提出Jacobi域GNN新模型，揭示稳定性和自适应的权衡关系。
L-JacobiNet and S-JacobiNet: An Analysis of Adaptive Generalization, Stabilization, and Spectral Domain Trade-offs in GNNs
- 在[-1,1]区间设计可学习参数的Jacobi滤波器，提升GNN泛化能力
- 发现静态模型加层归一化比自适应模型在多数数据集上表现更好
- 揭示高阶滤波下[-1,1]域更稳定，[0,∞)域更适合异质图建模
谱域GNN如ChebyNet受限于异质性建模和过平滑问题，源于其静态低通滤波设计。本文研究自适应正交多项式滤波器（AOPF）类方法，提出两个在[-1,1]域运行的新模型：1）L-JacobiNet，为ChebyNet的自适应泛化，具有可学习的alpha、beta形状参数；2）S-JacobiNet，一种新的基准模型，即采用层归一化的静态ChebyNet。通过与[0,∞)域的AOPF模型（如LaguerreNet）对比分析，揭示了此前未知的关键权衡。研究发现，[0,∞)域更适用于异质性建模，而[-1,1]域（Jacobi）在高阶滤波（K>20）下具有更优数值稳定性。最重要的是，发现ChebyNet的主要缺陷在于稳定性而非静态性。其静态版本S-JacobiNet（ChebyNet+LayerNorm）在5个基准数据集中的4个上优于自适应的L-JacobiNet，表明S-JacobiNet是一个被忽视的强大基线，提示[-1,1]域的自适应可能引发过拟合。
原文摘要 · Abstract (English)
Spectral GNNs, like ChebyNet, are limited by heterophily and over-smoothing due to their static, low-pass filter design. This work investigates the "Adaptive Orthogonal Polynomial Filter" (AOPF) class as a solution. We introduce two models operating in the [-1, 1] domain: 1) `L-JacobiNet`, the adaptive generalization of `ChebyNet` with learnable alpha, beta shape parameters, and 2) `S-JacobiNet`, a novel baseline representing a LayerNorm-stabilized static `ChebyNet`. Our analysis, comparing these models against AOPFs in the [0, infty) domain (e.g., `LaguerreNet`), reveals critical, previously unknown trade-offs. We find that the [0, infty) domain is superior for modeling heterophily, while the [-1, 1] domain (Jacobi) provides superior numerical stability at high K (K>20). Most significantly, we discover that `ChebyNet`'s main flaw is stabilization, not its static nature. Our static `S-JacobiNet` (ChebyNet+LayerNorm) outperforms the adaptive `L-JacobiNet` on 4 out of 5 benchmark datasets, identifying `S-JacobiNet` as a powerful, overlooked baseline and suggesting that adaptation in the [-1, 1] domain can lead to overfitting.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。