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Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to address its high computational complexity, some leading to approximate or…

Vector Quantization (VQ) has emerged as a prominent weight compression technique, showcasing substantially lower quantization errors than uniform quantization across diverse models, particularly in extreme compression scenarios. However,…

This paper shows how to reduce the computational cost for a variety of common machine vision tasks by operating directly in the compressed domain, particularly in the context of hardware acceleration. Pyramid Vector Quantization (PVQ) is…

Vector quantization, a problem rooted in Shannon's source coding theory, aims to quantize high-dimensional Euclidean vectors while minimizing distortion in their geometric structure. We propose TurboQuant to address both mean-squared error…

Sinkhorn algorithm has been used pervasively to approximate the solution to optimal transport (OT) and unbalanced optimal transport (UOT) problems. However, its practical application is limited due to the high computational complexity. To…

The mismatch capacity characterizes the highest information rate of the channel under a prescribed decoding metric and serves as a critical performance indicator in numerous practical communication scenarios. Compared to the commonly used…

Optimal transport (OT) has enjoyed great success in machine learning as a principled way to align datasets via a least-cost correspondence, driven in large part by the runtime efficiency of the Sinkhorn algorithm (Cuturi, 2013). However,…

Although Sinkhorn divergences are now routinely used in data sciences to compare probability distributions, the computational effort required to compute them remains expensive, growing in general quadratically in the size $n$ of the support…

Vector quantization (VQ) is a method for deterministically learning features through discrete codebook representations. Recent works have utilized visual tokenizers to discretize visual regions for self-supervised representation learning.…

The primary goal of reinforcement learning is to develop decision-making policies that prioritize optimal performance without considering risk or safety. In contrast, safe reinforcement learning aims to mitigate or avoid unsafe states. This…

We consider the entropic regularization of discretized optimal transport and propose to solve its optimality conditions via a logarithmic Newton iteration. We show a quadratic convergence rate and validate numerically that the method…

Vector quantization(VQ) is a lossy data compression technique from signal processing, which is restricted to feature vectors and therefore inapplicable for combinatorial structures. This contribution presents a theoretical foundation of…

Vector Quantization (VQ) underpins many modern generative frameworks such as VQ-VAE, VQ-GAN, and latent diffusion models. Yet, it suffers from the persistent problem of codebook collapse, where a large fraction of code vectors remains…

Efficient routing algorithms based on vehicular ad hoc networks (VANETs) play an important role in emerging intelligent transportation systems. This highly dynamic topology faces a number of wireless communication service challenges. In…

Recently, vision transformers (ViTs) have superseded convolutional neural networks in numerous applications, including classification, detection, and segmentation. However, the high computational requirements of ViTs hinder their widespread…

We propose a consistency model based on the optimal-transport flow. A physics-informed design of partially input-convex neural networks (PICNN) plays a central role in constructing the flow field that emulates the displacement…

This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…

This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely-used iterative Bregman projections algorithm (or Sinkhorn--Knopp…

Optimal transport is a machine learning problem with applications including distribution comparison, feature selection, and generative adversarial networks. In this paper, we propose feature-robust optimal transport (FROT) for…

In this paper, we propose a refinement strategy to the well-known Physics-Informed Neural Networks (PINNs) for solving partial differential equations (PDEs) based on the concept of Optimal Transport (OT). Conventional black-box PINNs…