Homomorphism Counts as Structural Encodings for Graph Learning
Keywords: graph transformers, structural encodings, homomorphism counts, expressivity
Abstract: 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 \emph{graph inductive biases} to condition the model on graph structure. In this work, we propose \emph{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 widely studied molecular property prediction datasets.
Primary Area: learning on graphs and other geometries & topologies
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Submission Number: 12618
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