arXiv AI
Jun 16

Optimal Transport for Machine Learners

arXiv:2505. 06589v2 Announce Type: replace-cross Abstract: Modern machine learning repeatedly manipulates probability measures: empirical datasets, generated samples, latent distributions, class-conditional laws, particle systems, weights of wide networks and attention patterns.

By Gabriel Peyr\'e
arXiv Machine Learning
Jun 30

Learning from samples: inverse problems over measures

arXiv:2505. 07124v3 Announce Type: replace Abstract: We study inverse problems where an unknown potential is observed only through samples from the measure it induces by a convex variational principle.

By Francisco Andrade, Gabriel Peyr\'e, Clarice Poon
arXiv AI
Jul 20

Energy-based Transport for Amortized Bayesian Inference

arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.

By Ricardo Baptista, Hojjat Kaveh, Andrew M. Stuart
arXiv Machine Learning
Aug 28

COFM: Consistent Optimal Transport Flow Matching via Partially Input Convex Neural Networks

The paper introduces COFM, a framework for consistent optimal transport flow matching that uses partially input convex neural networks (PICNN) to parameterize the transport potential. By adding a Hamilton‑Jacobi residual to the training objective, COFM enforces dynamical consistency and supports both one‑step transport and multi‑step ODE sampling without costly inner optimization. Experiments on benchmark datasets show that COFM achieves competitive performance while reducing L^2‑UVP by over 2× and cutting computational time by about 9× compared to state‑of‑the‑art models.

By Fanghui Song, Zhongjian Wang, Jiebao Sun