通过混合散射网络克服图卷积网络中的过平滑问题
Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networks
AI总结：
针对 GCN 低通滤波导致的过平滑及浅层网络感受野不足问题，提出融合几何散射带通滤波与节点级注意力的混合 GNN 框架，并从理论和实验上验证其优势。
摘要：
几何深度学习在将结构感知神经网络的设计从传统领域推广到非欧几里得领域方面取得了长足进展，催生了可应用于社交网络、生物化学和材料科学等领域中出现的图结构数据的图神经网络（GNN）。特别是图卷积网络（GCN），受其欧几里得对应模型启发，通过提取结构感知特征，在处理图数据方面取得了成功。然而，当前的 GNN 模型往往受到各种现象的制约，这些现象限制了它们的表达能力以及向更复杂图数据集泛化的能力。大多数模型本质上依赖于通过局部平均操作对图信号进行低通滤波，从而导致过平滑。此外，为了避免严重的过平滑，大多数流行的 GCN 风格网络往往较浅，感受野狭窄，从而导致欠达。在此，我们提出了一种混合 GNN 框架，将传统 GCN 滤波器与通过几何散射定义的带通滤波器相结合。我们进一步引入了一种注意力框架，使模型能够在节点级别局部关注来自不同滤波器的组合信息。我们的理论结果确立了散射滤波器在利用图中结构信息方面的互补优势，同时我们的实验展示了该方法在多种学习任务上的优势。
英文摘要：
Geometric deep learning has made great strides towards generalizing the design of structure-aware neural networks from traditional domains to non-Euclidean ones, giving rise to graph neural networks (GNN) that can be applied to graph-structured data arising in, e.g., social networks, biochemistry, and material science. Graph convolutional networks (GCNs) in particular, inspired by their Euclidean counterparts, have been successful in processing graph data by extracting structure-aware features. However, current GNN models are often constrained by various phenomena that limit their expressive power and ability to generalize to more complex graph datasets. Most models essentially rely on low-pass filtering of graph signals via local averaging operations, leading to oversmoothing. Moreover, to avoid severe oversmoothing, most popular GCN-style networks tend to be shallow, with narrow receptive fields, leading to underreaching. Here, we propose a hybrid GNN framework that combines traditional GCN filters with band-pass filters defined via geometric scattering. We further introduce an attention framework that allows the model to locally attend over combined information from different filters at the node level. Our theoretical results establish the complementary benefits of the scattering filters to leverage structural information from the graph, while our experiments show the benefits of our method on various learning tasks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
