{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:UJTZHBIBUML3T6VJ22AZ3V77GA","short_pith_number":"pith:UJTZHBIB","schema_version":"1.0","canonical_sha256":"a267938501a317b9faa9d6819dd7ff301b4bfd50bc18aef8d6fa4a05838f827e","source":{"kind":"arxiv","id":"2412.19366","version":3},"attestation_state":"computed","paper":{"title":"Constructive approximate transport maps with normalizing flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.OC","authors_text":"Antonio \\'Alvarez-L\\'opez, Borjan Geshkovski, Dom\\`enec Ruiz-Balet","submitted_at":"2024-12-26T22:09:33Z","abstract_excerpt":"We study an approximate controllability problem for the continuity equation and its application to constructing transport maps with normalizing flows. Specifically, we construct time-dependent controls $\\theta=(w, a, b)$ in the vector field $x\\mapsto w(a^\\top x + b)_+$ to approximately transport a known base density $\\rho_{\\mathrm{B}}$ to a target density $\\rho_*$. The approximation error is measured in relative entropy, and $\\theta$ are constructed piecewise constant, with bounds on the number of switches being provided. Our main result relies on an assumption on the relative tail decay of $\\"},"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":"2412.19366","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-12-26T22:09:33Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"dbddeb298bde0b4e7d450358a0a3bc8d72f87038a56f93f50f01d98f3b102ce5","abstract_canon_sha256":"bab4443b85f7d427e4475cb7efa74d8a2b4ba3ea47a5e298946565f5aca31a2a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:54:43.337356Z","signature_b64":"nIniJAIXZ8o30FP3J4ti28MU/PQiAuuIlUcclkwoqsAOa/1ye/JG1PaHaGqeUfi1ptpvivwVK3NM2GjspsBTDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a267938501a317b9faa9d6819dd7ff301b4bfd50bc18aef8d6fa4a05838f827e","last_reissued_at":"2026-07-05T11:54:43.336987Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:54:43.336987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constructive approximate transport maps with normalizing flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.OC","authors_text":"Antonio \\'Alvarez-L\\'opez, Borjan Geshkovski, Dom\\`enec Ruiz-Balet","submitted_at":"2024-12-26T22:09:33Z","abstract_excerpt":"We study an approximate controllability problem for the continuity equation and its application to constructing transport maps with normalizing flows. Specifically, we construct time-dependent controls $\\theta=(w, a, b)$ in the vector field $x\\mapsto w(a^\\top x + b)_+$ to approximately transport a known base density $\\rho_{\\mathrm{B}}$ to a target density $\\rho_*$. The approximation error is measured in relative entropy, and $\\theta$ are constructed piecewise constant, with bounds on the number of switches being provided. Our main result relies on an assumption on the relative tail decay of $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19366","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.19366/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2412.19366","created_at":"2026-07-05T11:54:43.337042+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.19366v3","created_at":"2026-07-05T11:54:43.337042+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.19366","created_at":"2026-07-05T11:54:43.337042+00:00"},{"alias_kind":"pith_short_12","alias_value":"UJTZHBIBUML3","created_at":"2026-07-05T11:54:43.337042+00:00"},{"alias_kind":"pith_short_16","alias_value":"UJTZHBIBUML3T6VJ","created_at":"2026-07-05T11:54:43.337042+00:00"},{"alias_kind":"pith_short_8","alias_value":"UJTZHBIB","created_at":"2026-07-05T11:54:43.337042+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2503.08927","citing_title":"Ensemble optimal control for managing drug resistance in cancer therapies","ref_index":3,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UJTZHBIBUML3T6VJ22AZ3V77GA","json":"https://pith.science/pith/UJTZHBIBUML3T6VJ22AZ3V77GA.json","graph_json":"https://pith.science/api/pith-number/UJTZHBIBUML3T6VJ22AZ3V77GA/graph.json","events_json":"https://pith.science/api/pith-number/UJTZHBIBUML3T6VJ22AZ3V77GA/events.json","paper":"https://pith.science/paper/UJTZHBIB"},"agent_actions":{"view_html":"https://pith.science/pith/UJTZHBIBUML3T6VJ22AZ3V77GA","download_json":"https://pith.science/pith/UJTZHBIBUML3T6VJ22AZ3V77GA.json","view_paper":"https://pith.science/paper/UJTZHBIB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.19366&json=true","fetch_graph":"https://pith.science/api/pith-number/UJTZHBIBUML3T6VJ22AZ3V77GA/graph.json","fetch_events":"https://pith.science/api/pith-number/UJTZHBIBUML3T6VJ22AZ3V77GA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UJTZHBIBUML3T6VJ22AZ3V77GA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UJTZHBIBUML3T6VJ22AZ3V77GA/action/storage_attestation","attest_author":"https://pith.science/pith/UJTZHBIBUML3T6VJ22AZ3V77GA/action/author_attestation","sign_citation":"https://pith.science/pith/UJTZHBIBUML3T6VJ22AZ3V77GA/action/citation_signature","submit_replication":"https://pith.science/pith/UJTZHBIBUML3T6VJ22AZ3V77GA/action/replication_record"}},"created_at":"2026-07-05T11:54:43.337042+00:00","updated_at":"2026-07-05T11:54:43.337042+00:00"}