# Accelerating Non-Smooth and Heavy-Tailed Sampling

arXiv: https://arxiv.org/abs/2610.11139 · HTML: https://mlsanity.com/paper/2610.11139/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 76 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 7 of 7)

- [Generalized EXTRA stochastic gradient Langevin dynamics](https://mlsanity.com/paper/2412.01993/) (2024)
- [Non-Reversible Langevin Algorithms for Constrained Sampling](https://mlsanity.com/paper/2501.11743/) (2025)
- [Non-Convex Optimization via Non-Reversible Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2004.02823/) (2020)
- [Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysis](https://mlsanity.com/paper/2503.19066/) (2025)
- [Anchored Langevin Algorithms](https://mlsanity.com/paper/2509.19455/) (2025)
- [Decentralized Proximal Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2605.00723/) (2026)
- [Reflected Anchored Langevin Algorithms](https://mlsanity.com/paper/2610.09522/) (2026)

## Abstract (arXiv)

Anchored Langevin dynamics (ALD) is useful for non-smooth sampling where the density of the target distribution is possibly non-differentiable and heavy-tailed; reflected anchored Langevin dynamics (RALD) can sample possibly non-differentiable target density on a constrained domain. In this paper, we propose and study non-reversible anchored Langevin dynamics (NALD) for sampling possibly non-differentiable and heavy-tailed target density in the Euclidean space and the non-reversible reflected anchored Langevin dynamics (NRALD) for sampling possibly non-differentiable target density in the constrained space. Our construction adds a circulation drift generated by a possibly state-dependent divergence-free skew-symmetric matrix field and a stream potential. It preserves the target distribution without requiring derivatives of target density, admits a random-time-change representation, and applies both on the whole Euclidean space and on bounded domains with normal reflection. By breaking reversibility, we show that NALD and NRALD can converge to their target distributions faster than their reversible counterparts via finite-time non-asymptotic convergence analysis, a large deviations analysis and asymptotic variance reduction. Numerical experiments demonstrate the efficiency of the proposed algorithms.