Graph Neural Networks with Learnable Structural and Positional Representations
This addresses a key limitation in GNNs for domains like molecular analysis, though it appears incremental as it builds on existing positional encoding methods.
The paper tackled the problem of graph neural networks lacking canonical positional information, which limits their ability to distinguish nodes and symmetries, by proposing a decoupled architecture for learnable structural and positional representations, resulting in performance increases of 1.79% to 64.14% on molecular datasets.
Graph neural networks (GNNs) have become the standard learning architectures for graphs. GNNs have been applied to numerous domains ranging from quantum chemistry, recommender systems to knowledge graphs and natural language processing. A major issue with arbitrary graphs is the absence of canonical positional information of nodes, which decreases the representation power of GNNs to distinguish e.g. isomorphic nodes and other graph symmetries. An approach to tackle this issue is to introduce Positional Encoding (PE) of nodes, and inject it into the input layer, like in Transformers. Possible graph PE are Laplacian eigenvectors. In this work, we propose to decouple structural and positional representations to make easy for the network to learn these two essential properties. We introduce a novel generic architecture which we call LSPE (Learnable Structural and Positional Encodings). We investigate several sparse and fully-connected (Transformer-like) GNNs, and observe a performance increase for molecular datasets, from 1.79% up to 64.14% when considering learnable PE for both GNN classes.