{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:2PR7UVZIWM6C3JLESC4PDQZ5GJ","short_pith_number":"pith:2PR7UVZI","schema_version":"1.0","canonical_sha256":"d3e3fa5728b33c2da56490b8f1c33d326449680af0aaedf1d054b92b88a0ce00","source":{"kind":"arxiv","id":"2606.10089","version":1},"attestation_state":"computed","paper":{"title":"A Theory on Flow Matching with Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Han Liu, Jianqing Fan, Qishuo Yin, Yihan He, Yuan Cao","submitted_at":"2026-06-08T19:16:32Z","abstract_excerpt":"In this work, we develop theoretical foundation for flow matching with neural-network-parameterized conditional velocity fields. We establish convergence guarantees for gradient descent in the over-parameterized 2-layered ReLU neural network regime. We derive generalization bounds for the conditional velocity-field matching objective. Building on these results, we provide Wasserstein-distance guarantees for the samples generated by the induced flow. Our analysis is based on generalization bound for multi-task representation learning with unbounded losses, which may be of independent interest b"},"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":"2606.10089","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-08T19:16:32Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"8ace797e1434727930392dbee0635bd6e0c39e644937f32f86332d2bebed62a3","abstract_canon_sha256":"c624e7cddd65f57d66cdf449ff981439ccbd558719e4936c4f031834c51cf497"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T00:08:48.691410Z","signature_b64":"TYxjpEOWLk5YSCfnWiRq9a/4/6bK7SLGgw9OmzT8gspV8zkSgz7WWmvjRe3QZ/I53NIxKtmUcJbjG6hCCX+dAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3e3fa5728b33c2da56490b8f1c33d326449680af0aaedf1d054b92b88a0ce00","last_reissued_at":"2026-06-10T00:08:48.690565Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T00:08:48.690565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Theory on Flow Matching with Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Han Liu, Jianqing Fan, Qishuo Yin, Yihan He, Yuan Cao","submitted_at":"2026-06-08T19:16:32Z","abstract_excerpt":"In this work, we develop theoretical foundation for flow matching with neural-network-parameterized conditional velocity fields. We establish convergence guarantees for gradient descent in the over-parameterized 2-layered ReLU neural network regime. We derive generalization bounds for the conditional velocity-field matching objective. Building on these results, we provide Wasserstein-distance guarantees for the samples generated by the induced flow. Our analysis is based on generalization bound for multi-task representation learning with unbounded losses, which may be of independent interest b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10089","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/2606.10089/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":"2606.10089","created_at":"2026-06-10T00:08:48.690707+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.10089v1","created_at":"2026-06-10T00:08:48.690707+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10089","created_at":"2026-06-10T00:08:48.690707+00:00"},{"alias_kind":"pith_short_12","alias_value":"2PR7UVZIWM6C","created_at":"2026-06-10T00:08:48.690707+00:00"},{"alias_kind":"pith_short_16","alias_value":"2PR7UVZIWM6C3JLE","created_at":"2026-06-10T00:08:48.690707+00:00"},{"alias_kind":"pith_short_8","alias_value":"2PR7UVZI","created_at":"2026-06-10T00:08:48.690707+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/2PR7UVZIWM6C3JLESC4PDQZ5GJ","json":"https://pith.science/pith/2PR7UVZIWM6C3JLESC4PDQZ5GJ.json","graph_json":"https://pith.science/api/pith-number/2PR7UVZIWM6C3JLESC4PDQZ5GJ/graph.json","events_json":"https://pith.science/api/pith-number/2PR7UVZIWM6C3JLESC4PDQZ5GJ/events.json","paper":"https://pith.science/paper/2PR7UVZI"},"agent_actions":{"view_html":"https://pith.science/pith/2PR7UVZIWM6C3JLESC4PDQZ5GJ","download_json":"https://pith.science/pith/2PR7UVZIWM6C3JLESC4PDQZ5GJ.json","view_paper":"https://pith.science/paper/2PR7UVZI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.10089&json=true","fetch_graph":"https://pith.science/api/pith-number/2PR7UVZIWM6C3JLESC4PDQZ5GJ/graph.json","fetch_events":"https://pith.science/api/pith-number/2PR7UVZIWM6C3JLESC4PDQZ5GJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2PR7UVZIWM6C3JLESC4PDQZ5GJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2PR7UVZIWM6C3JLESC4PDQZ5GJ/action/storage_attestation","attest_author":"https://pith.science/pith/2PR7UVZIWM6C3JLESC4PDQZ5GJ/action/author_attestation","sign_citation":"https://pith.science/pith/2PR7UVZIWM6C3JLESC4PDQZ5GJ/action/citation_signature","submit_replication":"https://pith.science/pith/2PR7UVZIWM6C3JLESC4PDQZ5GJ/action/replication_record"}},"created_at":"2026-06-10T00:08:48.690707+00:00","updated_at":"2026-06-10T00:08:48.690707+00:00"}