Graph Positional and Structural Encoder
Renming Liu Semih Cantürk Olivier Lapointe-Gagné Vincent Létourneau Guy Wolf Dominique Beaini Ladislav Rampášek
Positional and structural encodings (PSE) enable better identifiability of
nodes within a graph, as in general graphs lack a canonical node ordering. This
renders PSEs essential tools for empowering modern GNNs, and in particular
graph Transformers. However, designing PSEs that work optimally for a variety
of graph prediction tasks is a challenging and unsolved problem. Here, we
present the graph positional and structural encoder (GPSE), a first-ever
attempt to train a graph encoder that captures rich PSE representations for
augmenting any GNN. GPSE can effectively learn a common latent representation
for multiple PSEs, and is highly transferable. The encoder trained on a
particular graph dataset can be used effectively on datasets drawn from
significantly different distributions and even modalities. We show that across
a wide range of benchmarks, GPSE-enhanced models can significantly improve the
performance in certain tasks, while performing on par with those that employ
explicitly computed PSEs in other cases. Our results pave the way for the
development of large pre-trained models for extracting graph positional and
structural information and highlight their potential as a viable alternative to
explicitly computed PSEs as well as to existing self-supervised pre-training
approaches.