The estimation of optimal transport maps (a.k.a. Monge maps) is a central problem in optimal transport literature. Recent observations reveal that the flow map of the Wasserstein gradient flow of the relative entropy closely approximates—though does not exactly equal—the Monge map between a given source distribution and a Gaussian target. In this work, we demonstrate how the evolution equation governing this flow map can be corrected to form a constrained gradient flow that provably converges to the true Monge map.When the maps are parametrized as gradients of convex models (e.g. […]

Constant Bourdrez : "Learning To Sample From Diffusion Models Via Inverse Reinforcement Learning" Hanna Benarroch : "Certified Per-instance Unlearning using Individual Sensitivity Bounds"

Emmanuel Sérié: Harness over harnesses — demo of cosmon orchestrating Claude Code agents (noogram.org) Olivier Cappé: demo of Antigravity for doing useful things Gabriel Peyré: demo of Codex for making video games and doing math

Solving most image processing tasks, such as denoising, deblurring, inpainting, etc, require explicitly or implicitly a prior probability model of natural images. Classically, both learning (by maximizing likelihood) and using (via Bayes' rule) such prior models are intractable due to the curse of dimensionality. Diffusion models take a different approach, where the prior density is replaced by a family of score vector fields across noise levels. They have led to impressive success in generative modeling, but the learned density is not explicit nor is it readily usable as a prior […]

Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based training in which hierarchical feature learning becomes an explicit iterative spectral procedure. In this limit, the dynamics at each layer decouple: given the current representation, the next layer selects directions with maximal accessible low-degree correlation to the label. This yields a tractable surrogate mechanism for deep learning, together with a natural kernel-space interpretation. Neural LoFi provides […]