In this paper, we show that a simple coloring scheme can improve, both theoretically and empirically, the expressive power of Message Passing Neural Networks (MPNNs). More specifically, we introduce a graph neural network called Colored Local Iterative Procedure (CLIP) that uses colors to disambiguate identical node attributes, and show that this representation is a universal approximator of continuous functions on graphs with node attributes. Our method relies on separability, a key topological characteristic that allows to extend well-chosen neural networks into universal representations. Finally, we show experimentally that CLIP is capable of capturing structural characteristics that traditional MPNNs fail to distinguish, while being state-of-the-art on benchmark graph classification datasets.
The canonical coloring graph of trees and cycles
