Cone Extended Rayleigh Quotients for Directed Graph Learning: Minimax Spectral Certificates, Sensitivity, and Adaptive Control

The paper introduces a learning-oriented framework for spectral certification, sensitivity analysis, and adaptive control of directed graph learning models using cone extended Rayleigh quotients. It provides computable cone bounds and differentiable soft-min/max surrogates that enable rigorous one-sided spectral bounds without requiring symmetry or cone preservation. Experiments on directed networks, including the Cora citation graph, demonstrate that adaptive sensitivity recomputation can significantly reduce spectral levels while preserving test accuracy.

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