Rethinking local structural awareness in graph representation learning

Thesis

Graph-structured data lies at the heart of many modern applications, from molecular modeling and materials discovery to social networks and relational databases. For these types of problems, graph representation learning has emerged as a powerful framework for reasoning. Models such as graph neural networks (GNNs) are particularly appealing due to their ability to capture complex, implicit relationships. However, a key open question remains in how to best encode and generalize local structural information within these models. This affects both the ability of current methods to intelligently reason over structure in data as well as their applicability to more intricate, real-world scenarios. In this thesis, we examine existing methods for representing local structure in GNNs and propose two novel approaches for enhancing their representational capacity. The first uses graph homomorphism counts as a unifying framework for improving model expressivity, and the second introduces a new paradigm for leveraging local information to capture global symmetries in periodic data to enable large-scale, efficient learning. Together, these contributions advance our understanding of local structural representations in GNNs and expand their practical utility.

Authors: Jin, E

• DOI: 10.5287/ora-nov1ejyp4
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: graph representation learning; geometric deep learning; molecular property prediction; graph homomorphisms; crystal structure prediction
• Subjects: Machine learning; AI for science