{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GS23I7XJIYTO75E5T34KVS7YYU","short_pith_number":"pith:GS23I7XJ","canonical_record":{"source":{"id":"1806.07297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-19T14:57:18Z","cross_cats_sorted":["cs.AI","cs.LG","cs.SI"],"title_canon_sha256":"0fe889d5df288ac670f34e5174afc103fd3cf795b59f5bb2afe3a72c767c8d41","abstract_canon_sha256":"9221358b18785afb02b3e0b0411a5bf51e17b2bb73092a4715b9364b1c05ad76"},"schema_version":"1.0"},"canonical_sha256":"34b5b47ee94626eff49d9ef8aacbf8c50451406f23ea9b9bb197b66138ed038d","source":{"kind":"arxiv","id":"1806.07297","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07297","created_at":"2026-05-18T00:12:51Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07297v1","created_at":"2026-05-18T00:12:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07297","created_at":"2026-05-18T00:12:51Z"},{"alias_kind":"pith_short_12","alias_value":"GS23I7XJIYTO","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GS23I7XJIYTO75E5","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GS23I7XJ","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GS23I7XJIYTO75E5T34KVS7YYU","target":"record","payload":{"canonical_record":{"source":{"id":"1806.07297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-19T14:57:18Z","cross_cats_sorted":["cs.AI","cs.LG","cs.SI"],"title_canon_sha256":"0fe889d5df288ac670f34e5174afc103fd3cf795b59f5bb2afe3a72c767c8d41","abstract_canon_sha256":"9221358b18785afb02b3e0b0411a5bf51e17b2bb73092a4715b9364b1c05ad76"},"schema_version":"1.0"},"canonical_sha256":"34b5b47ee94626eff49d9ef8aacbf8c50451406f23ea9b9bb197b66138ed038d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:51.371044Z","signature_b64":"sE45f9hAMNpuHp9L0CH6ugjWro4vwCManTAwQSkzd74K1bj3Ee0TOEqVel1ekUJ8sp1ChRwIkh/YZPxEsDJ2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34b5b47ee94626eff49d9ef8aacbf8c50451406f23ea9b9bb197b66138ed038d","last_reissued_at":"2026-05-18T00:12:51.370510Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:51.370510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.07297","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":"2026-05-18T00:12:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"df0jQpJKeWtACMNH8/b4JJZDWkcJMJo9EE/Q5miMxiofXiIzK0jidnZneQSGWt7phakQAjXIS397sxW399oiAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T21:11:51.900963Z"},"content_sha256":"3d35451c1682d85a4ecf72e08bcce276213356125a4bdeeef1cd42363e6d8f3e","schema_version":"1.0","event_id":"sha256:3d35451c1682d85a4ecf72e08bcce276213356125a4bdeeef1cd42363e6d8f3e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GS23I7XJIYTO75E5T34KVS7YYU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Canonical Tensor Decomposition for Knowledge Base Completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG","cs.SI"],"primary_cat":"stat.ML","authors_text":"Guillaume Obozinski, Nicolas Usunier, Timoth\\'ee Lacroix","submitted_at":"2018-06-19T14:57:18Z","abstract_excerpt":"The problem of Knowledge Base Completion can be framed as a 3rd-order binary tensor completion problem. In this light, the Canonical Tensor Decomposition (CP) (Hitchcock, 1927) seems like a natural solution; however, current implementations of CP on standard Knowledge Base Completion benchmarks are lagging behind their competitors. In this work, we attempt to understand the limits of CP for knowledge base completion. First, we motivate and test a novel regularizer, based on tensor nuclear $p$-norms. Then, we present a reformulation of the problem that makes it invariant to arbitrary choices in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07297","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":"2026-05-18T00:12:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fFEbFE+f5qnSnwrfwzwlpKrHhPbPt+bqfLzZl9zxI2ALyPocm41bOd2EXrY4Qga3C2mnMKTjz7aCLC+cgQxtCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T21:11:51.901681Z"},"content_sha256":"df1e9c89f25745efe7795f0610e09fb1943f35d0e576915d3502476fdcc1a880","schema_version":"1.0","event_id":"sha256:df1e9c89f25745efe7795f0610e09fb1943f35d0e576915d3502476fdcc1a880"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GS23I7XJIYTO75E5T34KVS7YYU/bundle.json","state_url":"https://pith.science/pith/GS23I7XJIYTO75E5T34KVS7YYU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GS23I7XJIYTO75E5T34KVS7YYU/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":"2026-05-23T21:11:51Z","links":{"resolver":"https://pith.science/pith/GS23I7XJIYTO75E5T34KVS7YYU","bundle":"https://pith.science/pith/GS23I7XJIYTO75E5T34KVS7YYU/bundle.json","state":"https://pith.science/pith/GS23I7XJIYTO75E5T34KVS7YYU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GS23I7XJIYTO75E5T34KVS7YYU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GS23I7XJIYTO75E5T34KVS7YYU","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":"9221358b18785afb02b3e0b0411a5bf51e17b2bb73092a4715b9364b1c05ad76","cross_cats_sorted":["cs.AI","cs.LG","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-19T14:57:18Z","title_canon_sha256":"0fe889d5df288ac670f34e5174afc103fd3cf795b59f5bb2afe3a72c767c8d41"},"schema_version":"1.0","source":{"id":"1806.07297","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07297","created_at":"2026-05-18T00:12:51Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07297v1","created_at":"2026-05-18T00:12:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07297","created_at":"2026-05-18T00:12:51Z"},{"alias_kind":"pith_short_12","alias_value":"GS23I7XJIYTO","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GS23I7XJIYTO75E5","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GS23I7XJ","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:df1e9c89f25745efe7795f0610e09fb1943f35d0e576915d3502476fdcc1a880","target":"graph","created_at":"2026-05-18T00:12:51Z","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":"The problem of Knowledge Base Completion can be framed as a 3rd-order binary tensor completion problem. In this light, the Canonical Tensor Decomposition (CP) (Hitchcock, 1927) seems like a natural solution; however, current implementations of CP on standard Knowledge Base Completion benchmarks are lagging behind their competitors. In this work, we attempt to understand the limits of CP for knowledge base completion. First, we motivate and test a novel regularizer, based on tensor nuclear $p$-norms. Then, we present a reformulation of the problem that makes it invariant to arbitrary choices in","authors_text":"Guillaume Obozinski, Nicolas Usunier, Timoth\\'ee Lacroix","cross_cats":["cs.AI","cs.LG","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-19T14:57:18Z","title":"Canonical Tensor Decomposition for Knowledge Base Completion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07297","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":"sha256:3d35451c1682d85a4ecf72e08bcce276213356125a4bdeeef1cd42363e6d8f3e","target":"record","created_at":"2026-05-18T00:12:51Z","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":"9221358b18785afb02b3e0b0411a5bf51e17b2bb73092a4715b9364b1c05ad76","cross_cats_sorted":["cs.AI","cs.LG","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-19T14:57:18Z","title_canon_sha256":"0fe889d5df288ac670f34e5174afc103fd3cf795b59f5bb2afe3a72c767c8d41"},"schema_version":"1.0","source":{"id":"1806.07297","kind":"arxiv","version":1}},"canonical_sha256":"34b5b47ee94626eff49d9ef8aacbf8c50451406f23ea9b9bb197b66138ed038d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34b5b47ee94626eff49d9ef8aacbf8c50451406f23ea9b9bb197b66138ed038d","first_computed_at":"2026-05-18T00:12:51.370510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:51.370510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sE45f9hAMNpuHp9L0CH6ugjWro4vwCManTAwQSkzd74K1bj3Ee0TOEqVel1ekUJ8sp1ChRwIkh/YZPxEsDJ2Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:51.371044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.07297","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d35451c1682d85a4ecf72e08bcce276213356125a4bdeeef1cd42363e6d8f3e","sha256:df1e9c89f25745efe7795f0610e09fb1943f35d0e576915d3502476fdcc1a880"],"state_sha256":"e87faa540d54c0ffac52372620c5d7171c149f359e1651862ce4494f78cea93d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3b63MFiXJeQO5hNxo/BnR7ExJsMI9M86s3kVrTE9rVgteaCVZWUUOqm2UMB1JUWgyUe0Epv7AwsXkdG7YWA5Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T21:11:51.905775Z","bundle_sha256":"0452ac3761fefceb67ba48bd9668a4e90b99e3aec9ece9ef8a54fe93a8ea5479"}}