In this study, we present a novel computational method for generating molecular fingerprints using multiparameter persistent homology (MPPH). This technique holds considerable significance for drug discovery and materials science, where precise molecular property prediction is vital. By integrating SE(3)-invariance with Vietoris-Rips persistent homology, we effectively capture the three-dimensional representations of molecular chirality. This non-superimposable mirror image property directly influences the molecular interactions, serving as an essential factor in molecular property prediction. We explore the underlying topologies and patterns in molecular structures by applying Vietoris-Rips persistent homology across varying scales and parameters such as atomic weight, partial charge, bond type, and chirality. Our method's efficacy can be improved by incorporating additional parameters such as aromaticity, orbital hybridization, bond polarity, conjugated systems, as well as bond and torsion angles. Additionally, we leverage Stochastic Gradient Langevin Boosting in a Bayesian ensemble of GBDTs to obtain aleatoric and epistemic uncertainty estimates for gradient boosting models. With these uncertainty estimates, we prioritize high-uncertainty samples for active learning and model fine-tuning, benefiting scenarios where data labeling is costly or time consuming. Compared to conventional GNNs which usually suffer from oversmoothing and oversquashing, MPPH provides a more comprehensive and interpretable characterization of molecular data topology. We substantiate our approach with theoretical stability guarantees and demonstrate its superior performance over existing state-of-the-art methods in predicting molecular properties through extensive evaluations on the MoleculeNet benchmark datasets.

翻译：在本研究中，我们提出了一种基于多参数持续同调（MPPH）生成分子指纹的新计算方法。该方法对于药物发现和材料科学具有重要价值，在这些领域，精确的分子性质预测至关重要。通过将SE(3)-不变性与Vietoris-Rips持续同调相结合，我们有效捕获了分子手性的三维表征。这种非重叠镜像特性直接影响分子相互作用，是分子性质预测中的关键因素。我们通过在不同尺度和参数（如原子质量、局部电荷、键型及手性）下应用Vietoris-Rips持续同调，探索了分子结构中的潜在拓扑结构与模式。方法的有效性可通过引入芳香性、轨道杂化、键极性、共轭体系以及键角和扭转角等附加参数进一步提升。此外，我们利用随机梯度Langevin提升方法在梯度提升决策树的贝叶斯集成中获取其随机不确定性和认知不确定性估计。借助这些不确定性估计，我们优先选择高不确定性样本进行主动学习和模型微调，从而在数据标注成本高昂或耗时的情况下发挥优势。与通常存在过度平滑和过度挤压问题的传统图神经网络相比，MPPH提供了更全面且可解释的分子数据拓扑表征。我们通过理论稳定性保证证实了方法的可靠性，并在MoleculeNet基准数据集上的广泛评估中证明其优于现有最先进方法的分子性质预测性能。