Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …

Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare
in a geometrically faithful way point clouds and more generally probability distributions. The …

Normalizing flows are a class of deep generative models that are especially interesting for
modeling probability distributions in physics, where the exact likelihood of flows allows …

We consider the task of aligning two sets of points in high dimension, which has many
applications in natural language processing and computer vision. As an example, it was …

Neural networks embed the geometric structure of a data manifold lying in a high-
dimensional space into latent representations. Ideally, the distribution of the data points in …

As an essential operation of legal retrieval, legal case matching plays a central role in
intelligent legal systems. This task has a high demand on the explainability of matching …

Comparing metric measure spaces (ie a metric space endowed with a probability
distribution) is at the heart of many machine learning problems. The most popular distance …

Optimal transport aligns samples across distributions by minimizing the transportation cost
between them, eg, the geometric distances. Yet, it ignores coherence structure in the data …

Cross-domain imitation learning studies how to leverage expert demonstrations of one
agent to train an imitation agent with a different embodiment or morphology. Comparing …

The gap between speech and text modalities is a major challenge in speech-to-text
translation (ST). Different methods have been proposed to reduce this gap, but most of them …