论文标题
关于消息通讯神经网络作为全局特征图变形金刚的表达力
On the expressive power of message-passing neural networks as global feature map transformers
论文作者
论文摘要
我们研究了通话神经网络（MPNN）的功能，以转换存储在其输入图节点中的数值特征的能力。我们的重点是全局表达能力，在所有输入图上均匀或有界域的界图上具有来自有限域的特征。因此，我们介绍了全局特征图变压器（GFMT）的概念。作为表达能力的标准，我们使用一种基本语言来用于GFMT，我们称之为Mplang。每个MPNN都可以在mplang中表达，我们的结果阐明了匡威包容性的程度。我们考虑确切的表现力与近似表现力；使用任意激活功能；以及仅允许RELU激活函数的情况。
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.
