Pith Number

pith:QUHDCVBX

pith:2026:QUHDCVBXO645JMYQPSSBC6VYFB

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Finite Sample Bounds for Learning with Score Matching

Abhijith Jayakumar, Andrey Y. Lokhov, Devin Smedira, Marc Vuffray, Sidhant Misra

Score matching provides the first non-asymptotic sample bounds with polynomial dependence on dimension for exponential families of polynomials.

arxiv:2605.14168 v1 · 2026-05-13 · cs.LG · cs.DS · stat.ML

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Claims

C1strongest claim

we provide a non-asymptotic sample complexity analysis for learning the structure of exponential families of polynomials with score matching. The derived sample bounds show a polynomial dependence on the model dimension. These bounds are the first of its kind, as all prior work has shown only asymptotic bounds on the sample complexity.

C2weakest assumption

The target distribution exactly belongs to the exponential family of polynomials with unbounded support, and standard regularity conditions on the score function and Fisher information hold so that the derived polynomial sample bounds are valid.

C3one line summary

First non-asymptotic sample complexity bounds for structure learning of polynomial exponential families via score matching, with polynomial dependence on model dimension.

References

30 extracted · 30 resolved · 1 Pith anchors

[1] Convergence of diffusion models under the manifold hypothesis in high-dimensions

[2] International Conference on Machine Learning , pages= 2023

[3] International conference on artificial intelligence and statistics , pages= 2024

[4] arXiv preprint arXiv:2512.24378 , year=

[5] The Thirty Eighth Annual Conference on Learning Theory , pages= 2025

Receipt and verification

First computed	2026-05-17T23:39:11.388621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

850e31543777b9d4b3107ca4117ab82860e561f8283e93c4da206b2d9d555840

Aliases

arxiv: 2605.14168 · arxiv_version: 2605.14168v1 · doi: 10.48550/arxiv.2605.14168 · pith_short_12: QUHDCVBXO645 · pith_short_16: QUHDCVBXO645JMYQ · pith_short_8: QUHDCVBX

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QUHDCVBXO645JMYQPSSBC6VYFB \
  | 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: 850e31543777b9d4b3107ca4117ab82860e561f8283e93c4da206b2d9d555840

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bae6b23f8fd3863b10e6c610253028878a8f78ba61ee60d7321c29bb4d18b304",
    "cross_cats_sorted": [
      "cs.DS",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T22:48:18Z",
    "title_canon_sha256": "f21fdc78864aed1b0a22599ee18ecb2c375b5c433c0cb8406f5d2849f3dd1163"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14168",
    "kind": "arxiv",
    "version": 1
  }
}