用分布式神经网络协作计算矩阵最小特征值，更鲁棒高效。
Decentralized Neural Networks for Robust and Scalable Eigenvalue Computation
- 多个智能体通过局部神经网络协作，共享信息估算特征值。
- 实验显示估计值紧贴真实值，且在通信延迟下仍稳定收敛。
- 适合大规模矩阵计算，比传统集中式方法更适应复杂网络环境。
本文提出一种基于分布式协作神经网络框架的新型特征值计算方法。与传统方法在大规模系统中面临可扩展性挑战不同，该去中心化算法使多个自主智能体能够协同估计大型矩阵的最小特征值。每个智能体使用局部神经网络，通过与邻近智能体通信不断优化自身估计。实验证明算法能收敛至真实特征值，估计结果紧密聚集于真值附近。即使存在通信延迟或网络中断，方法仍表现出强鲁棒性和可扩展性。理论分析进一步验证了该方法的准确性和稳定性，实证测试表明其在大规模特征值计算中效率和精度均优于传统集中式算法。
原文摘要 · Abstract (English)
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.
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