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

arXiv · AI, language, vision and robotics · article · Aug 27, 2026 · UTC

Directed graph learning naturally leads to trainable nonsymmetric propagation operators with distinct right and left spectral structures. Building on the two-sided cone Rayleigh framework for generalized pencils \[ B_θ-λG, \] we develop a learning-oriented methodology for spectral certification, sensitivity analysis, and control without requiring symmetry, nonnegativity, or cone preservation. In the positive-orthant setting, computable lower and upper cone bounds provide an a posteriori enclosure of a distinguished cone level, while smooth soft-min/max surrogates preserve rigorous one-sided bo

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