Pith Number

pith:JVME5N5J

pith:2026:JVME5N5JR53QA5BEYA3FRTHYZN

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Learning Unbiased Permutations via Flow Matching

Carla P. Gomes, Yimeng Min

A flow matching model learns multimodal permutations by projecting trajectories onto the space of unit row and column sum matrices.

arxiv:2605.16755 v1 · 2026-05-16 · cs.LG · cs.AI

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Claims

C1strongest claim

A conditional flow matching framework that operates directly on the affine subspace of matrices with unit row and column sums. A closed-form tangent-space projector preserves these constraints exactly along every trajectory by construction rather than through iterative correction, and a nearest-target coupling routes distinct noisy initializations toward distinct valid permutations, enabling the model to capture multimodal permutation distributions rather than collapsing them to a single mode.

C2weakest assumption

That the closed-form tangent-space projector can be computed efficiently and remains numerically stable for the chosen flow schedules, and that the nearest-target coupling strategy is sufficient to train the model to distinguish and recover distinct modes without requiring extra regularization or assumptions on the underlying data distribution.

C3one line summary

PermFlow applies conditional flow matching on the affine subspace of doubly stochastic matrices with a closed-form tangent projector and nearest-target coupling to capture multimodal permutation distributions.

References

21 extracted · 21 resolved · 5 Pith anchors

[1] Improving and generalizing flow-based generative models with minibatch optimal transport · arXiv:2302.00482

[2] Forty-first international conference on machine learning , year=

[3] Advances in Neural Information Processing Systems , volume=

[4] Advances in Neural Information Processing Systems , volume=

[5] Flow matching on general geometries

Receipt and verification

First computed	2026-05-20T00:03:20.036117Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d584eb7a98f77007424c03658ccf8cb61a860fd138161dd63c5cdb357b9dd51

Aliases

arxiv: 2605.16755 · arxiv_version: 2605.16755v1 · doi: 10.48550/arxiv.2605.16755 · pith_short_12: JVME5N5JR53Q · pith_short_16: JVME5N5JR53QA5BE · pith_short_8: JVME5N5J

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JVME5N5JR53QA5BEYA3FRTHYZN \
  | 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: 4d584eb7a98f77007424c03658ccf8cb61a860fd138161dd63c5cdb357b9dd51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f86fa8730b9abab7b96099a40b6aa681b906422392ec63f99c1556c615bbad7b",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-16T02:10:35Z",
    "title_canon_sha256": "259a5c80fc8e7ebd88d68461cd211e64b45009e04335da96a0105a6e1bcb9ad0"
  },
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  "source": {
    "id": "2605.16755",
    "kind": "arxiv",
    "version": 1
  }
}