提出双谱滤波器GNN，揭示灵活性与稳定性之间的根本权衡。
DualLaguerreNet: A Decoupled Spectral Filter GNN and the Uncovering of the Flexibility-Stability Trade-off
- 将图拉普拉斯分解为高低频部分，分别学习两个独立自适应滤波器。
- 在复杂异质任务上超越现有模型，但在简单同质任务上表现下降。
- 揭示参数增多导致过拟合，说明简单模型的‘妥协’实为正则化机制。
基于谱滤波的图神经网络（如AOPF类的LaguerreNet）在统一处理异质性和过平滑问题上展现出潜力。然而，单滤波器模型存在‘妥协’问题：其单一自适应参数（如alpha）需在全图谱上学习次优平均响应。本文提出DualLaguerreNet，通过将图拉普拉斯分解为低频（L_low）和高频（L_high）算子，分别学习两个独立的自适应拉盖尔多项式滤波器（参数分别为alpha_1和alpha_2），实现解耦谱灵活性。实验表明，该架构在复杂异质任务上达到新SOTA，但同时在简单同质任务上表现更差。我们发现这是根本性的‘灵活性-稳定性权衡’：参数量增加（滤波器参数翻倍、模型参数翻倍）导致简单任务过拟合，证明简单模型的‘妥协’实际起到关键正则化作用。本文不仅提出异质性任务的新最优架构，还揭示了自适应GNN滤波设计中固有的偏差-方差权衡。
原文摘要 · Abstract (English)
Graph Neural Networks (GNNs) based on spectral filters, such as the Adaptive Orthogonal Polynomial Filter (AOPF) class (e.g., LaguerreNet), have shown promise in unifying the solutions for heterophily and over-smoothing. However, these single-filter models suffer from a "compromise" problem, as their single adaptive parameter (e.g., alpha) must learn a suboptimal, averaged response across the entire graph spectrum. In this paper, we propose DualLaguerreNet, a novel GNN architecture that solves this by introducing "Decoupled Spectral Flexibility." DualLaguerreNet splits the graph Laplacian into two operators, L_low (low-frequency) and L_high (high-frequency), and learns two independent, adaptive Laguerre polynomial filters, parameterized by alpha_1 and alpha_2, respectively. This work, however, uncovers a deeper finding. While our experiments show DualLaguerreNet's flexibility allows it to achieve state-of-the-art results on complex heterophilic tasks (outperforming LaguerreNet), it simultaneously underperforms on simpler, homophilic tasks. We identify this as a fundamental "Flexibility-Stability Trade-off". The increased parameterization (2x filter parameters and 2x model parameters) leads to overfitting on simple tasks, demonstrating that the "compromise" of simpler models acts as a crucial regularizer. This paper presents a new SOTA architecture for heterophily while providing a critical analysis of the bias-variance trade-off inherent in adaptive GNN filter design.
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