{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:37MAZ3KLOVFWX4K2SDSXVSPXLT","short_pith_number":"pith:37MAZ3KL","schema_version":"1.0","canonical_sha256":"dfd80ced4b754b6bf15a90e57ac9f75cf3b65d66072a7e041be3e43a82c3a679","source":{"kind":"arxiv","id":"2502.03795","version":1},"attestation_state":"computed","paper":{"title":"Distribution learning via neural differential equations: minimal energy regularization and approximation theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","stat.ME","stat.ML"],"primary_cat":"cs.LG","authors_text":"Jakob Zech, Youssef Marzouk, Zhi Ren","submitted_at":"2025-02-06T05:50:21Z","abstract_excerpt":"Neural ordinary differential equations (ODEs) provide expressive representations of invertible transport maps that can be used to approximate complex probability distributions, e.g., for generative modeling, density estimation, and Bayesian inference. We show that for a large class of transport maps $T$, there exists a time-dependent ODE velocity field realizing a straight-line interpolation $(1-t)x + tT(x)$, $t \\in [0,1]$, of the displacement induced by the map. Moreover, we show that such velocity fields are minimizers of a training objective containing a specific minimum-energy regularizati"},"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":"2502.03795","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-06T05:50:21Z","cross_cats_sorted":["math.CA","stat.ME","stat.ML"],"title_canon_sha256":"ccd24e0572fe3b000b4e483448455f32198116172b251f4b1fa6b6146b91096a","abstract_canon_sha256":"c86c5c5d97ff9f40c1fc5cbc1db7083caa407db8903b591611a2f557c4843ddc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:10:15.001242Z","signature_b64":"F3P43IOMJtlFDWiDLjKLpH76wiT54GjJMCUuRAr0Put5Rj0nAWYH6C7AxuW4nHVRR6M0AwsPJsCPdldraAyhAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfd80ced4b754b6bf15a90e57ac9f75cf3b65d66072a7e041be3e43a82c3a679","last_reissued_at":"2026-07-05T10:10:15.000879Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:10:15.000879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distribution learning via neural differential equations: minimal energy regularization and approximation theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","stat.ME","stat.ML"],"primary_cat":"cs.LG","authors_text":"Jakob Zech, Youssef Marzouk, Zhi Ren","submitted_at":"2025-02-06T05:50:21Z","abstract_excerpt":"Neural ordinary differential equations (ODEs) provide expressive representations of invertible transport maps that can be used to approximate complex probability distributions, e.g., for generative modeling, density estimation, and Bayesian inference. We show that for a large class of transport maps $T$, there exists a time-dependent ODE velocity field realizing a straight-line interpolation $(1-t)x + tT(x)$, $t \\in [0,1]$, of the displacement induced by the map. Moreover, we show that such velocity fields are minimizers of a training objective containing a specific minimum-energy regularizati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.03795","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.03795/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":"2502.03795","created_at":"2026-07-05T10:10:15.000935+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.03795v1","created_at":"2026-07-05T10:10:15.000935+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.03795","created_at":"2026-07-05T10:10:15.000935+00:00"},{"alias_kind":"pith_short_12","alias_value":"37MAZ3KLOVFW","created_at":"2026-07-05T10:10:15.000935+00:00"},{"alias_kind":"pith_short_16","alias_value":"37MAZ3KLOVFWX4K2","created_at":"2026-07-05T10:10:15.000935+00:00"},{"alias_kind":"pith_short_8","alias_value":"37MAZ3KL","created_at":"2026-07-05T10:10:15.000935+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2507.01533","citing_title":"Consistency of Learned Sparse Grid Quadrature Rules using NeuralODEs","ref_index":23,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/37MAZ3KLOVFWX4K2SDSXVSPXLT","json":"https://pith.science/pith/37MAZ3KLOVFWX4K2SDSXVSPXLT.json","graph_json":"https://pith.science/api/pith-number/37MAZ3KLOVFWX4K2SDSXVSPXLT/graph.json","events_json":"https://pith.science/api/pith-number/37MAZ3KLOVFWX4K2SDSXVSPXLT/events.json","paper":"https://pith.science/paper/37MAZ3KL"},"agent_actions":{"view_html":"https://pith.science/pith/37MAZ3KLOVFWX4K2SDSXVSPXLT","download_json":"https://pith.science/pith/37MAZ3KLOVFWX4K2SDSXVSPXLT.json","view_paper":"https://pith.science/paper/37MAZ3KL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.03795&json=true","fetch_graph":"https://pith.science/api/pith-number/37MAZ3KLOVFWX4K2SDSXVSPXLT/graph.json","fetch_events":"https://pith.science/api/pith-number/37MAZ3KLOVFWX4K2SDSXVSPXLT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/37MAZ3KLOVFWX4K2SDSXVSPXLT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/37MAZ3KLOVFWX4K2SDSXVSPXLT/action/storage_attestation","attest_author":"https://pith.science/pith/37MAZ3KLOVFWX4K2SDSXVSPXLT/action/author_attestation","sign_citation":"https://pith.science/pith/37MAZ3KLOVFWX4K2SDSXVSPXLT/action/citation_signature","submit_replication":"https://pith.science/pith/37MAZ3KLOVFWX4K2SDSXVSPXLT/action/replication_record"}},"created_at":"2026-07-05T10:10:15.000935+00:00","updated_at":"2026-07-05T10:10:15.000935+00:00"}