SPI-GCN: A Simple Permutation-Invariant Graph Convolutional Network

A wide range of machine learning problems involve handling graph-structured data. Existing machine learning approaches for graphs, however, often imply computing expensive graph similarity measures, preprocessing input graphs, or explicitly ordering graph nodes. In this work, we present a novel and simple convolutional neural network architecture for supervised learning on graphs that is provably invariant to node permutation. The proposed architecture operates directly on arbitrary graphs and performs no node sorting. It also uses a simple multi-layer perceptron for prediction as opposed to conventional convolution layers commonly used in other deep learning approaches for graphs. Despite its simplicity, our architecture is competitive with state-of-the-art graph kernels and existing graph neural networks on benchmark graph classification data sets. Our approach clearly outperforms other deep learning algorithms for graphs on multiple multiclass classification tasks. We also evaluate our approach on a real-world original application in materials science, on which we achieve extremely reasonable results.