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.

翻译：几何图神经网络（GNNs）与Transformer已成为从三维蛋白质结构中进行学习的先进方法。然而，其依赖消息传递的机制使其难以捕捉支配蛋白质功能的层次化相互作用，例如全局结构域和长程变构调控。本研究主张网络架构本身应反映这种生物层级性。我们提出了几何图U-Net——一种通过递归粗化与细化蛋白质图来学习多尺度表征的新型模型类别。我们证明这种层次化设计在理论上比标准几何GNN具有更强的表达能力。在蛋白质折叠分类任务的实证中，几何图U-Net显著优于不变性与等变性基线模型，展现了其学习定义蛋白质折叠的全局结构模式的能力。本研究为设计能够学习生物分子多尺度结构的几何深度学习架构提供了理论基础。