# Accelerated sampling using SamAdams variable timesteps and position-adaptive Langevin dynamics

arXiv: https://arxiv.org/abs/2606.26881 · HTML: https://mlsanity.com/paper/2606.26881/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 24 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 6 of 6)

- [Geometric integrators and the Hamiltonian Monte Carlo method](https://mlsanity.com/paper/1711.05337/) (2017)
- [Ensemble preconditioning for Markov chain Monte Carlo simulation](https://mlsanity.com/paper/1607.03954/) (2016)
- [Friction-adaptive descent: a family of dynamics-based optimization methods](https://mlsanity.com/paper/2306.06738/) (2023)
- [A Langevin sampling algorithm inspired by the Adam optimizer](https://mlsanity.com/paper/2504.18911/) (2025)
- [Adaptive Momentum and Nonlinear Damping for Neural Network Training](https://mlsanity.com/paper/2602.00334/) (2026)
- [Estimating standard errors for importance sampling estimators with multiple Markov chains](https://mlsanity.com/paper/1509.06310/) (2015)

## Abstract (arXiv)

We introduce an accelerated Langevin-based sampling method that is based on two complementary devices: SamAdams adaptive timestepping, which automatically shrinks the effective integration step in stiff regions of phase space using a relaxed stiffness monitor, and position-adaptive Langevin (PAL) dynamics, which concentrates friction along the local force direction while preserving the canonical distribution as the exact invariant measure. The resulting combined scheme (SA-PAL) is implemented in a palindromic integrator which requires only one force evaluation per iteration through suitable organisation of the integration steps and by exploiting the rank-one-plus-scalar structure of the PAL friction tensor. We test the method on various model problems: the Rosenbrock function, a thin entropic channel, the Mueller-Brown potential, and a Bayesian parameterisation problem with a sparsity-inducing shrinkage prior. On the Rosenbrock and Mueller-Brown potentials mixing rates are improved by 1.5-3 times compared to fixed stepsize integration. Efficiency gains of more than an order of magnitude are documented in the other examples.