# On Accelerated Mixing of the No-U-turn Sampler

arXiv: https://arxiv.org/abs/2507.13259 · HTML: https://mlsanity.com/paper/2507.13259/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 17 Jul 2025.

## Builds on (most cited first, 10 of 10)

- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Lower Bounds on Metropolized Sampling Methods for Well-Conditioned Distributions](https://mlsanity.com/paper/2106.05480/) (2021)
- [When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?](https://mlsanity.com/paper/2304.04724/) (2023)
- [GIST: Gibbs self-tuning for locally adaptive Hamiltonian Monte Carlo](https://mlsanity.com/paper/2404.15253/) (2024)
- [Hamiltonian Monte Carlo for efficient Gaussian sampling: long and random steps](https://mlsanity.com/paper/2209.12771/) (2022)
- [Incorporating Local Step-Size Adaptivity into the No-U-Turn Sampler using Gibbs Self Tuning](https://mlsanity.com/paper/2408.08259/) (2024)
- [Mixing of the No-U-Turn Sampler and the Geometry of Gaussian Concentration](https://mlsanity.com/paper/2410.06978/) (2024)
- [On the convergence of dynamic implementations of Hamiltonian Monte Carlo and No U-Turn Samplers](https://mlsanity.com/paper/2307.03460/) (2023)
- [The No-Underrun Sampler: A Locally-Adaptive, Gradient-Free MCMC Method](https://mlsanity.com/paper/2501.18548/) (2025)
- [The Within-Orbit Adaptive Leapfrog No-U-Turn Sampler](https://mlsanity.com/paper/2506.18746/) (2025)

## Built on by (most cited first, 2 of 2)

- [A Theoretical Comparison of No-U-Turn Sampler Variants: Necessary and Sufficient Convergence Conditions and Mixing Time Analysis under Gaussian Targets](https://mlsanity.com/paper/2603.18640/) (2026)
- [Accelerated Mixing Time of Randomized Hamiltonian Monte Carlo](https://mlsanity.com/paper/2607.12902/) (2026)

## Abstract (arXiv)

Recent progress on the theory of variational hypocoercivity established that Randomized Hamiltonian Monte Carlo -- at criticality -- can achieve pronounced acceleration in its convergence and hence sampling performance over diffusive dynamics. Manual critical tuning being unfeasible in practice has motivated automated algorithmic solutions, notably the No-U-turn Sampler. Beyond its empirical success, a rigorous study of this method's ability to achieve accelerated convergence has been missing. We initiate this investigation combining a concentration of measure approach to examine the automatic tuning mechanism with a coupling based mixing analysis for Hamiltonian Monte Carlo. In certain Gaussian target distributions, this yields a precise characterization of the sampler's behavior resulting, in particular, in rigorous mixing guarantees describing the algorithm's ability and limitations in achieving accelerated convergence.