Homomorphism Counts as Structural Encodings for Graph Learning
This work addresses the need for better graph inductive biases in graph learning models, particularly for tasks like molecular property prediction, but it is incremental as it builds on existing structural encoding methods.
The authors tackled the problem of improving graph structure representation in Graph Transformers by proposing motif structural encoding (MoSE) based on counting graph homomorphisms, which achieved state-of-the-art performance on a molecular property prediction dataset.
Graph Transformers are popular neural networks that extend the well-known Transformer architecture to the graph domain. These architectures operate by applying self-attention on graph nodes and incorporating graph structure through the use of positional encodings (e.g., Laplacian positional encoding) or structural encodings (e.g., random-walk structural encoding). The quality of such encodings is critical, since they provide the necessary $\textit{graph inductive biases}$ to condition the model on graph structure. In this work, we propose $\textit{motif structural encoding}$ (MoSE) as a flexible and powerful structural encoding framework based on counting graph homomorphisms. Theoretically, we compare the expressive power of MoSE to random-walk structural encoding and relate both encodings to the expressive power of standard message passing neural networks. Empirically, we observe that MoSE outperforms other well-known positional and structural encodings across a range of architectures, and it achieves state-of-the-art performance on a widely studied molecular property prediction dataset.