# Generalizing the No-U-Turn Sampler to Riemannian Manifolds

arXiv: https://arxiv.org/abs/1304.1920 · HTML: https://mlsanity.com/paper/1304.1920/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2013.

## Built on by (most cited first, 5 of 5)

- [Applications of the Free Energy Principle to Machine Learning and Neuroscience](https://mlsanity.com/paper/2107.00140/) (2021)
- [Mixing of the No-U-Turn Sampler and the Geometry of Gaussian Concentration](https://mlsanity.com/paper/2410.06978/) (2024)
- [A Mathematical Walkthrough and Discussion of the Free Energy Principle](https://mlsanity.com/paper/2108.13343/) (2021)
- [Antithetic Riemannian Manifold And Quantum-Inspired Hamiltonian Monte Carlo](https://mlsanity.com/paper/2107.02070/) (2021)
- [Fast Riemannian-manifold Hamiltonian Monte Carlo for hierarchical Gaussian-process models](https://mlsanity.com/paper/2511.06407/) (2025)

## Abstract (arXiv)

Hamiltonian Monte Carlo provides efficient Markov transitions at the expense of introducing two free parameters: a step size and total integration time. Because the step size controls discretization error it can be readily tuned to achieve certain accuracy criteria, but the total integration time is left unconstrained. Recently Hoffman and Gelman proposed a criterion for tuning the integration time in certain systems with their No U-Turn Sampler, or NUTS. In this paper I investigate the dynamical basis for the success of NUTS and generalize it to Riemannian Manifold Hamiltonian Monte Carlo.