# Manifold Sampling via Entropy Maximization

arXiv: https://arxiv.org/abs/2605.12338 · HTML: https://mlsanity.com/paper/2605.12338/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 38 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 17 of 17)

- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Reverse Curriculum Generation for Reinforcement Learning](https://mlsanity.com/paper/1707.05300/) (2017)
- [CIC: Contrastive Intrinsic Control for Unsupervised Skill Discovery](https://mlsanity.com/paper/2202.00161/) (2022)
- [Sampling from a log-concave distribution with Projected Langevin Monte Carlo](https://mlsanity.com/paper/1507.02564/) (2015)
- [Learning Multimodal Behaviors from Scratch with Diffusion Policy Gradient](https://mlsanity.com/paper/2406.00681/) (2024)
- [Discovering Many Diverse Solutions with Bayesian Optimization](https://mlsanity.com/paper/2210.10953/) (2022)
- [Efficient multivariate entropy estimation via k-nearest neighbour distances](https://mlsanity.com/paper/1606.00304/) (2016)
- [Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Space](https://mlsanity.com/paper/2202.01908/) (2022)
- [Accelerating Motion Planning via Optimal Transport](https://mlsanity.com/paper/2309.15970/) (2023)
- [Sampling in Constrained Domains with Orthogonal-Space Variational Gradient Descent](https://mlsanity.com/paper/2210.06447/) (2022)
- [Constrained Stein Variational Trajectory Optimization](https://mlsanity.com/paper/2308.12110/) (2023)
- [NLP Sampling: Combining MCMC and NLP Methods for Diverse Constrained Sampling](https://mlsanity.com/paper/2407.03035/) (2024)
- [Fast Non-Log-Concave Sampling under Nonconvex Equality and Inequality Constraints with Landing](https://mlsanity.com/paper/2510.22044/) (2025)
- [Combined Constrained Sampling and Reinforcement Learning for Robotic Manipulation](https://mlsanity.com/paper/2602.08557/) (2026)
- [Sequentially Constrained Monte Carlo](https://mlsanity.com/paper/1410.8209/) (2014)
- [Approximate Nearest Neighbour Search on Dynamic Datasets: An Investigation](https://mlsanity.com/paper/2404.19284/) (2024)

## Built on by (most cited first, 1 of 1)

- [Variance-Reduced Manifold Sampling via Polynomial-Maximization Density Estimation](https://mlsanity.com/paper/2605.19938/) (2026)

## Abstract (arXiv)

Sampling from constrained distributions has a wide range of applications, including in Bayesian optimization and robotics. Prior work establishes convergence and feasibility guarantees for constrained sampling, but assumes that the feasible set is connected. However, in practice, the feasible set often decomposes into multiple disconnected components, which makes efficient sampling under constraints challenging. In this paper, we propose MAnifold Sampling via Entropy Maximization (MASEM) for sampling on a manifold with an unknown number of disconnected components, implicitly defined by smooth equality and inequality constraints. The presented method uses a resampling scheme to maximize the entropy of the empirical distribution based on k-nearest neighbor density estimation. We show that, in the mean field, MASEM decreases the KL-divergence between the empirical distribution and the maximum-entropy target exponentially in the number of resampling steps. We instantiate MASEM with multiple local samplers and demonstrate its versatility and efficiency on synthetic and robotics-based benchmarks. MASEM enables fast and scalable mixing across a range of constrained sampling problems, improving over alternatives by an order of magnitude in Sinkhorn distance with competitive runtime.