Pith Number

pith:WDFVIT2M

pith:2026:WDFVIT2MXEEX7G2ZJ2MWIDGAQQ

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Complexity of Non-Log-Concave Sampling in Fisher Information

Andre Wibisono, Sinho Chewi

Leveraging log-concave sampling results gives non-log-concave sampling the same dimension dependence in relative Fisher information.

arxiv:2605.15859 v1 · 2026-05-15 · cs.DS · cs.LG · math.ST · stat.ML · stat.TH

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Claims

C1strongest claim

by leveraging the recent results for log-concave sampling with high-accuracy guarantees in Rényi divergence, we can obtain an approximate RGO implementation that -- when used with the proximal sampler -- yields a complexity guarantee in relative Fisher information that inherits the same dimension dependence as log-concave sampling, and improves upon prior work for non-log-concave sampling.

C2weakest assumption

The recent high-accuracy log-concave sampling results in Rényi divergence can be used to produce an approximate restricted Gaussian oracle whose error does not introduce worse dimension dependence when plugged into the proximal sampler for non-log-concave targets (abstract, paragraph describing the algorithm and RGO implementation).

C3one line summary

Proximal sampler with approximate RGO from log-concave Renyi results yields relative Fisher information complexity for non-log-concave sampling that matches log-concave dimension dependence, plus a converse reduction.

References

32 extracted · 32 resolved · 0 Pith anchors

[1] and Salim, Adil and Zhang, Matthew S 2022

[2] Optimal score estimation via empirical 2024

[3] Wibisono, Andre , journal=. 2026 , volume= 2026

[4] Sinho Chewi and Alkis Kalavasis and Anay Mehrotra and Omar Montasser , year=

[5] Proceedings of the 34th International Conference on Algorithmic Learning Theory , pages = 2023

Receipt and verification

First computed	2026-05-20T00:01:22.343170Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0cb544f4cb9097f9b594e99640cc08406dff47b0a20d5db3e47fbbe9b24e05a

Aliases

arxiv: 2605.15859 · arxiv_version: 2605.15859v1 · doi: 10.48550/arxiv.2605.15859 · pith_short_12: WDFVIT2MXEEX · pith_short_16: WDFVIT2MXEEX7G2Z · pith_short_8: WDFVIT2M

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WDFVIT2MXEEX7G2ZJ2MWIDGAQQ \
  | 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: b0cb544f4cb9097f9b594e99640cc08406dff47b0a20d5db3e47fbbe9b24e05a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5324568a20a39bcf99cf560e6299ea2cbef29fe9c4bf5da405fb6d681f8deead",
    "cross_cats_sorted": [
      "cs.LG",
      "math.ST",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-05-15T11:20:26Z",
    "title_canon_sha256": "12dec7eefd5adec411279f1dbb8370d041400fb5aa13f03e6c3c2de962692ed8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15859",
    "kind": "arxiv",
    "version": 1
  }
}