Graph Self-Supervised Learning with Learnable Structural and Positional Encodings

TL;DR

This paper introduces GenHopNet, a novel GNN framework with learnable structural and positional encodings, enhancing graph representation learning by capturing complex topological features and surpassing traditional expressiveness limits.

Contribution

The paper proposes GenHopNet with a $k$-hop message-passing scheme and a structural- and positional-aware GSSL framework, improving structural sensitivity and expressiveness in graph self-supervised learning.

Findings

GenHopNet surpasses Weisfeiler-Lehman test in expressiveness.

The proposed framework outperforms existing methods on graph classification tasks.

It maintains computational efficiency while improving structural sensitivity.

Abstract

Traditional Graph Self-Supervised Learning (GSSL) struggles to capture complex structural properties well. This limitation stems from two main factors: (1) the inadequacy of conventional Graph Neural Networks (GNNs) in representing sophisticated topological features, and (2) the focus of self-supervised learning solely on final graph representations. To address these issues, we introduce \emph{GenHopNet}, a GNN framework that integrates a $k$-hop message-passing scheme, enhancing its ability to capture local structural information without explicit substructure extraction. We theoretically demonstrate that \emph{GenHopNet} surpasses the expressiveness of the classical Weisfeiler-Lehman (WL) test for graph isomorphism. Furthermore, we propose a structural- and positional-aware GSSL framework that incorporates topological information throughout the learning process. This approach enables the learning of representations that are both sensitive to graph topology and invariant to specific structural and feature augmentations. Comprehensive experiments on graph classification datasets, including those designed to test structural sensitivity, show that our method consistently outperforms the existing approaches and maintains computational efficiency. Our work significantly advances GSSL's capability in distinguishing graphs with similar local structures but different global topologies.