Reviews: Universal Invariant and Equivariant Graph Neural Networks

This paper proves the universality of invariant and equivariant graph neural networks by using the Stone-Weierstrass theorem. The property of invariance and equivariance of graph neural networks has seldom been formalized in the existing literature. This paper lays a solid theoretical foundation on the universality of invariant and equivariant graph neural networks defined by a single set of parameters. However, unless the graph neural network proposed in Equation 1 covers a large number of existing graph neural networks, it is needed to validate the superiority of the proposed graph neural networks over other graph neural networks with empirical studies such as graph classification. Due to lack of generalization ability to existing graph neural networks or experimental studies, at this stage the contribution of this paper is of weak significance to the society of graph deep learning. Other aspects of this paper are summarized below: Quality The quality of this paper largely depends on the correctness on proof of the proposed theorems.