相关论文: Kernel Neural Optimal Transport

Deep neural networks (NN) have achieved great success in many applications. However, why do deep neural networks obtain good generalization at an over-parameterization regime is still unclear. To better understand deep NN, we establish the…

Real-world non-mydriatic retinal fundus photography is prone to artifacts, imperfections and low-quality when certain ocular or systemic co-morbidities exist. Artifacts may result in inaccuracy or ambiguity in clinical diagnoses. In this…

An interval transportation problem represents a model for a transportation problem in which the values of supply, demand, and transportation costs are affected by uncertainty and can vary independently within given interval ranges. One of…

Within the field of optimal transport (OT), the choice of ground cost is crucial to ensuring that the optimality of a transport map corresponds to usefulness in real-world applications. It is therefore desirable to use known information to…

A well-recognized limitation of kernel learning is the requirement to handle a kernel matrix, whose size is quadratic in the number of training examples. Many methods have been proposed to reduce this computational cost, mostly by using a…

Optimal mass transport is described by an approximation of transport cost via semi-discrete costs. The notions of optimal partition and optimal strong partition are given as well. We also suggest an algorithm for computation of Optimal…

Optimal transport (OT) serves as a natural framework for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistical estimation and exact computation of the OT distances…

We consider the model of a transportation problem with the objective of finding a minimum-cost transportation plan for shipping a given commodity from a set of supply centers to the customers. Since the exact values of supply and demand and…

Regularizing the optimal transport (OT) problem has proven crucial for OT theory to impact the field of machine learning. For instance, it is known that regularizing OT problems with entropy leads to faster computations and better…

Despite the success of deep learning-based algorithms, it is widely known that neural networks may fail to be robust. A popular paradigm to enforce robustness is adversarial training (AT), however, this introduces many computational and…

We present a study of the application of a variant of a recently introduced heuristic algorithm for the optimization of transport routes on complex networks to the problem of finding the optimal routes of communication between nodes on…

The design of artificial neural networks (ANNs) is inspired by the structure of the human brain, and in turn, ANNs offer a potential means to interpret and understand brain signals. Existing methods primarily align brain signals with…

Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph…

Optimal Transport, a theory for optimal allocation of resources, is widely used in various fields such as astrophysics, machine learning, and imaging science. However, many applications impose elementwise constraints on the transport plan…

This contribution presents substantial computational advancements to compare measures even with varying masses. Specifically, we utilize the nonequispaced fast Fourier transform to accelerate the radial kernel convolution in unbalanced…

We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…

This article introduces a new notion of optimal transport (OT) between tensor fields, which are measures whose values are positive semidefinite (PSD) matrices. This "quantum" formulation of OT (Q-OT) corresponds to a relaxed version of the…

Random cost simulations were introduced as a method to investigate optimization problems in systems with conflicting constraints. Here I study the approach in connection with the training of a feed-forward multilayer perceptron, as used in…

Optimal transport methods have recently established state of the art accuracy and efficiency for holographic laser beam shaping. However, use of such methods is hindered by severe $\mathcal{O}(N^2)$ memory and $\mathcal{O}(N^2)$ time…

We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches. Our key idea is to parameterize a single potential in the…