Learning Harmonic Molecular Representations on Riemannian Manifold

TL;DR

This paper introduces a harmonic molecular representation framework using Laplace-Beltrami eigenfunctions on molecular surfaces, enhancing the expressiveness and versatility of molecular encoding in drug discovery tasks.

Contribution

It proposes a novel spectral message passing method on Riemannian manifolds for improved molecular representation learning, addressing limitations of Euclidean neural networks.

Findings

Achieves comparable accuracy in small molecule property prediction.

Outperforms state-of-the-art models in ligand-binding pocket classification.

Excels in rigid protein docking tasks.

Abstract

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.