Empowering Active Learning for 3D Molecular Graphs with Geometric Graph Isomorphism

Abstract

Molecular learning is pivotal in many real-world applications, such as drug discovery. Supervised learning requires heavy human annotation, which is particularly challenging for molecular data, e.g., the commonly used density functional theory (DFT) is computationally very expensive. Active Learning (AL) automatically queries labels for most informative samples, thereby remarkably alleviating the annotation hurdle. In this paper, we present a novel and powerful AL paradigm for molecular learning, where we treat molecules as 3D molecular graphs. Specifically, we propose a new diversity sampling method to eliminate mutual redundancy built on distributions of 3D geometries. We first propose a set of new 3D graph isometrics for 3D graph isomorphism analysis. Our method is provably more powerful than the geometric Weisfeiler-Lehman (GWL) test. The moments of the distributions of the associated geometries are then extracted for efficient diversity computing. To ensure our AL paradigm selects samples with maximal uncertainties, we carefully design a Bayesian geometric graph neural network to compute uncertainties specifically for 3D molecular graphs. We pose active sampling as a quadratic programming (QP) problem using the novel components and conduct extensive experiments on the QM9 dataset. Results demonstrate the effectiveness of our AL paradigm, as well as the proposed diversity and uncertainty methods.