{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:JHTGIGG3X3ZMRUS6X4CZ6XRUZY","short_pith_number":"pith:JHTGIGG3","schema_version":"1.0","canonical_sha256":"49e66418dbbef2c8d25ebf059f5e34ce316ca17a2eab572c236f3172f576d4ac","source":{"kind":"arxiv","id":"1905.02325","version":2},"attestation_state":"computed","paper":{"title":"Sum-of-Squares Polynomial Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Kira A. Selby, Priyank Jaini, Yaoliang Yu","submitted_at":"2019-05-07T02:16:10Z","abstract_excerpt":"Triangular map is a recent construct in probability theory that allows one to transform any source probability density function to any target density function. Based on triangular maps, we propose a general framework for high-dimensional density estimation, by specifying one-dimensional transformations (equivalently conditional densities) and appropriate conditioner networks. This framework (a) reveals the commonalities and differences of existing autoregressive and flow based methods, (b) allows a unified understanding of the limitations and representation power of these recent approaches and"},"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":"1905.02325","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-07T02:16:10Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"4dfb17fe766e6062c6a0ede078c9832e6b5eecc9dcc4e2743d371614fafe2800","abstract_canon_sha256":"c1ea626dd0a533e0a3dd4d8f4a6c33174972d78ad00ac283ead25573f72292f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:42.264345Z","signature_b64":"49L/gkje9fvAWSdMXG0W1QT4ACTeHWWC+kQ61NNk40SLT9cplESxWPyjUWgVLMC7wbPa6QEsU/vTBL0YojA3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49e66418dbbef2c8d25ebf059f5e34ce316ca17a2eab572c236f3172f576d4ac","last_reissued_at":"2026-05-17T23:43:42.263718Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:42.263718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sum-of-Squares Polynomial Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Kira A. Selby, Priyank Jaini, Yaoliang Yu","submitted_at":"2019-05-07T02:16:10Z","abstract_excerpt":"Triangular map is a recent construct in probability theory that allows one to transform any source probability density function to any target density function. Based on triangular maps, we propose a general framework for high-dimensional density estimation, by specifying one-dimensional transformations (equivalently conditional densities) and appropriate conditioner networks. This framework (a) reveals the commonalities and differences of existing autoregressive and flow based methods, (b) allows a unified understanding of the limitations and representation power of these recent approaches and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02325","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":"1905.02325","created_at":"2026-05-17T23:43:42.263871+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.02325v2","created_at":"2026-05-17T23:43:42.263871+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.02325","created_at":"2026-05-17T23:43:42.263871+00:00"},{"alias_kind":"pith_short_12","alias_value":"JHTGIGG3X3ZM","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"JHTGIGG3X3ZMRUS6","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"JHTGIGG3","created_at":"2026-05-18T12:33:21.387695+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2402.09848","citing_title":"Parameterized quantum circuits as universal generative models for continuous multivariate distributions","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JHTGIGG3X3ZMRUS6X4CZ6XRUZY","json":"https://pith.science/pith/JHTGIGG3X3ZMRUS6X4CZ6XRUZY.json","graph_json":"https://pith.science/api/pith-number/JHTGIGG3X3ZMRUS6X4CZ6XRUZY/graph.json","events_json":"https://pith.science/api/pith-number/JHTGIGG3X3ZMRUS6X4CZ6XRUZY/events.json","paper":"https://pith.science/paper/JHTGIGG3"},"agent_actions":{"view_html":"https://pith.science/pith/JHTGIGG3X3ZMRUS6X4CZ6XRUZY","download_json":"https://pith.science/pith/JHTGIGG3X3ZMRUS6X4CZ6XRUZY.json","view_paper":"https://pith.science/paper/JHTGIGG3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.02325&json=true","fetch_graph":"https://pith.science/api/pith-number/JHTGIGG3X3ZMRUS6X4CZ6XRUZY/graph.json","fetch_events":"https://pith.science/api/pith-number/JHTGIGG3X3ZMRUS6X4CZ6XRUZY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JHTGIGG3X3ZMRUS6X4CZ6XRUZY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JHTGIGG3X3ZMRUS6X4CZ6XRUZY/action/storage_attestation","attest_author":"https://pith.science/pith/JHTGIGG3X3ZMRUS6X4CZ6XRUZY/action/author_attestation","sign_citation":"https://pith.science/pith/JHTGIGG3X3ZMRUS6X4CZ6XRUZY/action/citation_signature","submit_replication":"https://pith.science/pith/JHTGIGG3X3ZMRUS6X4CZ6XRUZY/action/replication_record"}},"created_at":"2026-05-17T23:43:42.263871+00:00","updated_at":"2026-05-17T23:43:42.263871+00:00"}