Beyond Lipschitz: Ranking Binding Affinity in Hyperbolic Space

Abstract

Despite the importance of protein-ligand affinity ranking in drug discovery, existing deep learning models struggle to distinguish hard inactives that are structurally similar to active compounds but biologically inactive. We theoretically show this failure stems from the Lipschitz continuity constraint in Euclidean space, which makes neural networks locally insensitive to subtle yet critical structural perturbations. To overcome this, we propose AlphaRank, which demonstrates that scoring affinity as the negative hyperbolic geodesic distance allows subtle tangential variations to bypass Lipschitz constraints, intuitively corresponding to pivotal binding mode factors such as conformational fit. Meanwhile, AlphaRank employs joint optimization to simultaneously ranking affinity scores among actives in a proximity-aware manner and separate actives from decoy inactives through a geometric cone constraint. Experiments demonstrate that AlphaRank outperforms state-of-the-art models like Boltz-2 in both affinity ranking and active-inactive discrimination, while providing a interpretable representation space.