{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:JAIICLSUBCLN2LWDOYBXQYAOH2","short_pith_number":"pith:JAIICLSU","schema_version":"1.0","canonical_sha256":"4810812e540896dd2ec3760378600e3e8249353330fca41cc1f680403f4080f4","source":{"kind":"arxiv","id":"1506.07540","version":1},"attestation_state":"computed","paper":{"title":"Global Optimality in Tensor Factorization, Deep Learning, and Beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.NA","authors_text":"Benjamin D. Haeffele, Rene Vidal","submitted_at":"2015-06-24T20:08:47Z","abstract_excerpt":"Techniques involving factorization are found in a wide range of applications and have enjoyed significant empirical success in many fields. However, common to a vast majority of these problems is the significant disadvantage that the associated optimization problems are typically non-convex due to a multilinear form or other convexity destroying transformation. Here we build on ideas from convex relaxations of matrix factorizations and present a very general framework which allows for the analysis of a wide range of non-convex factorization problems - including matrix factorization, tensor fac"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1506.07540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-06-24T20:08:47Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"946102d9e887989a97b858bb2ddc39f50b563d8e51eaf90254d021839c9a4a34","abstract_canon_sha256":"1aea7906d717128ba13973e3646fee5cc80a896f1a94d79ae38bd8295b25d432"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:51.557040Z","signature_b64":"itV75c0oeOn8gIKq0eSSozO5GSeKN2D8I5tZ6y5bxy9iQZPEvICPYVRn6mDwKj+l62qcYRR0SIX0io7wSylYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4810812e540896dd2ec3760378600e3e8249353330fca41cc1f680403f4080f4","last_reissued_at":"2026-05-18T01:38:51.556485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:51.556485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global Optimality in Tensor Factorization, Deep Learning, and Beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.NA","authors_text":"Benjamin D. Haeffele, Rene Vidal","submitted_at":"2015-06-24T20:08:47Z","abstract_excerpt":"Techniques involving factorization are found in a wide range of applications and have enjoyed significant empirical success in many fields. However, common to a vast majority of these problems is the significant disadvantage that the associated optimization problems are typically non-convex due to a multilinear form or other convexity destroying transformation. Here we build on ideas from convex relaxations of matrix factorizations and present a very general framework which allows for the analysis of a wide range of non-convex factorization problems - including matrix factorization, tensor fac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07540","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.07540","created_at":"2026-05-18T01:38:51.556560+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.07540v1","created_at":"2026-05-18T01:38:51.556560+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07540","created_at":"2026-05-18T01:38:51.556560+00:00"},{"alias_kind":"pith_short_12","alias_value":"JAIICLSUBCLN","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"JAIICLSUBCLN2LWD","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"JAIICLSU","created_at":"2026-05-18T12:29:27.538025+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2502.07189","citing_title":"Exploring Vision Neural Network Pruning via Screening Methodology","ref_index":13,"is_internal_anchor":true},{"citing_arxiv_id":"2401.01335","citing_title":"Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models","ref_index":124,"is_internal_anchor":true},{"citing_arxiv_id":"2605.09991","citing_title":"Optimizer-Induced Mode Connectivity: From AdamW to Muon","ref_index":154,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JAIICLSUBCLN2LWDOYBXQYAOH2","json":"https://pith.science/pith/JAIICLSUBCLN2LWDOYBXQYAOH2.json","graph_json":"https://pith.science/api/pith-number/JAIICLSUBCLN2LWDOYBXQYAOH2/graph.json","events_json":"https://pith.science/api/pith-number/JAIICLSUBCLN2LWDOYBXQYAOH2/events.json","paper":"https://pith.science/paper/JAIICLSU"},"agent_actions":{"view_html":"https://pith.science/pith/JAIICLSUBCLN2LWDOYBXQYAOH2","download_json":"https://pith.science/pith/JAIICLSUBCLN2LWDOYBXQYAOH2.json","view_paper":"https://pith.science/paper/JAIICLSU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.07540&json=true","fetch_graph":"https://pith.science/api/pith-number/JAIICLSUBCLN2LWDOYBXQYAOH2/graph.json","fetch_events":"https://pith.science/api/pith-number/JAIICLSUBCLN2LWDOYBXQYAOH2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JAIICLSUBCLN2LWDOYBXQYAOH2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JAIICLSUBCLN2LWDOYBXQYAOH2/action/storage_attestation","attest_author":"https://pith.science/pith/JAIICLSUBCLN2LWDOYBXQYAOH2/action/author_attestation","sign_citation":"https://pith.science/pith/JAIICLSUBCLN2LWDOYBXQYAOH2/action/citation_signature","submit_replication":"https://pith.science/pith/JAIICLSUBCLN2LWDOYBXQYAOH2/action/replication_record"}},"created_at":"2026-05-18T01:38:51.556560+00:00","updated_at":"2026-05-18T01:38:51.556560+00:00"}