arXiv Machine Learning

Manifold Sampling via Entropy Maximization

The paper introduces MASEM, a method for uniform sampling on manifolds that may have multiple disconnected components defined by smooth constraints. It employs a resampling scheme that maximizes the entropy of the empirical distribution using k‑nearest neighbor density estimation, and shows that this approach reduces KL‑divergence exponentially with the number of resampling steps. Experiments on synthetic and robotics benchmarks demonstrate that MASEM achieves faster mixing and improves Sinkhorn distance by an order of magnitude compared to existing alternatives while maintaining competitive runtime.

arXiv Machine Learning

Oct 2

Manifold-Aware Perturbations for Constrained Generative Modeling

The paper introduces a new method for perturbing data distributions in a way that respects equality constraints, allowing generative models to better handle constrained data. By adjusting the distribution while preserving the manifold geometry, the approach ensures support matches the ambient space dimension. Experiments with diffusion models and normalizing flows demonstrate improved data recovery and stable sampling across several tasks.

By Katherine Keegan, Lars Ruthotto

diffusion

arXiv Statistics ML

Oct 2

On skew-symmetric distributions and their use in Monte Carlo sampling algorithms: coordinate-free, Gibbs-style and manifold versions of the Barker proposal

arXiv:2610.01448v1 Announce Type: cross Abstract: Skew-symmetric probability distributions provide a principled mechanism for incorporating gradient information into Markov chain Monte Carlo algorith...

By Minh Vu, Samuel Livingstone, Pantelis Samartsidis

arXiv Statistics ML

Oct 19

Computing Fr\'echet on Unknown Submanifolds of Riemannian Manifolds

arXiv:2610. 22592v1 Announce Type: cross Abstract: Empirical averages are fundamental statistical primitives.

By Ian McPherson, Mauro Maggioni

arXiv AI

Jul 7

CuBAS: Information Geometric Curvature-Based Adaptive Sampling for Supervised Classification

arXiv:2607. 03145v1 Announce Type: cross Abstract: The informativeness of a training set is as consequential as its size, yet most sampling strategies remain agnostic to the intrinsic geometry of the data distribution.

By Alexandre L. M. Levada

benchmarks

arXiv Machine Learning

Jul 2

Constrained Bayesian Optimisation with Multiple Information Sources

arXiv:2607. 00865v1 Announce Type: new Abstract: Bayesian Optimisation (BO) under unknown constraints is particularly challenging when feasible regions are small.

By Hauke Maathuis, Roeland De Breuker, Saullo Castro, Maike Osborne

benchmarks

arXiv Machine Learning

Jun 2

Efficient Diffusion Models under Nonconvex Equality and Inequality constraints via Landing

arXiv:2604. 17838v2 Announce Type: replace Abstract: Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.

By Kijung Jeon, Michael Muehlebach, Molei Tao

diffusion robotics benchmarks safety

arXiv Machine Learning

Jun 17

Randomized Midpoint Method for Log-Concave Sampling under Constraints

arXiv:2405. 15379v3 Announce Type: replace-cross Abstract: In this paper, we study the problem of sampling from log-concave distributions supported on convex and compact sets, with a particular focus on the randomized midpoint discretization of both overdamped and kinetic Langevin diffusions in constrained domains.

By Yifeng Yu, Shijie Zhang, Lu Yu

diffusion

arXiv Machine Learning

Oct 5

Light Entropic Optimal Transport on Riemannian Manifolds

Light Entropic Optimal Transport on Riemannian Manifolds introduces ManifoldLightOT, a lightweight method for learning kernel‑induced entropic optimal transport couplings directly on common manifolds such as spheres, tori, SO(3), and SE(3). By constructing geometry‑specific Gibbs kernels and compatible potential parameterizations, the approach yields closed‑form normalization and directly sampleable conditional distributions. The formulation extends naturally to products of manifolds and optimizes potentials from samples using Monte Carlo estimates, demonstrating superior performance over existing manifold OT methods in synthetic and real‑world experiments.

By Xavier Aramayo-Carrasco, Petr Mokrov, Alexander Korotin

fine-tuning

arXiv Statistics ML

Oct 22

A Computable Measure of Suboptimality for Entropy-Regularised Variational Objectives

arXiv:2509.10393v5 Announce Type: replace-cross Abstract: Several methods in statistics and machine learning target a probability distribution for which an entropy-regularised variational objective i...

By Cl\'ementine Chazal, Heishiro Kanagawa, Zheyang Shen, Anna Korba, Chris. J. Oates

arXiv Machine Learning

Aug 18

Density-Reweighted Entropic Optimal Transport: Decoupling Geometry from Sampling Density

arXiv:2608. 16506v1 Announce Type: cross Abstract: Dataset alignment is a central step in data analysis across science and engineering, where the goal is to match observations between datasets.

By Keyi Li, Yuval Kluger, Boris Landa

safety

arXiv Machine Learning

Jul 22

Information Theoretic Bayesian Optimization over the Probability Simplex

arXiv:2603. 09793v2 Announce Type: replace Abstract: Bayesian optimization is a data-efficient technique that has been shown to be extremely powerful to optimize expensive, black-box, and possibly noisy objective functions.

By Federico Pavesi, Antonio Candelieri, No\'emie Jaquier

robotics benchmarks

arXiv Machine Learning

Jul 8

EntroPath: Maximum Entropy Path Ensemble Embedding for Manifold Learning

arXiv:2607. 06497v1 Announce Type: new Abstract: We introduce EntroPath, a manifold learning method that recovers geodesic geometry from data graphs through ensembles of diffusion paths.

By Przemys{\l}aw Rola

rag diffusion benchmarks

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