Related papers: OT-Net: A Reusable Neural Optimal Transport Solver
Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…
Energy-based models (EBMs) are known in the Machine Learning community for decades. Since the seminal works devoted to EBMs dating back to the noughties, there have been a lot of efficient methods which solve the generative modelling…
Comparing unpaired samples of a distribution or population taken at different points in time is a fundamental task in many application domains where measuring populations is destructive and cannot be done repeatedly on the same sample, such…
Optimal Transport (OT) is a fundamental tool for comparing probability distributions, but its exact computation remains prohibitive for large datasets. In this work, we introduce novel families of upper and lower bounds for the OT problem…
In this paper we consider utilizing a residual neural network (ResNet) to solve ordinary differential equations. Stochastic gradient descent method is applied to obtain the optimal parameter set of weights and biases of the network. We…
In this paper, we present a neural network approach to address the dynamic unbalanced optimal transport problem on surfaces with point cloud representation. For surfaces with point cloud representation, traditional method is difficult to…
Hyperbolic-spaces are better suited to represent data with underlying hierarchical relationships, e.g., tree-like data. However, it is often necessary to incorporate, through alignment, different but related representations meaningfully.…
This paper considers the decentralized (discrete) optimal transport (D-OT) problem. In this setting, a network of agents seeks to design a transportation plan jointly, where the cost function is the sum of privately held costs for each…
Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In this paper, we develop computational tools for solving AOT…
We introduce the transport-and-pack(TAP) problem, a frequently encountered instance of real-world packing, and develop a neural optimization solution based on reinforcement learning. Given an initial spatial configuration of boxes, we seek…
We present a numerical method to solve the optimal transport problem with a quadratic cost when the source and target measures are periodic probability densities. This method is based on a numerical resolution of the corresponding…
Over the last several years, there has been significant progress in developing neural solvers for the Schr\"odinger Bridge (SB) problem and applying them to generative modelling. This new research field is justifiably fruitful as it is…
Training data are usually limited or heterogeneous in many chemical and biological applications. Existing machine learning models for chemistry and materials science fail to consider generalizing beyond training domains. In this article, we…
Balancing the trade-off between safety and efficiency is of significant importance for path planning under uncertainty. Many risk-aware path planners have been developed to explicitly limit the probability of collision to an acceptable…
A method for approximating sixth-order ordinary differential equations is proposed, which utilizes a deep learning feedforward artificial neural network, referred to as a neural solver. The efficacy of this unsupervised machine learning…
An equation of Monge-Amp\`ere type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport…
Although deep neural networks are well-known for their outstanding performance in tackling complex tasks, their hunger for computational resources remains a significant hurdle, posing energy-consumption issues and restricting their…
The inverse reflector problem aims to design a freeform reflecting surface that can direct the light from a specified source to produce the desired illumination in the target area, which is significant in the field of geometrical…
At present, a major challenge for the application of automatic driving technology is the accurate prediction of vehicle trajectory. With the vigorous development of computer technology and the emergence of convolution depth neural network,…
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…