Related papers: Low-rank Optimal Transport: Approximation, Statist…
The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…
Transformers have proven highly effective across modalities, but standard softmax attention scales quadratically with sequence length, limiting long context modeling. Linear attention mitigates this by approximating attention with kernel…
We introduce \emph{in-context operator learning on probability measure spaces} for optimal transport (OT). The goal is to learn a single solution operator that maps a pair of distributions to the OT map, using only few-shot samples from…
We study the estimation of optimal transport (OT) maps between an arbitrary source probability measure and a log-concave target probability measure. Our contributions are twofold. First, we propose a new evolution equation in the set of…
While optimal transport (OT) enforces a rigid constraint by requiring two measures to be matched exactly, partial optimal transport relaxes this requirement by allowing mass to remain unmatched through a global budget, scalar rebate, or…
We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchical OT problems to standard OT problems, allowing efficient…
We study the problem of designing hard negative sampling distributions for unsupervised contrastive representation learning. We propose and analyze a novel min-max framework that seeks a representation which minimizes the maximum…
Optimal transport (OT) theory has attracted much attention in machine learning and signal processing applications. OT defines a notion of distance between probability distributions of source and target data points. A crucial factor that…
We propose dynamical optimal transport (OT) problems constrained in a parameterized probability subset. In application problems such as deep learning, the probability distribution is often generated by a parameterized mapping function. In…
Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision. The core assumption in the OT problem is the equal total amount of mass in source and target measures, which limits its…
Point sets matching problems can be handled by optimal transport. The mechanism behind it is that optimal transport recovers the point-to-point correspondence associated with the least curl deformation. Optimal transport is a special form…
Multimarginal optimal transport (MOT) is a powerful framework for modeling interactions between multiple distributions, yet its applicability is bottlenecked by a high computational overhead. Entropic regularization provides computational…
Multi-task learning (MTL) is a widely explored paradigm that enables the simultaneous learning of multiple tasks using a single model. Despite numerous solutions, the key issues of optimization conflict and task imbalance remain…
In this paper, we tackle the inductive semi-supervised learning problem that aims to obtain label predictions for out-of-sample data. The proposed approach, called Optimal Transport Induction (OTI), extends efficiently an optimal transport…
The Optimal transport (OT) problem is rapidly finding its way into machine learning. Favoring its use are its metric properties. Many problems admit solutions with guarantees only for objects embedded in metric spaces, and the use of…
Alignment plays a fundamental role in many machine learning problems, such as multi-network analysis, multimodal learning, and point cloud registration. Recent works increasingly leverage optimal transport (OT) for distributional alignment,…
An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…
Algorithmic trading refers to executing buy and sell orders for specific assets based on automatically identified trading opportunities. Strategies based on reinforcement learning (RL) have demonstrated remarkable capabilities in addressing…
Low-rank approximation is a technique to approximate a tensor or a matrix with a reduced rank to reduce the memory required and computational cost for simulation. Its broad applications include dimension reduction, signal processing,…
The optimal transport (OT) map offers the most economical way to transfer one probability measure distribution to another. Classical OT theory does not involve a discussion of preserving topological connections and orientations in…