# Resonances in reflective Hamiltonian Monte Carlo

arXiv: https://arxiv.org/abs/2504.12374 · HTML: https://mlsanity.com/paper/2504.12374/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 55 references that are in the map.
- First posted on arXiv 16 Apr 2025.

## Builds on (most cited first, 11 of 11)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Optimal Transport Tools (OTT): A JAX Toolbox for all things Wasserstein](https://mlsanity.com/paper/2201.12324/) (2022)
- [Improving Gradient-guided Nested Sampling for Posterior Inference](https://mlsanity.com/paper/2312.03911/) (2023)
- [Efficient Random-Walk Methods for Approximating Polytope Volume](https://mlsanity.com/paper/1312.2873/) (2013)
- [Efficient computation of the volume of a polytope in high-dimensions using Piecewise Deterministic Markov Processes](https://mlsanity.com/paper/2202.09129/) (2022)
- [Kernel-, mean- and noise-marginalised Gaussian processes for exoplanet transits and H0 inference](https://mlsanity.com/paper/2311.04153/) (2023)

## Built on by (most cited first, 4 of 4)

- [Automatic Laplace Collapsed Sampling: Scalable Marginalisation of Latent Parameters via Automatic Differentiation](https://mlsanity.com/paper/2603.26644/) (2026)
- [Generative Nested Sampling of Atomistic Thermodynamic Landscapes](https://mlsanity.com/paper/2609.03193/) (2026)
- [Quenched Ensemble Sampling](https://mlsanity.com/paper/2609.15894/) (2026)
- [Neural Transport Nested Sampling](https://mlsanity.com/paper/2609.29413/) (2026)

## Abstract (arXiv)

In high dimensions, reflective Hamiltonian Monte Carlo with inexact reflections exhibits slow mixing when the particle ensemble is initialised from a Dirac delta distribution and the uniform distribution is targeted. By quantifying the instantaneous non-uniformity of the distribution with the Sinkhorn divergence, we elucidate the principal mechanisms underlying the mixing problems. In spheres and cubes, we show that the collective motion transitions between fluid-like and discretisation-dominated behaviour, with the critical step size scaling as a power law in the dimension. In both regimes, the particles can spontaneously unmix, leading to resonances in the particle density and the aforementioned problems. Additionally, low-dimensional toy models of the dynamics are constructed which reproduce the dominant features of the high-dimensional problem. Finally, the dynamics is contrasted with the exact Hamiltonian particle flow and tuning practices are discussed.