Molecular representation learning plays a crucial role in AI-assisted drug discovery research. Encoding 3D molecular structures through Euclidean neural networks has become the prevailing method in the geometric deep learning community. However, the equivariance constraints and message passing in Euclidean space may limit the network expressive power. In this work, we propose a Harmonic Molecular Representation learning (HMR) framework, which represents a molecule using the Laplace-Beltrami eigenfunctions of its molecular surface. HMR offers a multi-resolution representation of molecular geometric and chemical features on 2D Riemannian manifold. We also introduce a harmonic message passing method to realize efficient spectral message passing over the surface manifold for better molecular encoding. Our proposed method shows comparable predictive power to current models in small molecule property prediction, and outperforms the state-of-the-art deep learning models for ligand-binding protein pocket classification and the rigid protein docking challenge, demonstrating its versatility in molecular representation learning.

翻译：分子表示学习在人工智能辅助药物发现研究中扮演着关键角色。通过欧几里得神经网络编码三维分子结构已成为几何深度学习领域的主流方法。然而，欧几里得空间中的等变约束与消息传递可能限制网络的表达能力。本文提出谐波分子表示学习（HMR）框架，该框架利用分子表面的拉普拉斯-贝尔特拉米本征函数表示分子。HMR在二维黎曼流形上提供分子几何与化学特征的多分辨率表示。我们还引入了一种谐波消息传递方法，以在表面流形上实现高效的谱消息传递，从而改进分子编码。所提出方法在分子属性预测任务中与现有模型具有可比的预测能力，并在配体结合蛋白口袋分类和刚性蛋白质对接挑战中超越当前最先进的深度学习模型，展现了其在分子表示学习中的通用性。