902e17e154729a779812a6a8f3821816225ebe","sha256:8b2793554c1eb4d544101533fb231210e21de63f0a64964485f4c5484b6def9d"],"state_sha256":"aff941533a9370a5f1194e7da9aea7826158a6fc0ebddf489c026919fd14cb5b"}