We investigate the power of message-passing neural networks (MPNNs) in their
capacity to transform the numerical features stored in the nodes of their input
graphs. Our focus is on global expressive power, uniformly over all input
graphs, or over graphs of bounded degree with features from a bounded domain.
Accordingly, we introduce the notion of a global feature map transformer
(GFMT). As a yardstick for expressiveness, we use a basic language for GFMTs,
which we call MPLang. Every MPNN can be expressed in MPLang, and our results
clarify to which extent the converse inclusion holds. We consider exact versus
approximate expressiveness; the use of arbitrary activation functions; and the
case where only the ReLU activation function is allowed.

本文探讨了消息传递神经网络（MPNN）在转换其输入图中节点存储的数字特征方面的能力。我们引入了全局特征映射变换器（GFMT）的概念，并以 GFMT 的基本语言 MPLang 作为表现能力的标准。我们考虑了精确与近似表现力、任意激活函数的使用以及只允许使用 ReLU 激活函数的情况。