Graph Neural Networks (GNNs) and Transformer have been increasingly adopted to learn the complex vector representations of spatio-temporal graphs, capturing intricate spatio-temporal dependencies crucial for applications such as traffic datasets. Although many existing methods utilize multi-head attention mechanisms and message-passing neural networks (MPNNs) to capture both spatial and temporal relations, these approaches encode temporal and spatial relations independently, and reflect the graph's topological characteristics in a limited manner. In this work, we introduce the Cycle to Mixer (Cy2Mixer), a novel spatio-temporal GNN based on topological non-trivial invariants of spatio-temporal graphs with gated multi-layer perceptrons (gMLP). The Cy2Mixer is composed of three blocks based on MLPs: A message-passing block for encapsulating spatial information, a cycle message-passing block for enriching topological information through cyclic subgraphs, and a temporal block for capturing temporal properties. We bolster the effectiveness of Cy2Mixer with mathematical evidence emphasizing that our cycle message-passing block is capable of offering differentiated information to the deep learning model compared to the message-passing block. Furthermore, empirical evaluations substantiate the efficacy of the Cy2Mixer, demonstrating state-of-the-art performances across various traffic benchmark datasets.

翻译：图神经网络（GNN）和Transformer已被越来越多地应用于学习时空图的复杂向量表示，以捕获对交通数据集等应用至关重要的复杂时空依赖关系。尽管现有许多方法利用多头注意力机制和消息传递神经网络（MPNN）来捕获空间和时间关系，但这些方法独立地编码时间和空间关系，并以有限的方式反映图的拓扑特征。在这项工作中，我们提出了基于时空图拓扑非平凡不变量与门控多层感知器（gMLP）的新型时空GNN——Cycle to Mixer（Cy2Mixer）。Cy2Mixer由三个基于MLP的模块组成：用于封装空间信息的消息传递模块、通过循环子图丰富拓扑信息的循环消息传递模块，以及用于捕获时间属性的时间模块。我们通过数学证据强化了Cy2Mixer的有效性，强调与消息传递模块相比，我们的循环消息传递模块能够为深度学习模型提供差异化信息。此外，实证评估证实了Cy2Mixer的有效性，其在多个交通基准数据集上展现出最先进的性能。