Multi-Scale Protein Structure Modelling with Geometric Graph U-Nets

TL;DR

This paper introduces Geometric Graph U-Nets, a hierarchical neural network architecture that captures multi-scale protein structures more effectively than existing models, improving protein fold classification accuracy.

Contribution

The paper proposes a novel hierarchical GNN architecture that mirrors biological protein hierarchies, with theoretical and empirical advantages over standard GNNs.

Findings

Hierarchical design is more expressive than standard GNNs.

Geometric U-Nets outperform baselines on protein fold classification.

The model captures global structural patterns effectively.

Abstract

Geometric Graph Neural Networks (GNNs) and Transformers have become state-of-the-art for learning from 3D protein structures. However, their reliance on message passing prevents them from capturing the hierarchical interactions that govern protein function, such as global domains and long-range allosteric regulation. In this work, we argue that the network architecture itself should mirror this biological hierarchy. We introduce Geometric Graph U-Nets, a new class of models that learn multi-scale representations by recursively coarsening and refining the protein graph. We prove that this hierarchical design can theoretically more expressive than standard Geometric GNNs. Empirically, on the task of protein fold classification, Geometric U-Nets substantially outperform invariant and equivariant baselines, demonstrating their ability to learn the global structural patterns that define protein folds. Our work provides a principled foundation for designing geometric deep learning architectures that can learn the multi-scale structure of biomolecules.