Graph Neural Networks with Learnable Structural and Positional Representations

TL;DR

This paper introduces LSPE, a novel GNN architecture that decouples structural and positional node representations, significantly improving performance on molecular datasets by learning these properties adaptively.

Contribution

The paper proposes a new architecture called LSPE that learns structural and positional encodings separately, enhancing GNNs' ability to distinguish graph symmetries.

Findings

Performance increase of up to 64.14% on molecular datasets.

Learnable positional encodings improve GNN expressiveness.

Decoupling structural and positional info benefits various GNN architectures.

Abstract

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.