# Generalizing Hamiltonian Monte Carlo with Neural Networks

arXiv: https://arxiv.org/abs/1711.09268 · HTML: https://mlsanity.com/paper/1711.09268/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2017.

## Built on by (most cited first, 30 of 52)

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- [Applications of Machine Learning to Lattice Quantum Field Theory](https://mlsanity.com/paper/2202.05838/) (2022)
- [Optimal Preconditioning and Fisher Adaptive Langevin Sampling](https://mlsanity.com/paper/2305.14442/) (2023)
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- [Entropy-based Training Methods for Scalable Neural Implicit Sampler](https://mlsanity.com/paper/2306.04952/) (2023)
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- [Hamiltonian Dynamics with Non-Newtonian Momentum for Rapid Sampling](https://mlsanity.com/paper/2111.02434/) (2021)
- [Deep Learning Hamiltonian Monte Carlo](https://mlsanity.com/paper/2105.03418/) (2021)
- [LSB: Local Self-Balancing MCMC in Discrete Spaces](https://mlsanity.com/paper/2109.03867/) (2021)
- [Delayed rejection Hamiltonian Monte Carlo for sampling multiscale distributions](https://mlsanity.com/paper/2110.00610/) (2021)
- [Accelerating Hamiltonian Monte Carlo via Chebyshev Integration Time](https://mlsanity.com/paper/2207.02189/) (2022)
- [Energy based diffusion generator for efficient sampling of Boltzmann distributions](https://mlsanity.com/paper/2401.02080/) (2024)
- [Hamiltonian Score Matching and Generative Flows](https://mlsanity.com/paper/2410.20470/) (2024)
- [Zero-shot-Learning Cross-Modality Data Translation Through Mutual Information Guided Stochastic Diffusion](https://mlsanity.com/paper/2301.13743/) (2023)
- [Entropy-based adaptive Hamiltonian Monte Carlo](https://mlsanity.com/paper/2110.14625/) (2021)
- [Bootstrap Your Flow](https://mlsanity.com/paper/2111.11510/) (2021)

## Abstract (arXiv)

We present a general-purpose method to train Markov chain Monte Carlo kernels, parameterized by deep neural networks, that converge and mix quickly to their target distribution. Our method generalizes Hamiltonian Monte Carlo and is trained to maximize expected squared jumped distance, a proxy for mixing speed. We demonstrate large empirical gains on a collection of simple but challenging distributions, for instance achieving a 106x improvement in effective sample size in one case, and mixing when standard HMC makes no measurable progress in a second. Finally, we show quantitative and qualitative gains on a real-world task: latent-variable generative modeling. We release an open source TensorFlow implementation of the algorithm.