{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YILOOTCEMASCH5LW7ROFTBS3TJ","short_pith_number":"pith:YILOOTCE","schema_version":"1.0","canonical_sha256":"c216e74c44602423f576fc5c59865b9a556fbd91bb458080e2dc74c7056f7418","source":{"kind":"arxiv","id":"1705.07603","version":2},"attestation_state":"computed","paper":{"title":"Multi-output Polynomial Networks and Factorization Machines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Mathieu Blondel, Naonori Ueda, Takuma Otsuka, Vlad Niculae","submitted_at":"2017-05-22T08:20:31Z","abstract_excerpt":"Factorization machines and polynomial networks are supervised polynomial models based on an efficient low-rank decomposition. We extend these models to the multi-output setting, i.e., for learning vector-valued functions, with application to multi-class or multi-task problems. We cast this as the problem of learning a 3-way tensor whose slices share a common basis and propose a convex formulation of that problem. We then develop an efficient conditional gradient algorithm and prove its global convergence, despite the fact that it involves a non-convex basis selection step. On classification ta"},"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":"1705.07603","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-05-22T08:20:31Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"008aee5483313bea397512406e3d3b5b3143d1370d003c1255a476b1ae426b7e","abstract_canon_sha256":"492c14ee8feebfd4875ad8d97293a20792de699b58eaef4de56208a04a32eabd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:19.468444Z","signature_b64":"nWnbFsWjOMcJlxtHt4z76jpi58HSCh5nFhuCRWRH4qHoK43PdTF1ZiuvgYKtg5xEK4SMYLkGcWF44eXN7HFuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c216e74c44602423f576fc5c59865b9a556fbd91bb458080e2dc74c7056f7418","last_reissued_at":"2026-05-18T00:31:19.467570Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:19.467570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multi-output Polynomial Networks and Factorization Machines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Mathieu Blondel, Naonori Ueda, Takuma Otsuka, Vlad Niculae","submitted_at":"2017-05-22T08:20:31Z","abstract_excerpt":"Factorization machines and polynomial networks are supervised polynomial models based on an efficient low-rank decomposition. We extend these models to the multi-output setting, i.e., for learning vector-valued functions, with application to multi-class or multi-task problems. We cast this as the problem of learning a 3-way tensor whose slices share a common basis and propose a convex formulation of that problem. We then develop an efficient conditional gradient algorithm and prove its global convergence, despite the fact that it involves a non-convex basis selection step. On classification ta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07603","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":""},"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":"1705.07603","created_at":"2026-05-18T00:31:19.467805+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.07603v2","created_at":"2026-05-18T00:31:19.467805+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07603","created_at":"2026-05-18T00:31:19.467805+00:00"},{"alias_kind":"pith_short_12","alias_value":"YILOOTCEMASC","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YILOOTCEMASCH5LW","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YILOOTCE","created_at":"2026-05-18T12:31:56.362134+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YILOOTCEMASCH5LW7ROFTBS3TJ","json":"https://pith.science/pith/YILOOTCEMASCH5LW7ROFTBS3TJ.json","graph_json":"https://pith.science/api/pith-number/YILOOTCEMASCH5LW7ROFTBS3TJ/graph.json","events_json":"https://pith.science/api/pith-number/YILOOTCEMASCH5LW7ROFTBS3TJ/events.json","paper":"https://pith.science/paper/YILOOTCE"},"agent_actions":{"view_html":"https://pith.science/pith/YILOOTCEMASCH5LW7ROFTBS3TJ","download_json":"https://pith.science/pith/YILOOTCEMASCH5LW7ROFTBS3TJ.json","view_paper":"https://pith.science/paper/YILOOTCE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.07603&json=true","fetch_graph":"https://pith.science/api/pith-number/YILOOTCEMASCH5LW7ROFTBS3TJ/graph.json","fetch_events":"https://pith.science/api/pith-number/YILOOTCEMASCH5LW7ROFTBS3TJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YILOOTCEMASCH5LW7ROFTBS3TJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YILOOTCEMASCH5LW7ROFTBS3TJ/action/storage_attestation","attest_author":"https://pith.science/pith/YILOOTCEMASCH5LW7ROFTBS3TJ/action/author_attestation","sign_citation":"https://pith.science/pith/YILOOTCEMASCH5LW7ROFTBS3TJ/action/citation_signature","submit_replication":"https://pith.science/pith/YILOOTCEMASCH5LW7ROFTBS3TJ/action/replication_record"}},"created_at":"2026-05-18T00:31:19.467805+00:00","updated_at":"2026-05-18T00:31:19.467805+00:00"}