{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LW6VXZEY5LUVYDN43URBPTONTS","short_pith_number":"pith:LW6VXZEY","canonical_record":{"source":{"id":"1805.00184","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-05-01T04:41:58Z","cross_cats_sorted":["cs.AI","cs.LG"],"title_canon_sha256":"028f09cbf58d8a187e9e41aeef11730f0702835b19bf87e3a271b68f65ef63a3","abstract_canon_sha256":"afafa33964bfb52b1b7bfae69c654c68db9cd856c37cd6b6a804bd1af53b7e41"},"schema_version":"1.0"},"canonical_sha256":"5dbd5be498eae95c0dbcdd2217cdcd9c89a646b2190b0f80894ebdd83dc2cc33","source":{"kind":"arxiv","id":"1805.00184","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00184","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00184v1","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00184","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"LW6VXZEY5LUV","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LW6VXZEY5LUVYDN4","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LW6VXZEY","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LW6VXZEY5LUVYDN43URBPTONTS","target":"record","payload":{"canonical_record":{"source":{"id":"1805.00184","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-05-01T04:41:58Z","cross_cats_sorted":["cs.AI","cs.LG"],"title_canon_sha256":"028f09cbf58d8a187e9e41aeef11730f0702835b19bf87e3a271b68f65ef63a3","abstract_canon_sha256":"afafa33964bfb52b1b7bfae69c654c68db9cd856c37cd6b6a804bd1af53b7e41"},"schema_version":"1.0"},"canonical_sha256":"5dbd5be498eae95c0dbcdd2217cdcd9c89a646b2190b0f80894ebdd83dc2cc33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:10.356982Z","signature_b64":"NtawwDHgO/WhzlfSXGcGdmIbv4MjCYaEObrgmNUlhPUAVYrVyPZNyRIXo/kTM6U/+ebwVaQTT+KD/Thy40yCBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5dbd5be498eae95c0dbcdd2217cdcd9c89a646b2190b0f80894ebdd83dc2cc33","last_reissued_at":"2026-05-18T00:17:10.356082Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:10.356082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.00184","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xC33AMPiaJEdRd2yxtJismOZI6CdbDYTbow+74G9e6iLKfUrKuTvlzLoN/fWmMXr02NEsBlCEBIju/uySQwnCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:18:27.514155Z"},"content_sha256":"ab01b55b0323da624ebaf818bb72e6ab2af5da99705e07327379e2e2d8b6b277","schema_version":"1.0","event_id":"sha256:ab01b55b0323da624ebaf818bb72e6ab2af5da99705e07327379e2e2d8b6b277"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LW6VXZEY5LUVYDN43URBPTONTS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compact Factorization of Matrices Using Generalized Round-Rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG"],"primary_cat":"stat.ML","authors_text":"Carlos Guestrin, Pouya Pezeshkpour, Sameer Singh","submitted_at":"2018-05-01T04:41:58Z","abstract_excerpt":"Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a non-linear link function used within factorization. In particular, by applying the round function on a factorization to obtain ordinal-valued matrices, we introduce generalized round-rank (GRR). We show that not only are there many full-rank matrices that are low GRR, but further, that these matrices cannot be approximated well by low-rank linear factorization. We pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00184","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"do7FkdYUbuugzy8wJ8pvQsRcW82ybnylsvnnmkSqDjV2QXHRW8jZbc4aTBQBWkcgbpinUu3zYQRcwBLt1huZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:18:27.514834Z"},"content_sha256":"027c60ec0497cd293a1f651b5083fb5ff68820e9965157d048aa73d379c897a2","schema_version":"1.0","event_id":"sha256:027c60ec0497cd293a1f651b5083fb5ff68820e9965157d048aa73d379c897a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LW6VXZEY5LUVYDN43URBPTONTS/bundle.json","state_url":"https://pith.science/pith/LW6VXZEY5LUVYDN43URBPTONTS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LW6VXZEY5LUVYDN43URBPTONTS/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":"2026-06-08T14:18:27Z","links":{"resolver":"https://pith.science/pith/LW6VXZEY5LUVYDN43URBPTONTS","bundle":"https://pith.science/pith/LW6VXZEY5LUVYDN43URBPTONTS/bundle.json","state":"https://pith.science/pith/LW6VXZEY5LUVYDN43URBPTONTS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LW6VXZEY5LUVYDN43URBPTONTS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LW6VXZEY5LUVYDN43URBPTONTS","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":"afafa33964bfb52b1b7bfae69c654c68db9cd856c37cd6b6a804bd1af53b7e41","cross_cats_sorted":["cs.AI","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-05-01T04:41:58Z","title_canon_sha256":"028f09cbf58d8a187e9e41aeef11730f0702835b19bf87e3a271b68f65ef63a3"},"schema_version":"1.0","source":{"id":"1805.00184","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00184","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00184v1","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00184","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"LW6VXZEY5LUV","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LW6VXZEY5LUVYDN4","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LW6VXZEY","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:027c60ec0497cd293a1f651b5083fb5ff68820e9965157d048aa73d379c897a2","target":"graph","created_at":"2026-05-18T00:17:10Z","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":"Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a non-linear link function used within factorization. In particular, by applying the round function on a factorization to obtain ordinal-valued matrices, we introduce generalized round-rank (GRR). We show that not only are there many full-rank matrices that are low GRR, but further, that these matrices cannot be approximated well by low-rank linear factorization. We pr","authors_text":"Carlos Guestrin, Pouya Pezeshkpour, Sameer Singh","cross_cats":["cs.AI","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-05-01T04:41:58Z","title":"Compact Factorization of Matrices Using Generalized Round-Rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00184","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:ab01b55b0323da624ebaf818bb72e6ab2af5da99705e07327379e2e2d8b6b277","target":"record","created_at":"2026-05-18T00:17:10Z","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":"afafa33964bfb52b1b7bfae69c654c68db9cd856c37cd6b6a804bd1af53b7e41","cross_cats_sorted":["cs.AI","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-05-01T04:41:58Z","title_canon_sha256":"028f09cbf58d8a187e9e41aeef11730f0702835b19bf87e3a271b68f65ef63a3"},"schema_version":"1.0","source":{"id":"1805.00184","kind":"arxiv","version":1}},"canonical_sha256":"5dbd5be498eae95c0dbcdd2217cdcd9c89a646b2190b0f80894ebdd83dc2cc33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5dbd5be498eae95c0dbcdd2217cdcd9c89a646b2190b0f80894ebdd83dc2cc33","first_computed_at":"2026-05-18T00:17:10.356082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:10.356082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NtawwDHgO/WhzlfSXGcGdmIbv4MjCYaEObrgmNUlhPUAVYrVyPZNyRIXo/kTM6U/+ebwVaQTT+KD/Thy40yCBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:10.356982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00184","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab01b55b0323da624ebaf818bb72e6ab2af5da99705e07327379e2e2d8b6b277","sha256:027c60ec0497cd293a1f651b5083fb5ff68820e9965157d048aa73d379c897a2"],"state_sha256":"27ec4d76fec661d5e1360688269d8b8ff871f8b5be8fa31d572bbdfe0a6cd258"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ig0zxeg3N2HYeTBFqhZPlGRkyB1eGDmlyng/0XdTWbtF9Scr+l8xEcxjJYvvJmRmnu44HMIVLQFP4mrUHk8nCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T14:18:27.518287Z","bundle_sha256":"63b12f4a35485efc0be3602570c62fbebec3214cf4e8d3e2e2c8a2fd25b4332a"}}