Cone Extended Rayleigh Quotients for Directed Graph Learning: Minimax Spectral Certificates, Sensitivity, and Adaptive Control 待解读
新用户看这篇论文该怎么开始
- 先点「赞助解读」，AI 会把论文转成可直接执行的行动清单。
- 看完“可执行改进行动”后，可快速决定是否值得立项。
- 用上面的卡片内容直接发给团队，减少重复阅读。
摘要
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.
分析报告
暂无报告。点击“分析”开始生成。
个性化解读 与社区共享解读不同
用自己的话告诉 AI 你想要什么样的解读（比如"用大白话讲给非专业人士听"、"重点分析对我们团队 RAG 系统的可迁移性"），生成一份只属于你自己的版本；生成后也可以选择设为"愿意共享"，被更多人看到、点赞。