{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:OUD4GWMDP5YSJKZAWITBPQSEDO","short_pith_number":"pith:OUD4GWMD","canonical_record":{"source":{"id":"2110.07631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-10-14T18:00:31Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"c1296993bb8730d6e6a596a7479abb0b03d0e909dfd81493977c8a2bf46691ba","abstract_canon_sha256":"f2c7b7fab0afa985244470b6fcaddc806aee9f72896f1f7153209ca9f591cbb6"},"schema_version":"1.0"},"canonical_sha256":"7507c359837f7124ab20b22617c2441b85c507d388ae0bbc5308120a2f2cb15d","source":{"kind":"arxiv","id":"2110.07631","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.07631","created_at":"2026-07-05T04:32:52Z"},{"alias_kind":"arxiv_version","alias_value":"2110.07631v2","created_at":"2026-07-05T04:32:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.07631","created_at":"2026-07-05T04:32:52Z"},{"alias_kind":"pith_short_12","alias_value":"OUD4GWMDP5YS","created_at":"2026-07-05T04:32:52Z"},{"alias_kind":"pith_short_16","alias_value":"OUD4GWMDP5YSJKZA","created_at":"2026-07-05T04:32:52Z"},{"alias_kind":"pith_short_8","alias_value":"OUD4GWMD","created_at":"2026-07-05T04:32:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:OUD4GWMDP5YSJKZAWITBPQSEDO","target":"record","payload":{"canonical_record":{"source":{"id":"2110.07631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-10-14T18:00:31Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"c1296993bb8730d6e6a596a7479abb0b03d0e909dfd81493977c8a2bf46691ba","abstract_canon_sha256":"f2c7b7fab0afa985244470b6fcaddc806aee9f72896f1f7153209ca9f591cbb6"},"schema_version":"1.0"},"canonical_sha256":"7507c359837f7124ab20b22617c2441b85c507d388ae0bbc5308120a2f2cb15d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:32:52.112960Z","signature_b64":"Ir47WUk9Ynmg1L1AZ33RbhCc9FSmqvR9Lkrpuo9QHN5/ZYhLUMDVsq+7Svi59kqjpmANslwsBWqIU0hT8MQoCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7507c359837f7124ab20b22617c2441b85c507d388ae0bbc5308120a2f2cb15d","last_reissued_at":"2026-07-05T04:32:52.112536Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:32:52.112536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.07631","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:32:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hu0TRcy764S8Bp4ThGo4pdK/k5HpTE0QU/mNUOXpEvADPO20xqRXeo9gB6/toe0KVKriuGsp7OQVg31FA4/nBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T15:41:18.190680Z"},"content_sha256":"3f32842cf09f30daf1417318b0521c57465b91d9d71625e242de3ff9751bcb5d","schema_version":"1.0","event_id":"sha256:3f32842cf09f30daf1417318b0521c57465b91d9d71625e242de3ff9751bcb5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:OUD4GWMDP5YSJKZAWITBPQSEDO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA"],"primary_cat":"math.NA","authors_text":"Osman Asif Malik","submitted_at":"2021-10-14T18:00:31Z","abstract_excerpt":"Recent papers have developed alternating least squares (ALS) methods for CP and tensor ring decomposition with a per-iteration cost which is sublinear in the number of input tensor entries for low-rank decomposition. However, the per-iteration cost of these methods still has an exponential dependence on the number of tensor modes when parameters are chosen to achieve certain worst-case guarantees. In this paper, we propose sampling-based ALS methods for the CP and tensor ring decompositions whose cost does not have this exponential dependence, thereby significantly improving on the previous st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.07631","kind":"arxiv","version":2},"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/2110.07631/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":"2026-07-05T04:32:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l0wPDBdGnrI3qEAktaLLA/N6wDI3qBoR1/ezPn1vCzdd36e4wy5A6mVS1H5S6ZoDGs7LxOBIooYtokjzNOPbCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T15:41:18.191049Z"},"content_sha256":"e6140797c474281700429c71ac515efa24ca9a7055ffbf9b06a5cce8ae5fdbe3","schema_version":"1.0","event_id":"sha256:e6140797c474281700429c71ac515efa24ca9a7055ffbf9b06a5cce8ae5fdbe3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OUD4GWMDP5YSJKZAWITBPQSEDO/bundle.json","state_url":"https://pith.science/pith/OUD4GWMDP5YSJKZAWITBPQSEDO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OUD4GWMDP5YSJKZAWITBPQSEDO/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":"2026-07-06T15:41:18Z","links":{"resolver":"https://pith.science/pith/OUD4GWMDP5YSJKZAWITBPQSEDO","bundle":"https://pith.science/pith/OUD4GWMDP5YSJKZAWITBPQSEDO/bundle.json","state":"https://pith.science/pith/OUD4GWMDP5YSJKZAWITBPQSEDO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OUD4GWMDP5YSJKZAWITBPQSEDO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:OUD4GWMDP5YSJKZAWITBPQSEDO","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":"f2c7b7fab0afa985244470b6fcaddc806aee9f72896f1f7153209ca9f591cbb6","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-10-14T18:00:31Z","title_canon_sha256":"c1296993bb8730d6e6a596a7479abb0b03d0e909dfd81493977c8a2bf46691ba"},"schema_version":"1.0","source":{"id":"2110.07631","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.07631","created_at":"2026-07-05T04:32:52Z"},{"alias_kind":"arxiv_version","alias_value":"2110.07631v2","created_at":"2026-07-05T04:32:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.07631","created_at":"2026-07-05T04:32:52Z"},{"alias_kind":"pith_short_12","alias_value":"OUD4GWMDP5YS","created_at":"2026-07-05T04:32:52Z"},{"alias_kind":"pith_short_16","alias_value":"OUD4GWMDP5YSJKZA","created_at":"2026-07-05T04:32:52Z"},{"alias_kind":"pith_short_8","alias_value":"OUD4GWMD","created_at":"2026-07-05T04:32:52Z"}],"graph_snapshots":[{"event_id":"sha256:e6140797c474281700429c71ac515efa24ca9a7055ffbf9b06a5cce8ae5fdbe3","target":"graph","created_at":"2026-07-05T04:32:52Z","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/2110.07631/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recent papers have developed alternating least squares (ALS) methods for CP and tensor ring decomposition with a per-iteration cost which is sublinear in the number of input tensor entries for low-rank decomposition. However, the per-iteration cost of these methods still has an exponential dependence on the number of tensor modes when parameters are chosen to achieve certain worst-case guarantees. In this paper, we propose sampling-based ALS methods for the CP and tensor ring decompositions whose cost does not have this exponential dependence, thereby significantly improving on the previous st","authors_text":"Osman Asif Malik","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-10-14T18:00:31Z","title":"More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.07631","kind":"arxiv","version":2},"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":"sha256:3f32842cf09f30daf1417318b0521c57465b91d9d71625e242de3ff9751bcb5d","target":"record","created_at":"2026-07-05T04:32:52Z","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":"f2c7b7fab0afa985244470b6fcaddc806aee9f72896f1f7153209ca9f591cbb6","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-10-14T18:00:31Z","title_canon_sha256":"c1296993bb8730d6e6a596a7479abb0b03d0e909dfd81493977c8a2bf46691ba"},"schema_version":"1.0","source":{"id":"2110.07631","kind":"arxiv","version":2}},"canonical_sha256":"7507c359837f7124ab20b22617c2441b85c507d388ae0bbc5308120a2f2cb15d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7507c359837f7124ab20b22617c2441b85c507d388ae0bbc5308120a2f2cb15d","first_computed_at":"2026-07-05T04:32:52.112536Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:32:52.112536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ir47WUk9Ynmg1L1AZ33RbhCc9FSmqvR9Lkrpuo9QHN5/ZYhLUMDVsq+7Svi59kqjpmANslwsBWqIU0hT8MQoCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:32:52.112960Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.07631","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f32842cf09f30daf1417318b0521c57465b91d9d71625e242de3ff9751bcb5d","sha256:e6140797c474281700429c71ac515efa24ca9a7055ffbf9b06a5cce8ae5fdbe3"],"state_sha256":"e870782dbc005f7aeedebfa4b25ddaa612d06e9bb8c5110cd217b52789c42b1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uY90Ft4l+2criSWi8jKtFQn6uHaz7l8E0f0EpKtkpjFa5c2IXYDXi5/rATsnwR6yHmNY8ldkNCMdM9LsD2APDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T15:41:18.193047Z","bundle_sha256":"7ab959bf19fcde8449ac47dc06adeb84f16ec44ece987f4084a8d60401d5a2fd"}}