GeoPMR: Preserving Relational and Hierarchical Geometry in Multimodal Molecular Representation Learning

Multimodal molecular representation learning aligns heterogeneous chemical and cellular signals to predict molecular properties. The dominant paradigm is instance-level contrastive alignment, such as InfoNCE and VICReg, which implicitly treats every modality as a point cloud in a shared Euclidean space. This paradigm overlooks two structural properties of molecular-cellular data. \textit{First}, each modality, from atomic fingerprints to cell morphology to transcriptomic response, carries its own intrinsic geometry; directly pulling individual embeddings together can distort the relational structure each modality has learned to express. \textit{Second}, the modalities form a directed biological cascade, from molecular structure to conformation, gene perturbation, cellular phenotype, and transcriptomic response, whose branching grows exponentially with depth, a regime that Euclidean spaces cannot embed without distortion. We therefore propose \textbf{GeoPMR}, a pre-training framework that addresses both properties through two complementary geometric modules: Metric-Guided Gromov-Wasserstein alignment (MGW) and a Hyperbolic Hierarchical Module (HHM). \textbf{MGW} equips each modality with a learnable diagonal Riemannian metric and aligns distance matrices rather than individual embeddings via entropic optimal transport, so cross-modal alignment preserves relational rather than merely pointwise structure. \textbf{HHM} lifts all modality latents onto the Poincaré ball and applies a probabilistic parent-child and sibling contrastive loss along the cascade, exploiting the exponential volume growth of negatively curved space to embed the hierarchy with low distortion. On seven molecular property prediction benchmarks spanning toxicity, bioactivity, and ADME, GeoPMR sets a new state of the art by improving the classification AUC by 1.4\% and regression MAE by 1.7\%.