A Learning-Based Decentralized Approach to Eigenspectrum Optimization of Network Graphs

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This thesis presents a novel learning-based decentralized approach to eigenspectrum optimization for network graphs, aimed at mitigating vulnerability to adversarial resonance attacks. Traditional centralized methods, while effective, facescalability and feasibility challenges in large or decentralized networks. To address these limitations, we propose a deep neural network (DNN) model trained on localized outcomes from centralized eigenspectrum optimization. The model learns to predict edge weight adjustments based on local graph topologies, enabling decentralized control without global network knowledge. Our methodology involves generating diverse graph datasets, embedding maximal subgraphs to standardize
inputs, and iteratively refining the DNN architecture for optimal performance. Experimental results demonstrate that the decentralized approach achieves significant spectral flattening, reducing network vulnerability while adhering to constraints
such as fixed total edge weight and preserved topology. The Decentralized Optimization Performance Ratio (DOPR), a novel evaluation metric introduced in this thesis, quantifies the effectiveness of our method, revealing strong performance,
particularly in densely connected graphs. This work bridges the gap between centralized and decentralized optimization, offering a scalable and practical solution for enhancing network resilience against adversarial attacks.

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