DrugPrism: Target-Conditioned Riemannian Metrics on Mixed-Curvature Product Spaces for Protein–Ligand Affinity Ranking

Recent spherical and hyperbolic affinity ranking models exhibit complementary performance across protein targets, suggesting that a fixed comparison geometry may be restrictive. We show that target specific geometry alone does not guarantee ranking adaptation, as single geometry rescaling changes intrinsic curvature but preserves rankings for fixed representations. This motivates relative scaling across multiple geometric components. We introduce DrugPrism, which maps protein and ligand features into a shared product manifold with spherical, Euclidean, and hyperbolic components, while a pocket conditioned metric head predicts target specific coefficients that rescale the component metrics. Under the resulting product metric, the squared geodesic distance is exactly a weighted sum of the component squared distances, allowing relative weighting to alter rankings when the components disagree. DrugPrism improves mean Spearman correlation over HypSeek by 13.8% on Merck and 19.7% on Hermite. Controlled ablations show that target conditioned weighting substantially outperforms both uniform product weighting and all single geometry variants. On an unseen OpenBind target, DrugPrism with only five tuning compounds already surpasses LigUnity and HypSeek with 25 compounds. The learned metric weights further reveal clear protein family level structure, with related proteins tending to share similar geometric preferences.