Molecular Uncertainty Gradients: Exact Decomposition of Predictive Variance Onto Molecular Substructures

Most explainability methods for molecular property prediction target predictions rather than uncertainty. Techniques for localizing predictive uncertainty to specific substructures remain comparatively underdeveloped, limiting our ability to identify which substructures drive uncertainty and which chemical patterns the model has not learned reliably. We present Molecular Uncertainty Gradients (MUG), a method that distributes a model's epistemic uncertainty, estimated as the variance across ensemble predictions, over the atoms of a molecule. By differentiating this variance with respect to intermediate atom representations, MUG computes signed atom-level contributions that sum exactly to the molecule’s predictive variance. These attributions can be aggregated over any group of atoms using a single backward pass. MUG requires no retraining and works with the dropout-based uncertainty estimates already standard in practice. We show that MUG localizes uncertainty to molecular substructures absent from the training data. Across six molecular property prediction benchmarks, MUG achieves the highest occlusion-controlled fidelity, and its decomposition holds. Crucially, masking the features of its highest-ranked atoms reduces model uncertainty substantially more than masking other fragments. We further demonstrate that MUG’s fragment-level uncertainty attributions can guide iterative library design toward compounds with favorable docking scores. Together, these results establish MUG as a complete and faithful approach to localizing predictive uncertainty, with practical applications in uncertainty-guided molecular design.