Related papers: Optimal and Diffusion Transports in Machine Learni…

Optimal transport is a powerful framework for the efficient allocation of resources between sources and targets. However, traditional models often struggle to scale effectively in the presence of large and heterogeneous populations. In this…

The rapid advancements in machine learning have made its application to anomalous diffusion analysis both essential and inevitable. This review systematically introduces the integration of machine learning techniques for enhanced analysis…

This work develops a distributed optimization strategy with guaranteed exact convergence for a broad class of left-stochastic combination policies. The resulting exact diffusion strategy is shown in Part II to have a wider stability range…

We consider distributed multitask learning problems over a network of agents where each agent is interested in estimating its own parameter vector, also called task, and where the tasks at neighboring agents are related according to a set…

Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…

Unmanned Aerial Vehicles (UAVs) are increasingly adopted in modern communication networks. However, challenges in decision-making and digital modeling continue to impede their rapid advancement. Reinforcement Learning (RL) algorithms face…

We present a machine learning based approach to address the study of transport processes, ubiquitous in continuous mechanics, with particular attention to those phenomena ruled by complex micro-physics, impractical to theoretical…

To remedy the drawbacks of full-mass or fixed-mass constraints in classical optimal transport, we propose adaptive optimal transport which is distinctive from the classical optimal transport in its ability of adaptive-mass preserving. It…

This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it…

We present a general (i.e., independent of the underlying model) interpolation technique based on optimal transportation of Gaussian models for parametric advection-dominated problems. The approach relies on a scalar testing function to…

This article gives an introduction to optimal transport, a mathematical theory that makes it possible to measure distances between functions (or distances between more general objects), to interpolate between objects or to enforce…

We tackle the problem of sampling from intractable high-dimensional density functions, a fundamental task that often appears in machine learning and statistics. We extend recent sampling-based approaches that leverage controlled stochastic…

Multi-modal large language models (MLLMs) achieve strong visual-language reasoning but suffer from high inference cost due to redundant visual tokens. Recent work explores visual token pruning to accelerate inference, while existing pruning…

Diffusion Models represent a significant advancement in generative modeling, employing a dual-phase process that first degrades domain-specific information via Gaussian noise and restores it through a trainable model. This framework enables…

Diffusion-based planning, learning, and control methods present a promising branch of powerful and expressive decision-making solutions. Given the growing interest, such methods have undergone numerous refinements over the past years.…

Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…

Machine learning has demonstrated remarkable promise for solving the trajectory generation problem and in paving the way for online use of trajectory optimization for resource-constrained spacecraft. However, a key shortcoming in current…

The goal of this tutorial is to introduce key models, algorithms, and open questions related to the use of optimization methods for solving problems arising in machine learning. It is written with an INFORMS audience in mind, specifically…

Heterogeneity within data distribution poses a challenge in many modern federated learning tasks. We formalize it as an optimization problem involving a computationally heavy composite under data similarity. By employing different sets of…

Diffusion-based inpainting can reconstruct missing image areas with high quality from sparse data, provided that their location and their values are well optimised. This is particularly useful for applications such as image compression,…