[论文解读] Graph Neural Networks with Adaptive Frequency Response Filter.

Yushun Dong, Kaize Ding+3 more|arXiv (Cornell University)|Apr 26, 2021

Advanced Graph Neural Networks参考文献 54被引用 6

一句话总结

本文提出AdaGNN，一种新型图神经网络，通过在多层中采用可学习的自适应频率响应滤波器，动态捕捉节点表示中不同频率分量的重要性。通过学习随特征通道和层深度变化的滤波器权重，AdaGNN缓解了过平滑问题并提升了模型表达能力，在基准图学习任务上实现了最先进性能。

ABSTRACT

Graph Neural Networks have recently become a prevailing paradigm for various high-impact graph learning tasks. Existing efforts can be mainly categorized as spectral-based and spatial-based methods. The major challenge for the former is to find an appropriate graph filter to distill discriminative information from input signals for learning. Recently, attempts such as Graph Convolutional Network (GCN) leverage Chebyshev polynomial truncation to seek an approximation of graph filters and bridge these two families of methods. It has been shown in recent studies that GCN and its variants are essentially employing fixed low-pass filters to perform information denoising. Thus their learning capability is rather limited and may over-smooth node representations at deeper layers. To tackle these problems, we develop a novel graph neural network framework AdaGNN with a well-designed adaptive frequency response filter. At its core, AdaGNN leverages a simple but elegant trainable filter that spans across multiple layers to capture the varying importance of different frequency components for node representation learning. The inherent differences among different feature channels are also well captured by the filter. As such, it empowers AdaGNN with stronger expressiveness and naturally alleviates the over-smoothing problem. We empirically validate the effectiveness of the proposed framework on various benchmark datasets. Theoretical analysis is also provided to show the superiority of the proposed AdaGNN. The implementation of AdaGNN is available at \url{this https URL}.

研究动机与目标

• 解决现有基于谱方法的GNN依赖固定低通滤波器的局限性，此类滤波器限制了模型表达能力，并在深层架构中引发过平滑问题。
• 通过引入可学习的多层频率滤波器，弥合谱方法与空间方法GNN之间的差距，该滤波器能根据节点特征和层深度自适应调整。
• 通过捕捉不同特征通道中频率分量重要性的变化，改进节点表示学习。
• 开发一个理论基础扎实且实证有效的GNN框架，自然缓解深层网络中的过平滑问题。

提出的方法

• 设计一种可在多层中运行的可学习频率响应滤波器，替代GCN等模型中使用的固定滤波器。
• 提出一种可学习的滤波器参数化方法，使其能根据输入信号的频率内容和特征通道特性自适应调整。
• 采用多层架构，使滤波器响应在每层动态调整，实现对高频与低频分量的选择性聚合。
• 通过自适应滤波器权重对图卷积进行简化近似，避免昂贵的特征分解计算。
• 通过允许滤波器按通道变化，捕捉特征重要性在通道间的差异，增强表示多样性。
• 理论分析表明，自适应滤波器相比GCN及其变体中使用的固定低通滤波器，具有更好的谱敏感性和泛化能力。

实验结果

研究问题

• RQ1 与固定滤波器相比，可学习的自适应频率响应滤波器是否能提升图神经网络的表达能力？
• RQ2 自适应滤波器在深层GNN架构中如何缓解过平滑问题？
• RQ3 该滤波器在不同特征通道中对频率分量重要性的捕捉程度如何？
• RQ4 所提出的AdaGNN框架在标准图基准数据集上的性能是否优于现有的谱方法和空间方法GNN？

主要发现

• AdaGNN在多个基准图学习数据集上实现了最先进性能，展现出优越的泛化能力。
• 自适应滤波器通过选择性保留高频信息，显著减少了深层网络中的过平滑现象。
• 实验结果表明，模型学习到了随特征通道和层深度变化的有意义频率响应。
• 理论分析证实，AdaGNN的滤波器相比GCN及其变体中使用的固定低通滤波器，具有更好的谱敏感性。
• 代码实现已公开，支持可复现性，并推动自适应谱滤波在GNN中的进一步研究。