Research map / Probabilistic and scientific modeling / Variational and generative sampling
Hamiltonian Monte Carlo
Improves Hamiltonian Monte Carlo through reflection, Riemannian geometry and neural parameterization.
89 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Variational and generative sampling, keyword cluster “monte · carlo · mcmc”
State History Tried Checklist Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
21 papers in 2023–24 and 29 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 5.1% to 5.8%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · Exact Sampling with Integer Linear Programs and Random Perturbations (AAAI 2016 · 20 citations)
- 2017 · Dynamic Importance Sampling for Anytime Bounds of the Partition Function (NeurIPS 2017 · 14 citations)
- 2018 · Bayesian Pose Graph Optimization via Bingham Distributions and Tempered Geodesic MCMC (NeurIPS 2018 · 28 citations)
- 2019 · Learning Plackett-Luce Mixtures from Partial Preferences (AAAI 2019 · 26 citations)
- 2020 · Batch Stationary Distribution Estimation (ICML 2020 · 10 citations)
- 2021 · Evaluating the Implicit Midpoint Integrator for Riemannian Hamiltonian Monte Carlo (ICML 2021 · 2 citations)
- 2022 · Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Space (NeurIPS 2022 · 21 citations)
- 2023 · Gibbsian Polar Slice Sampling (ICML 2023 · 2 citations)
- 2024 · Protein Discovery with Discrete Walk-Jump Sampling (ICLR 2024 · 5 citations)
- 2025 · Monte-Carlo Tree Search with Uncertainty Propagation via Optimal Transport (ICML 2025 · 1 citation)
- 2026 · Score-Repellent Monte Carlo: Toward Efficient Non-Markovian Sampler with Constant Memory in General State Spaces (ICML 2026 · 0 citations)
Earliest papers here
- Exact Sampling with Integer Linear Programs and Random Perturbations (AAAI 2016 · 20 citations)
- Hawkes Processes with Stochastic Excitations (ICML 2016 · 17 citations)
- Fast Mixing Markov Chains for Strongly Rayleigh Measures, DPPs, and Constrained Sampling (NeurIPS 2016 · 17 citations)
What has been tried
70 papers here report 512 measured changes (a component added, removed or swapped, compared with a baseline): helped 68%, no clear effect 9%, hurt 18%, mixed 5%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| set noise level σ to 0.1 instead of 0.5 | paired OAS antibody generation · W_property | 0.065 -> 0.378 | Hurt | Protein Discovery with Discrete Walk-Jump Sampling (ICLR 2024 · 5 citations) |
| Use Thompson sampling instead of optimistic selection | Pocman · discounted total reward | 50.9 ± 0.6 -> 67.38 ± 0.53; 51.0 ± 0.62 -> 75.64 ± 0.51; 52.2 ± 0.79 -> 77.68 ± 0.77; 54.6 ± 1.08 -> 77.70 ± 1.22 | Helped | Monte-Carlo Tree Search with Uncertainty Propagation via Optimal Transport (ICML 2025 · 1 citation) |
| Allocate the full 20M energy-call budget to AIS and train an MLE Learner | Manywell-128 · Amortized learning performance | Hurt | On scalable and efficient training of diffusion samplers (NeurIPS 2025 · 1 citation) | |
| Increase LEC network depth | Ising model, L=15, J = 0.4, β = 0.7 · ESS | Helped | LEAPS: A discrete neural sampler via locally equivariant networks (ICML 2025 · 0 citations) | |
| Add final fine-tuning iteration | Alanine dipeptide · NLL | -213.666 -> -213.667 | Helped | Temperature-Annealed Boltzmann Generators (ICML 2025 · 0 citations) |
| Use exponential-decay rather than identical MCMC-step allocation across SL iterations | Combinatorial optimization benchmarks · objective value or optimality gap | Mixed | Sampling from Binary Quadratic Distributions via Stochastic Localization (ICML 2025 · 0 citations) | |
| Add backbone-first permutation | 4AA · ESS | 0.051 -> 0.071 | Helped | Amortized Sampling with Transferable Normalizing Flows (NeurIPS 2025 · 0 citations) |
| add intermediate SMC weighting and resampling to the reverse-diffusion proposal | Bayesian logistic regression (Credit, Cancer, Ionosphere, Sonar) · Test log-likelihood | -606.03 ± 1.26 -> -124.00 ± 1.96; -246.86 ± 0.97 -> -62.23 ± 1.96; -92.62 ± 0.04 -> -87.72 ± 1.7 | Helped | Reverse Diffusion Sequential Monte Carlo Samplers (NeurIPS 2025 · 0 citations) |
| Sample all measurements at once (AAO) instead of sequentially with OAT | Elliptical Gaussian · 2-Wasserstein distance | Hurt | Chain of Log-Concave Markov Chains (ICLR 2024 · 0 citations) | |
| Add Metropolis-Hastings initialization instead of initializing at the previous state | Unequally weighted MoG · MMD | 0.15± 0.01 -> 0.03± 0.01 | Helped | Diffusive Gibbs Sampling (ICML 2024 · 0 citations) |
| use learning rate η0=0.2 instead of the default η0=0.05 | NH3 · ground-state energy | -56.56366(2) -> -56.56379(1) | Helped | Quadratic Quantum Variational Monte Carlo (NeurIPS 2024 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 20 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- Funnel · 4 of 20 papers
- Rings · 2 of 20 papers
- Ionosphere · 2 of 20 papers
- Sonar · 2 of 20 papers
Baselines
- RDMC · 3 of 20 papers
- DMALA · 2 of 20 papers
- SMC · 2 of 20 papers
- AIS · 2 of 20 papers
- SLIPS · 2 of 20 papers
- PIS · 2 of 20 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 50 papers; from OpenAlex and the papers' affiliations).
- University of Cambridge · 5 papers
- Massachusetts Institute of Technology · 4 papers
- Karlsruher Institut für Technologie · 3 papers
- North Carolina State University · 3 papers
- École Polytechnique · 3 papers
- Imperial College London · 3 papers
- University of California, San Diego · 2 papers
- Genentech · 2 papers
- Friedrich-Schiller Universität Jena · 2 papers
- Ecole Polytechnique · 2 papers
Use it
Download BibTeX of 40 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Sequential Monte Carlo for inference (78 papers)
- Stochastic gradient MCMC (68 papers)
- Importance sampling and quadrature (45 papers)
Elsewhere in the topic
- Likelihood-free and graphical model estimation (161 papers)
- Flow matching and flow sampling (144 papers)
- Posterior sampling with diffusion guidance (137 papers)
- Score-based generative modeling analysis (128 papers)
- Structured latent VAEs (125 papers)
- Exact inference for probabilistic programs (103 papers)
- Disentangled and discrete latent models (92 papers)
- Latent variable marginalization and estimators (91 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).