We characterize the computational power of neural networks that follow the graph neural network (GNN) architecture, not restricted to aggregate-combine GNNs or other particular types. We establish an exact correspondence between the expressivity of GNNs using diverse activation functions and arithmetic circuits over real numbers. In our results the activation function of the network becomes a gate type in the circuit. Our result holds for families of constant depth circuits and networks, both uniformly and non-uniformly, for all common activation functions.

翻译：我们刻画了遵循图神经网络（GNN）架构的神经网络的计算能力，且不局限于聚合-组合型GNN或其他特定类型。我们在使用多种激活函数的GNN的表达能力与实数域上的算术电路之间建立了精确对应关系。在我们的结果中，网络的激活函数成为电路中的一种门类型。该结论适用于恒定深度电路与网络族，无论是在一致计算还是非一致计算框架下，且对所有常见激活函数均成立。