Geometric deep learning (GDL) has made great strides towards generalizing the design of structure-aware neural network architectures from traditional domains to non-Euclidean ones, such as graphs. This gave rise to graph neural network (GNN) models that can be applied to graph-structured datasets arising, for example, in 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 (and GCNs in particular) are known to be 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, thus leading to oversmoothing. Here, we propose a hybrid GNN framework that combines traditional GCN filters with band-pass filters defined via the geometric scattering transform. We further introduce an attention framework that allows the model to locally attend over the combined information from different GNN 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.
翻译:几何深层学习(GDL)在从传统领域到非欧洲气候网络结构的设计上取得了长足的进步,例如图表。这产生了可应用于诸如社会网络、生物化学和材料科学等图形结构数据集的图形神经网络模型(GNN),特别是在社会网络、生物化学和材料科学方面。图变网络(GCN)在其欧洲对口单位的启发下,成功地通过提取结构观测特征来处理图形数据。然而,目前GNN模型(特别是GCN)已知受到各种现象的限制,这些现象限制了其表达力和能力,无法将其推广到更复杂的图形数据集。大多数模型基本上依靠通过本地平均操作低空过滤图形信号,从而导致超动。在这里,我们提议了一个混合的GNNN框架,将传统的GCN过滤器与通过地球测量分布变异异样定义的带式过滤器结合起来。我们进一步引入了一个关注框架,允许模型到本地,这些模型受到各种现象的制约,这些现象限制了其表达力和能力,无法将其推广到更复杂的图形数据集集成,同时通过不同的GNNNNM法的模型展示结果,从我们不同的结构过滤法的模型上建立不同的分析。