  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.
