{"paper":{"title":"A Generalized Sinkhorn Algorithm for Mean-Field Schr\\\"odinger Bridge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A generalized Hopf-Cole transform yields a Sinkhorn-type recursive algorithm for mean-field Schrödinger bridge problems.","cross_cats":["cs.LG","cs.MA","cs.SY","eess.SY","stat.ML"],"primary_cat":"math.OC","authors_text":"Abhishek Halder, Asmaa Eldesoukey, Yongxin Chen","submitted_at":"2026-04-08T00:04:52Z","abstract_excerpt":"The mean-field Schr\\\"odinger bridge (MFSB) problem concerns designing a minimum-effort controller that guides a diffusion process with nonlocal interaction to reach a given distribution from another by a fixed deadline. Unlike the standard Schr\\\"odinger bridge, the dynamical constraint for MFSB is the mean-field limit of a population of interacting agents with controls. It serves as a natural model for large-scale multi-agent systems. The MFSB is computationally challenging because the nonlocal interaction makes the problem nonconvex. We propose a generalization of the Hopf-Cole transform for "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We propose a generalization of the Hopf-Cole transform for MFSB and, building on it, design a Sinkhorn-type recursive algorithm to solve the associated system of integro-PDEs. Under mild assumptions on the interaction potential, we discuss convergence guarantees for the proposed algorithm.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The mild assumptions on the interaction potential are sufficient to guarantee convergence of the recursive algorithm; the abstract does not specify what these assumptions are or whether they hold for typical repulsive/attractive potentials used in applications.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A generalized Hopf-Cole transform enables a convergent Sinkhorn-type algorithm for solving the nonconvex mean-field Schrödinger bridge problem via integro-PDEs.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A generalized Hopf-Cole transform yields a Sinkhorn-type recursive algorithm for mean-field Schrödinger bridge problems.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"884e8d5d5675b8221e7f0427dcc8a14b3c71718b063d17b43fce4965ab86df59"},"source":{"id":"2604.06531","kind":"arxiv","version":3},"verdict":{"id":"f79ef262-ad30-4474-bc20-4924aae4ae9b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T18:39:15.811107Z","strongest_claim":"We propose a generalization of the Hopf-Cole transform for MFSB and, building on it, design a Sinkhorn-type recursive algorithm to solve the associated system of integro-PDEs. Under mild assumptions on the interaction potential, we discuss convergence guarantees for the proposed algorithm.","one_line_summary":"A generalized Hopf-Cole transform enables a convergent Sinkhorn-type algorithm for solving the nonconvex mean-field Schrödinger bridge problem via integro-PDEs.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The mild assumptions on the interaction potential are sufficient to guarantee convergence of the recursive algorithm; the abstract does not specify what these assumptions are or whether they hold for typical repulsive/attractive potentials used in applications.","pith_extraction_headline":"A generalized Hopf-Cole transform yields a Sinkhorn-type recursive algorithm for mean-field Schrödinger bridge problems."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.06531/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":2,"snapshot_sha256":"762f2a07a18068b7b86c7ddb5fa560b674dc50fe2d225ceb4f49d0124b31eefd"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}