Title: Graph Alignment for Benchmarking Graph Neural Networks and Learning Positional Encodings
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: Graph Neural Network, Benchmark, Positional Encodings, Molecular Regression, Graph Alignment

Abstract: We propose a novel benchmarking methodology for graph neural networks (GNNs)
based on the graph alignment problem, a combinatorial optimization task that
generalizes graph isomorphism by aligning two unlabeled graphs to maximize
overlapping edges. We frame this problem as a self-supervised learning task and
present several methods to generate graph alignment datasets using synthetic ran-
dom graphs and real-world graph datasets from multiple domains. For a given
graph dataset, we generate a family of graph alignment datasets with increasing
difficulty, allowing us to rank the performance of various architectures. Our ex-
periments indicate that anisotropic graph neural networks outperform standard
convolutional architectures. To further demonstrate the utility of the graph align-
ment task, we show its effectiveness for unsupervised GNN pre-training, where the
learned node embeddings outperform other positional encodings on three molecular
regression tasks and achieve state-of-the-art results on the PCQM4Mv2 dataset
with significantly fewer parameters. To support reproducibility and further research,
we provide an open-source Python package to generate graph alignment datasets
and benchmark new GNN architectures.

TL;DR: We introduce a new task to benchmark GNNs and show how it can be leveraged to generate high quality positional encodings.