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Despite the robust security guarantees of Quantum Key Distribution (QKD), its practical deployment is significantly challenged by the dynamic nature of quantum channels and the complexity of real-time parameter optimization. In this paper,…

In this note, we generalize the classical optimal partial transport (OPT) problem by modifying the mass destruction/creation term to function-based terms, introducing what we term ``generalized optimal partial transport'' problems. We then…

Vector quantization (VQ) transforms continuous image features into discrete representations, providing compressed, tokenized inputs for generative models. However, VQ-based frameworks suffer from several issues, such as non-smooth latent…

Sinkhorn's algorithm is a method of choice to solve large-scale optimal transport (OT) problems. In this context, it involves an inverse temperature parameter $\beta$ that determines the speed-accuracy trade-off. To improve this trade-off,…

Although quantum computing holds promise for solving Combinatorial Optimization Problems (COPs), the limited qubit capacity of NISQ hardware makes large-scale instances intractable. Conventional methods attempt to bridge this gap through…

This paper addresses the advancements in on-road trajectory planning for Autonomous Passenger Vehicles (APV). Trajectory planning aims to produce a globally optimal route for APVs, considering various factors such as vehicle dynamics,…

Vector Quantization (VQ) is a method for discretizing latent representations and has become a major part of the deep learning toolkit. It has been theoretically and empirically shown that discretization of representations leads to improved…

By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of…

In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…

Optimal Transport (OT) problems are a cornerstone of many applications, but solving them is computationally expensive. To address this problem, we propose UNOT (Universal Neural Optimal Transport), a novel framework capable of accurately…

Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two…

With the advent of large language models (LLMs), numerous Post-Training Quantization (PTQ) strategies have been proposed to alleviate deployment barriers created by their enormous parameter counts. Quantization achieves compression by…

Optimal Transport (OT) theory investigates the cost-minimizing transport map that moves a source distribution to a target distribution. Recently, several approaches have emerged for learning the optimal transport map for a given cost…

We study the Neural Optimal Transport (NOT) algorithm which uses the general optimal transport formulation and learns stochastic transport plans. We show that NOT with the weak quadratic cost might learn fake plans which are not optimal. To…

One of the limiting factors of using support vector machines (SVMs) in large scale applications are their super-linear computational requirements in terms of the number of training samples. To address this issue, several approaches that…

Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…

Network quantification (NQ) is the problem of estimating the proportions of nodes belonging to each class in subsets of unlabelled graph nodes. When prior probability shift is at play, this task cannot be effectively addressed by first…

RWKV is a modern RNN architecture with comparable performance to Transformer, but still faces challenges when deployed to resource-constrained devices. Post Training Quantization (PTQ), which is a an essential technique to reduce model size…

In this paper we study general Schatten-$p$ quasi-norm (SPQN) regularized matrix minimization problems. In particular, we first introduce a class of first-order stationary points for them, and show that the first-order stationary points…

Approximate nearest neighbor (ANN) query in high-dimensional Euclidean space is a key operator in database systems. For this query, quantization is a popular family of methods developed for compressing vectors and reducing memory…