Related papers: Mean-field methods and algorithmic perspectives fo…

Machine learning is at the heart of managing the real-world problems associated with massive data. With the success of neural networks on such large-scale problems, more research in machine learning is being conducted now than ever before.…

This paper develops a new deep learning algorithm to solve a class of finite-horizon mean-field games. The proposed hybrid algorithm uses Markov chain approximation method combined with a stochastic approximation-based iterative deep…

This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that…

This article conducts a large dimensional study of a simple yet quite versatile classification model, encompassing at once multi-task and semi-supervised learning, and taking into account uncertain labeling. Using tools from random matrix…

This paper investigates the use of transformers to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental in modeling phenomena across physics, biology, and…

In recent years, machine learning has been adopted to complex networks, but most existing works concern about the structural properties. To use machine learning to detect phase transitions and accurately identify the critical transition…

Probabilistic mixture models have been widely used for different machine learning and pattern recognition tasks such as clustering, dimensionality reduction, and classification. In this paper, we focus on trying to solve the most common…

Bayesian inference provides a methodology for parameter estimation and uncertainty quantification in machine learning and deep learning methods. Variational inference and Markov Chain Monte-Carlo (MCMC) sampling methods are used to…

This work explores multi-modal inference in a high-dimensional simplified model, analytically quantifying the performance gain of multi-modal inference over that of analyzing modalities in isolation. We present the Bayes-optimal performance…

Representation learning has been widely studied in the context of meta-learning, enabling rapid learning of new tasks through shared representations. Recent works such as MAML have explored using fine-tuning-based metrics, which measure the…

Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of complex…

We extend previous mean-field approaches for non-equilibrium neural network models to estimate correlations in the system. This offers a powerful tool for approximating the system dynamics as well as a fast method to infer network…

We develop a framework for the analysis of deep neural networks and neural ODE models that are trained with stochastic gradient algorithms. We do that by identifying the connections between control theory, deep learning and theory of…

Transformer-based models have demonstrated exceptional performance across diverse domains, becoming the state-of-the-art solution for addressing sequential machine learning problems. Even though we have a general understanding of the…

Memetic algorithms are techniques that orchestrate the interplay between population-based and trajectory-based algorithmic components. In particular, some memetic models can be regarded under this broad interpretation as a group of…

The recent work arXiv:2407.17373 proposes a derivative-free consensus-based particle method that computes global solutions to nonconvex-nonconcave min-max problems and establishes global exponential convergence in the sense of the…

To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…

Understanding the relationship between the heterogeneous structure of complex networks and cooperative phenomena occurring on them remains a key problem in network science. Mean-field theories of spin models on networks constitute a…

A principled method to obtain approximate solutions of general constrained integer optimization problems is introduced. The approach is based on the calculation of a mean field probability distribution for the decision variables which is…

A basic challenge in experimental physics is the extraction of information related to variables that are not directly measured. The challenge is particularly severe in quantum systems where one may be interested in correlations of operators…