Graph convolutional learning has led to many exciting discoveries in diverse areas. However, in some applications, traditional graphs are insufficient to capture the structure and intricacies of the data. In such scenarios, multigraphs arise naturally as discrete structures in which complex dynamics can be embedded. In this paper, we develop convolutional information processing on multigraphs and introduce convolutional multigraph neural networks (MGNNs). To capture the complex dynamics of information diffusion within and across each of the multigraph's classes of edges, we formalize a convolutional signal processing model, defining the notions of signals, filtering, and frequency representations on multigraphs. Leveraging this model, we develop a multigraph learning architecture, including a sampling procedure to reduce computational complexity. The introduced architecture is applied towards optimal wireless resource allocation and a hate speech localization task, offering improved performance over traditional graph neural networks.

中文翻译：

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多图上的卷积学习

图卷积学习在不同领域带来了许多令人兴奋的发现。然而，在某些应用中，传统的图表不足以捕捉数据的结构和复杂性。在这种情况下，多重图自然地作为离散结构出现，其中可以嵌入复杂的动态。在本文中，我们开发了多图上的卷积信息处理，并介绍了卷积多图神经网络 (MGNN)。为了捕捉多重图的每个边缘类别内和跨边的复杂动态信息扩散，我们形式化了卷积信号处理模型，定义了多重图上的信号、过滤和频率表示的概念。利用这个模型，我们开发了一个多图学习架构，包括一个抽样程序，以降低计算复杂性。引入的架构适用于优化无线资源分配和仇恨言论定位任务，提供优于传统图神经网络的性能。