Performance on complex property prediction tasks.

Maximizing information transfer across different structural scales is critical for effective molecular representation learning. Current molecular graph neural networks fail to fully capture the multi-scale nature of molecular geometry, leading to suboptimal information propagation between local and global structural features. We propose Multi-Scale Geometric Pre-training (MSG-Pre), an information-theoretic framework that hierarchically integrates molecular information across atomic, functional group, and conformer levels through entropy-guided mechanisms. Our approach employs a scale-adaptive attention mechanism that dynamically weights geometric features based on their information content, coupled with a hierarchical contrastive learning scheme that maximizes mutual information between complementary structural views. This is further reinforced by a geometric regularization strategy that minimizes information loss of essential conformational properties. Rigorous empirical validation on 14 molecular benchmark datasets demonstrates state-of-the-art performance with improvements up to 5.2% over previous methods. Notably, MSG-Pre significantly enhances information extraction for nanomedicine applications including nanoparticle-protein interactions and surface functionalization efficacy. Theoretical analysis reveals that MSG-Pre effectively maximizes cross-scale mutual information while minimizing intra-scale redundancy, maintaining an optimal information-entropy balance in molecular representations. Our work establishes an information-theoretic foundation for geometric pre-training that improves molecular understanding and enhances prediction capabilities for both drug discovery and nanomaterial design applications.