Pith Number

pith:BCX4YKGN

pith:2026:BCX4YKGN7DRWK4XKDRWKH3IUOT

not attested not anchored not stored refs pending

Implicit Neural Optimal Transport via Fixed-Point Optimization

Eric Gelphman, Samy Wu Fung, Stanley Osher, Yesom Park

A single neural network solves optimal transport by reformulating the c-transform as a proximal fixed-point problem, enforcing dual feasibility exactly without adversarial training or implicit differentiation.

arxiv:2605.10792 v2 · 2026-05-11 · math.OC · cs.LG

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Claims

C1strongest claim

We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches. Our key idea is to parameterize a single potential in the Kantorovich dual and reformulate the associated c-transform as a proximal fixed-point problem.

C2weakest assumption

That the proximal fixed-point reformulation of the c-transform can be solved accurately enough in practice to enforce dual feasibility exactly and that gradients computed without implicit differentiation remain faithful to the true optimal transport objective.

C3one line summary

A single-network fixed-point formulation for neural optimal transport eliminates adversarial min-max optimization and implicit differentiation while enforcing dual feasibility exactly.

Receipt and verification

First computed	2026-06-08T01:04:07.191269Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08afcc28cdf8e36572ea1c6ca3ed1474df2d0d32883aee91de14ed8b2f210243

Aliases

arxiv: 2605.10792 · arxiv_version: 2605.10792v2 · doi: 10.48550/arxiv.2605.10792 · pith_short_12: BCX4YKGN7DRW · pith_short_16: BCX4YKGN7DRWK4XK · pith_short_8: BCX4YKGN

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BCX4YKGN7DRWK4XKDRWKH3IUOT \
  | 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: 08afcc28cdf8e36572ea1c6ca3ed1474df2d0d32883aee91de14ed8b2f210243

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10642c82112b5a20f0efd6d8eb5645ea8f3a33c2475c01781951705107e879de",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-11T16:22:06Z",
    "title_canon_sha256": "bbcebb08e33dc1967f2dfcf667cda4b4383225e76269e17c3d15bb3742ecd9f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.10792",
    "kind": "arxiv",
    "version": 2
  }
}