Inductive biases for graph neural networks

Graph structured representations are a powerful inductive bias applicable across a wide spectrum of systems in nature, ranging from atom interactions in molecular systems to complex human interactions such as social networks. Part of the success of Graph Neural Networks (GNNs) can be attributed to their broad applicability in capturing these complex interactions. This thesis aims to extend the capabilities of GNNs by incorporating additional physics-based inductive biases.
The thesis begins by enriching GNN architectures with traditional graphical inference methods to craft hybrid models. These models leverage the prior knowledge inherent in conventional graphical models along with the adaptive inference from data-driven learning. The resulting algorithms outperform the individual approaches when run in isolation.
We then implement inductive biases as a symmetry constraint by creating E(n) Equivariant Graph Neural Networks (EGNNs), which improve upon standard GNNs through the inclusion of the Euclidean symmetry. This improves generalization for data within n-dimensional Euclidean spaces, a characteristic particularly relevant in molecular data. Subsequently, we demonstrate the benefits of EGNNs in various applications in the domain of deep learning for molecular modelling.
The concluding part of this work is the incorporation of euclidean symmetries into generative models by building upon the proposed EGNNs. The presented generative model significantly outperforms previous 3D molecular generative models, showing potential to be disruptive in the future of molecular modeling.