Decentralized Neural Networks for Robust and Scalable Eigenvalue Computation
This addresses scalability challenges in eigenvalue computation for large-scale systems, though it appears incremental as an adaptation of neural networks to a distributed setting.
The paper tackles the problem of eigenvalue computation in large systems by introducing a decentralized neural network framework where multiple agents collaboratively estimate the smallest eigenvalue, achieving convergence with estimates clustered around the true value and demonstrating robustness against communication delays.
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.