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pith:LHGLWCVN

pith:2026:LHGLWCVN3S4Q4UMW4JRJSF735E

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Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixtures

Josselin Garnier, Knut Solna, Lorenzo Baldassari, Maarten V. de Hoop

Exponential-integrator discretization of preconditioned annealed Langevin dynamics yields dimension-uniform KL bounds for Gaussian mixtures under spectral summability conditions.

arxiv:2605.16473 v1 · 2026-05-15 · stat.ML · cs.LG · cs.NA · math.NA · math.PR

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Claims

C1strongest claim

Under explicit spectral summability conditions coupling the smoothing covariance, the component covariance spectra, and the preconditioner, we prove a dimension-uniform Kullback-Leibler (KL) bound for this scheme. This bound can be made arbitrarily small, uniformly in dimension, by allowing enough time for annealing and then refining the time mesh accordingly. Importantly, these conditions allow regimes in which the KL divergence between the target and the initial smoothed law diverges with dimension.

C2weakest assumption

The target is a finite Gaussian mixture whose component covariance spectra satisfy the stated summability conditions together with the chosen smoothing covariance and preconditioner (abstract, paragraph on exponential-integrator scheme).

C3one line summary

Proves dimension-uniform KL bounds for exponential-integrator discretization of preconditioned ALD on Gaussian mixtures under spectral summability, showing EM stability restrictions are scheme-dependent rather than intrinsic.

References

54 extracted · 54 resolved · 0 Pith anchors

[1] Lorenzo Baldassari, Josselin Garnier, Knut Sølna, and Maarten V . de Hoop. Preconditioned Langevin dynamics with score-based generative models for infinite-dimensional linear Bayesian inverse problems 2025

[2] Dimension-free multimodal sampling via preconditioned annealed langevin dynamics 2026

[3] Lorenzo Baldassari, Ali Siahkoohi, Josselin Garnier, Knut Sølna, and Maarten V . de Hoop. Conditional score-based diffusion models for Bayesian inference in infinite dimensions. In Proceedings of the 2023

[4] year = 2024, month = may, number = 2024

[5] Geometric MCMC for infinite-dimensional inverse problems.Journal of Computational Physics, 335:327–351, 2017 2017

Receipt and verification

First computed	2026-05-20T00:02:23.774846Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59ccbb0aaddcb90e5196e2629917fbe937dcc2fcdd1a1f2798045e318c06b1ca

Aliases

arxiv: 2605.16473 · arxiv_version: 2605.16473v1 · doi: 10.48550/arxiv.2605.16473 · pith_short_12: LHGLWCVN3S4Q · pith_short_16: LHGLWCVN3S4Q4UMW · pith_short_8: LHGLWCVN

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LHGLWCVN3S4Q4UMW4JRJSF735E \
  | 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: 59ccbb0aaddcb90e5196e2629917fbe937dcc2fcdd1a1f2798045e318c06b1ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6c10207d858186bdebf3e5c1df2282c84af3d20d3ea10b5c5de7864cdee4776",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.NA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-15T15:18:32Z",
    "title_canon_sha256": "8f6b3e0fb90c86e5c115a5c5ce98c85b496e42735a6de670b6583d02cb56e95c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16473",
    "kind": "arxiv",
    "version": 1
  }
}