Understanding the dynamics of message passing algorithms: a free probability heuristics
Statistical Mechanics
2023-07-19 v1 Disordered Systems and Neural Networks
Machine Learning
Machine Learning
Abstract
We use freeness assumptions of random matrix theory to analyze the dynamical behavior of inference algorithms for probabilistic models with dense coupling matrices in the limit of large systems. For a toy Ising model, we are able to recover previous results such as the property of vanishing effective memories and the analytical convergence rate of the algorithm.
Cite
@article{arxiv.2002.02533,
title = {Understanding the dynamics of message passing algorithms: a free probability heuristics},
author = {Manfred Opper and Burak Çakmak},
journal= {arXiv preprint arXiv:2002.02533},
year = {2023}
}
Comments
11 pages, 2 figures. Presented at the conference "Random Matrix Theory: Applications in the Information Era'' 2019 Krak\'{o}w