Graph Neural Networks and Arithmetic Circuits

Timon Barlag, Vivian Holzapfel, Laura Strieker, Jonni Virtema, Heribert Vollmer

Keywords: Machine Learning, Graph Neural Networks, Arithmetic Circuits, Computational Complexity

TL;DR: We obtain a characterization of the computational power/expressivity of graph neural networks in terms of arithmetic circuits over the reals.

Abstract: 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.

Primary Area: Graph neural networks

Submission Number: 15878