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.

翻译：图卷积学习已在多个领域带来了许多激动人心的发现。然而，在某些应用中，传统图结构不足以捕捉数据的结构与复杂性。在此类场景中，多图作为能够嵌入复杂动态过程的离散结构自然涌现。本文在多图上发展了卷积信息处理方法，并引入卷积多图神经网络（MGNNs）。为捕捉信息在多图各类边内部及跨边扩散的复杂动态，我们形式化了一个卷积信号处理模型，定义了多图上的信号、滤波和频域表示等概念。基于该模型，我们构建了一种多图学习架构，包括一个用于降低计算复杂度的采样过程。所提出的架构被应用于最优无线资源分配和仇恨言论定位任务，相比传统图神经网络取得了更优的性能。