Graph Neural Networks With Parallel Neighborhood Aggregations for Graph Classification

We focus on graph classification using a graph neural network (GNN) model that precomputes node features using a bank of neighborhood aggregation graph operators arranged in parallel. These GNN models have a natural advantage of reduced training and inference time due to the precomputations but are also fundamentally different from popular GNN variants that update node features through a sequential neighborhood aggregation procedure during training. We provide theoretical conditions under which a generic GNN model with parallel neighborhood aggregations (PA-GNNs, in short) are provably as powerful as the well-known Weisfeiler-Lehman (WL) graph isomorphism test in discriminating non-isomorphic graphs. Although PA-GNN models do not have an apparent relationship with the WL test, we show that the graph embeddings obtained from these two methods are injectively related. We then propose a specialized PA-GNN model, called simple and parallel graph isomorphism network (SPIN), which obeys the developed conditions. We demonstrate via numerical experiments that the developed model achieves state-of-the-art performance on many diverse real-world datasets while maintaining the discriminative power of the WL test and the computational advantage of preprocessing graphs before the training process.