这篇论文提出了一种新的有向图学习方法，能在保持精度的同时优化谱特性，对图神经网络研究很有价值。
该研究提出了一种针对有向图学习的可训练非对称传播算子方法。在Cora引文网络实验中，该方法通过自适应重新计算左右敏感性，在边权重减少0.5%的预算下，将特殊谱级别降低了约21.5%，同时保持测试精度不变。该方法不要求对称性、非负性或锥保持，适用于非锥保持算子和有向学习场景。
Cone Extended Rayleigh Quotients for Directed Graph Learning: Minimax Spectral Certificates, Sensitivity, and Adaptive Control
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 bounds with explicit approximation errors and remain differentiable with respect to the trainable parameters. For a simple interior level, the right and left modes satisfy \[ Dλ_C(B)[H]=v_C^T H u_C, \] yielding first-order optimal graph-supported interventions under prescribed perturbation budgets and motivating adaptive spectral control. Numerical experiments demonstrate the applicability of the approach beyond cone-preserving operators and in directed learning settings. Signed nonsymmetric perturbations reveal a transition from interior eigenpairs to boundary complementary quasi-pairs, including non-spectral cone levels, while controlled experiments show that symmetrization can remove predictive information carried solely by edge direction. On the directed Cora citation network, adaptive recomputation of the right--left sensitivity reduces the distinguished spectral level by approximately $21.5\%$ under a cumulative edge-weight reduction budget of $0.5\%$, with no observed change in test accuracy for the trained model and data split considered.