相关论文: Kernel Neural Optimal Transport

Optimal transport is a fundamental topic that has attracted a great amount of attention from the optimization community in the past decades. In this paper, we consider an interesting discrete dynamic optimal transport problem: can we…

We investigate unpaired image inverse problems, a challenging setting where only independent, non-paired sets of noisy measurements and clean target signals are available for training. We propose a novel inverse problem solver based on…

During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, which is a setup…

In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation…

We introduce the framework of quadratic-form optimal transport (QOT), whose transport cost has the form $\iint c\,\mathrm{d}\pi \otimes\mathrm{d}\pi$ for some coupling $\pi$ between two marginals. Interesting examples of quadratic-form…

Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This paper is concerned with the derivation of distributional limits for the empirical OT value when the cost…

This paper addresses the Optimal Transport problem, which is regularized by the square of Euclidean $\ell_2$-norm. It offers theoretical guarantees regarding the iteration complexities of the Sinkhorn--Knopp algorithm, Accelerated Gradient…

Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this…

We design a quantum version of neural networks with sinusoidal activation functions and compare its performance to the classical case. We create a general quantum sine circuit implementing a discretised sinusoidal activation function. Along…

Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex…

Reinforcement learning can acquire complex behaviors from high-level specifications. However, defining a cost function that can be optimized effectively and encodes the correct task is challenging in practice. We explore how inverse optimal…

Selecting input features of top relevance has become a popular method for building self-explaining models. In this work, we extend this selective rationalization approach to text matching, where the goal is to jointly select and align text…

Neural networks have been achieving high generalization performance on many tasks despite being highly over-parameterized. Since classical statistical learning theory struggles to explain this behavior, much effort has recently been focused…

Robustness and safety are critical for the trustworthy deployment of deep reinforcement learning. Real-world decision making applications require algorithms that can guarantee robust performance and safety in the presence of general…

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…

Federated unlearning (FU) aims to remove a participant's data contributions from a trained federated learning (FL) model, ensuring privacy and regulatory compliance. Traditional FU methods often depend on auxiliary storage on either the…

Can near-term gate model based quantum processors offer quantum advantage for practical applications in the pre-fault tolerance noise regime? A class of algorithms which have shown some promise in this regard are the so-called…

The non-equilibrium Green's function method combined with density functional theory (NEGF-DFT) provides a rigorous framework for simulating nanoscale electronic transport, but its computational cost scales steeply with system size. Recent…

Taking inspiration from how the brain coordinates multiple learning systems is an appealing strategy to endow robots with more flexibility. One of the expected advantages would be for robots to autonomously switch to the least costly system…

In this article we revisit the weak optimal transport (WOT) problem, introduced by Gozlan, Roberto, Samson and Tetali (2017). We work on the real line, with barycentric cost functions, and as our first result give the following…