{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:TBRQCMYO5DLBKCUN5N6HN3WUJR","short_pith_number":"pith:TBRQCMYO","schema_version":"1.0","canonical_sha256":"986301330ee8d6150a8deb7c76eed44c60f93747d11d26c2a4b707ae61dca8b6","source":{"kind":"arxiv","id":"2110.11291","version":5},"attestation_state":"computed","paper":{"title":"Likelihood Training of Schr\\\"odinger Bridge using Forward-Backward SDEs Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.AP","math.OC"],"primary_cat":"stat.ML","authors_text":"Evangelos A. Theodorou, Guan-Horng Liu, Tianrong Chen","submitted_at":"2021-10-21T17:18:59Z","abstract_excerpt":"Schr\\\"odinger Bridge (SB) is an entropy-regularized optimal transport problem that has received increasing attention in deep generative modeling for its mathematical flexibility compared to the Scored-based Generative Model (SGM). However, it remains unclear whether the optimization principle of SB relates to the modern training of deep generative models, which often rely on constructing log-likelihood objectives.This raises questions on the suitability of SB models as a principled alternative for generative applications. In this work, we present a novel computational framework for likelihood "},"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":"2110.11291","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-10-21T17:18:59Z","cross_cats_sorted":["cs.LG","math.AP","math.OC"],"title_canon_sha256":"1e1300a0e09021976fe2949553a436254e1cb184a0f29b2c36ab7711c851c07f","abstract_canon_sha256":"c1107d7a9007f801a6ef297eafa4b57c9cf54692e40d8382e9e962466f2c7761"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:57:09.855166Z","signature_b64":"9OHwDXdkq01rsLVRjZoZbDezQ3dYgXr3wcZd8mCRBw+lvsFDfhgew+Y80f+pSjczxitO0JRciarhV/bGdwBgAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"986301330ee8d6150a8deb7c76eed44c60f93747d11d26c2a4b707ae61dca8b6","last_reissued_at":"2026-07-05T05:57:09.854731Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:57:09.854731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Likelihood Training of Schr\\\"odinger Bridge using Forward-Backward SDEs Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.AP","math.OC"],"primary_cat":"stat.ML","authors_text":"Evangelos A. Theodorou, Guan-Horng Liu, Tianrong Chen","submitted_at":"2021-10-21T17:18:59Z","abstract_excerpt":"Schr\\\"odinger Bridge (SB) is an entropy-regularized optimal transport problem that has received increasing attention in deep generative modeling for its mathematical flexibility compared to the Scored-based Generative Model (SGM). However, it remains unclear whether the optimization principle of SB relates to the modern training of deep generative models, which often rely on constructing log-likelihood objectives.This raises questions on the suitability of SB models as a principled alternative for generative applications. In this work, we present a novel computational framework for likelihood "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.11291","kind":"arxiv","version":5},"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/2110.11291/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":"2110.11291","created_at":"2026-07-05T05:57:09.854788+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.11291v5","created_at":"2026-07-05T05:57:09.854788+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.11291","created_at":"2026-07-05T05:57:09.854788+00:00"},{"alias_kind":"pith_short_12","alias_value":"TBRQCMYO5DLB","created_at":"2026-07-05T05:57:09.854788+00:00"},{"alias_kind":"pith_short_16","alias_value":"TBRQCMYO5DLBKCUN","created_at":"2026-07-05T05:57:09.854788+00:00"},{"alias_kind":"pith_short_8","alias_value":"TBRQCMYO","created_at":"2026-07-05T05:57:09.854788+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.05575","citing_title":"SB-RF: Schr\\\"odinger Bridge Rectified Flow for One-Step Robust Speech Enhancement","ref_index":26,"is_internal_anchor":false},{"citing_arxiv_id":"2508.21435","citing_title":"MedShift: Implicit Conditional Transport for X-Ray Domain Adaptation","ref_index":2,"is_internal_anchor":false},{"citing_arxiv_id":"2512.18928","citing_title":"The Ensemble Schr{\\\"o}dinger Bridge filter for Nonlinear Data Assimilation","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2605.01568","citing_title":"Unifying Deep Stochastic Processes for Image Enhancement","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"2604.07762","citing_title":"Generative optimal transport via forward-backward HJB matching","ref_index":28,"is_internal_anchor":false},{"citing_arxiv_id":"2209.03003","citing_title":"Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow","ref_index":7,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TBRQCMYO5DLBKCUN5N6HN3WUJR","json":"https://pith.science/pith/TBRQCMYO5DLBKCUN5N6HN3WUJR.json","graph_json":"https://pith.science/api/pith-number/TBRQCMYO5DLBKCUN5N6HN3WUJR/graph.json","events_json":"https://pith.science/api/pith-number/TBRQCMYO5DLBKCUN5N6HN3WUJR/events.json","paper":"https://pith.science/paper/TBRQCMYO"},"agent_actions":{"view_html":"https://pith.science/pith/TBRQCMYO5DLBKCUN5N6HN3WUJR","download_json":"https://pith.science/pith/TBRQCMYO5DLBKCUN5N6HN3WUJR.json","view_paper":"https://pith.science/paper/TBRQCMYO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.11291&json=true","fetch_graph":"https://pith.science/api/pith-number/TBRQCMYO5DLBKCUN5N6HN3WUJR/graph.json","fetch_events":"https://pith.science/api/pith-number/TBRQCMYO5DLBKCUN5N6HN3WUJR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TBRQCMYO5DLBKCUN5N6HN3WUJR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TBRQCMYO5DLBKCUN5N6HN3WUJR/action/storage_attestation","attest_author":"https://pith.science/pith/TBRQCMYO5DLBKCUN5N6HN3WUJR/action/author_attestation","sign_citation":"https://pith.science/pith/TBRQCMYO5DLBKCUN5N6HN3WUJR/action/citation_signature","submit_replication":"https://pith.science/pith/TBRQCMYO5DLBKCUN5N6HN3WUJR/action/replication_record"}},"created_at":"2026-07-05T05:57:09.854788+00:00","updated_at":"2026-07-05T05:57:09.854788+00:00"}