Pith Number

pith:25Q7SQPZ

pith:2026:25Q7SQPZMJAOPX3RLM44A6JHMV

not attested not anchored not stored refs pending

A Generalized Sinkhorn Algorithm for Mean-Field Schr\"odinger Bridge

Abhishek Halder, Asmaa Eldesoukey, Yongxin Chen

A generalized Hopf-Cole transform yields a Sinkhorn-type recursive algorithm for mean-field Schrödinger bridge problems.

arxiv:2604.06531 v3 · 2026-04-08 · math.OC · cs.LG · cs.MA · cs.SY · eess.SY · stat.ML

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\pithnumber{25Q7SQPZMJAOPX3RLM44A6JHMV}

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Record completeness

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4 Citations open

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-19T16:09:57.963602Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d761f941f96240e7df715b39c07927655261717af370aa559426005d79529497

Aliases

arxiv: 2604.06531 · arxiv_version: 2604.06531v3 · doi: 10.48550/arxiv.2604.06531 · pith_short_12: 25Q7SQPZMJAO · pith_short_16: 25Q7SQPZMJAOPX3R · pith_short_8: 25Q7SQPZ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/25Q7SQPZMJAOPX3RLM44A6JHMV \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: d761f941f96240e7df715b39c07927655261717af370aa559426005d79529497

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd10599143f844ac615b30ed1b0ca55d4b5a2ac88c5223198c59743ce3cf61b9",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.MA",
      "cs.SY",
      "eess.SY",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-04-08T00:04:52Z",
    "title_canon_sha256": "ca6d193d7b0700966f32bcb9ebfcad48127f8a1b3178eb07792c49cde03731b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.06531",
    "kind": "arxiv",
    "version": 3
  }
}