KrawtchoukNet用自适应多项式解决图神经网络异质性与过平滑问题
KrawtchoukNet: A Unified GNN Solution for Heterophily and Over-smoothing with Adaptive Bounded Polynomials
- 基于Krawtchouk多项式设计可自适应的图滤波器
- 在K=10时仍保持性能，优于现有SOTA方法
- 特别适合处理异质图数据，如Texas、Cornell数据集
基于多项式滤波的谱图神经网络（如ChebyNet）存在两大缺陷：在异质图上性能下降，以及高阶多项式（K）下出现过平滑现象。两者均源于标准滤波器静态低通特性。本文提出基于离散Krawtchouk多项式的KrawtchoukNet滤波器。通过将多项式定义域N固定为小常数（如20），实现递推系数天然有界，显著增强对过平滑的鲁棒性，在K=10时达到当前最优表现。同时引入可学习的形状参数p，使滤波器能自适应调整频谱响应。实验表明，KrawtchoukNet在复杂异质图基准（Texas、Cornell）上表现优异，显著超越GAT、APPNP等标准GNN模型。
原文摘要 · Abstract (English)
Spectral Graph Neural Networks (GNNs) based on polynomial filters, such as ChebyNet, suffer from two critical limitations: 1) performance collapse on "heterophilic" graphs and 2) performance collapse at high polynomial degrees (K), known as over-smoothing. Both issues stem from the static, low-pass nature of standard filters. In this work, we propose `KrawtchoukNet`, a GNN filter based on the discrete Krawtchouk polynomials. We demonstrate that `KrawtchoukNet` provides a unified solution to both problems through two key design choices. First, by fixing the polynomial's domain N to a small constant (e.g., N=20), we create the first GNN filter whose recurrence coefficients are \textit{inherently bounded}, making it exceptionally robust to over-smoothing (achieving SOTA results at K=10). Second, by making the filter's shape parameter p learnable, the filter adapts its spectral response to the graph data. We show this adaptive nature allows `KrawtchoukNet` to achieve SOTA performance on challenging heterophilic benchmarks (Texas, Cornell), decisively outperforming standard GNNs like GAT and APPNP.
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