Abstract
Aqueous solubility prediction is central to drug discovery. Most molecular learning pipelines represent each molecule with a single graph and one selected conformer, offering limited leverage to study conformer-ensemble variability. This study presents the Geometric Sheaf Neural Network (GSNN), a sheaf-diffusion architecture whose bond restriction maps are computed from Procrustes-aligned conformer-ensemble covariance tensors and used as structured geometric gates. Its symmetry guarantee is conditional: intermediate vector features transform covariantly when coordinates and restriction maps are rotated consistently, while the scalar prediction is invariant. On a curated subset of the Aqueous Solubility Database (AqSolDB; N = 7188), five leakage-free runs on the paired conformer/spectral test set (n = 1435) give R2 = 0.683 ± 0.025 for GSNN, below EGNN (0.785 ± 0.015) and XGBoost+EGNN (0.806 ± 0.011). On five matched scaffold holdouts, the corresponding values are 0.505 ± 0.060, 0.740 ± 0.051, and 0.750 ± 0.045. In the fixed-seed control, forced λ = 0 and identity maps slightly improve R2 from 0.688 to 0.691, whereas random and shuffled covariance substitutions substantially degrade accuracy. Thus, the learned maps remain active but do not provide a predictive advantage over identity diffusion in this setting; arbitrary map substitutions are disruptive. The main contribution is a diagnostic framework for examining conformer-covariance gating and its chemically structured, alignment-dependent variation.