Graph neural networks (GNNs) have recently been adapted to temporal settings, often employing temporal versions of the message-passing mechanism known from GNNs. We divide temporal message passing mechanisms from literature into two main types: global and local, and establish Weisfeiler-Leman characterisations for both. This allows us to formally analyse expressive power of temporal message-passing models. We show that global and local temporal message-passing mechanisms have incomparable expressive power when applied to arbitrary temporal graphs. However, the local mechanism is strictly more expressive than the global mechanism when applied to colour-persistent temporal graphs, whose node colours are initially the same in all time points. Our theoretical findings are supported by experimental evidence, underlining practical implications of our analysis.

翻译：近年来，图神经网络（GNNs）已被应用于时序场景，通常采用源自GNN的消息传递机制的时序版本。我们将文献中的时序消息传递机制划分为两种主要类型：全局型和局部型，并为两者建立了Weisfeiler-Leman特征刻画。这使我们能够形式化地分析时序消息传递模型的表达能力。我们证明，当应用于任意时序图时，全局与局部时序消息传递机制的表达能力不可比较。然而，当应用于颜色持久性时序图（即所有时间点上节点初始颜色均相同的时序图）时，局部机制的表达能力严格强于全局机制。我们的理论发现得到了实验证据的支持，从而凸显了本分析的实际意义。