Decentralized Neural Networks for Robust and Scalable Eigenvalue Computation

TL;DR

This paper presents a decentralized neural network approach for scalable and robust eigenvalue computation in large systems, enabling autonomous agents to collaboratively estimate eigenvalues with high accuracy.

Contribution

It introduces a novel distributed neural network framework that improves scalability and robustness in eigenvalue estimation compared to traditional centralized methods.

Findings

Converges accurately to true eigenvalues

Robust against communication delays and network disruptions

Outperforms traditional centralized algorithms in large-scale settings

Abstract

This paper introduces a novel method for eigenvalue computation using a distributed cooperative neural network framework. Unlike traditional techniques that face scalability challenges in large systems, our decentralized algorithm enables multiple autonomous agents to collaboratively estimate the smallest eigenvalue of large matrices. Each agent employs a localized neural network, refining its estimates through communication with neighboring agents. Our empirical results confirm the algorithm's convergence towards the true eigenvalue, with estimates clustered closely around the true value. Even in the presence of communication delays or network disruptions, the method demonstrates strong robustness and scalability. Theoretical analysis further validates the accuracy and stability of the proposed approach, while empirical tests highlight its efficiency and precision, surpassing traditional centralized algorithms in large-scale eigenvalue computations.