Capturing Motif Topological Diversity via Geometry-Adaptive Riemannian Molecular Representation Learning

Abstract

Molecular properties are often governed by a small number of local substructures, or motifs, whose topologies can vary drastically across molecules. Existing molecular representation learning approaches typically embed all motifs into a single Euclidean or fixed-curvature space, which fails to capture the motif-level topological heterogeneity and leads to geometric mismatch, impairing property prediction. To address this challenge, we propose a geometry-adaptive Riemannian framework for molecular representation learning, which explicitly models motifs as the basic units and learns their embeddings across multiple constant-curvature spaces. Each motif is adaptively aligned with the geometric space that best fits its intrinsic topology, enabling simultaneous modeling of cyclic, hierarchical, and tree-like structures. Motif embeddings are then aggregated into molecule-level representations, emphasizing functional substructures while suppressing irrelevant background. Extensive experiments on benchmark molecular property prediction datasets demonstrate that our approach outperforms state-of-the-art baselines, shows strong generalization under distribution shifts, and provides interpretable motif-level insights, offering a general and scalable framework for scientific molecular modeling. Our code is available at https://github.com/qimuya/mo-mi-r.