  The Transformer architecture has gained growing attention in graph
representation learning recently, as it naturally overcomes several limitations
of graph neural networks (GNNs) by avoiding their strict structural inductive
biases and instead only encoding the graph structure via positional encoding.
Here, we show that the node representations generated by the Transformer with
positional encoding do not necessarily capture structural similarity between
them. To address this issue, we propose the Structure-Aware Transformer, a
class of simple and flexible graph Transformers built upon a new self-attention
mechanism. This new self-attention incorporates structural information into the
original self-attention by extracting a subgraph representation rooted at each
node before computing the attention. We propose several methods for
automatically generating the subgraph representation and show theoretically
that the resulting representations are at least as expressive as the subgraph
representations. Empirically, our method achieves state-of-the-art performance
on five graph prediction benchmarks. Our structure-aware framework can leverage
any existing GNN to extract the subgraph representation, and we show that it
systematically improves performance relative to the base GNN model,
successfully combining the advantages of GNNs and Transformers. Our code is
available at https://github.com/BorgwardtLab/SAT.
