Geometric Embedding Alignment via Curvature Matching in Transfer Learning

Geometrical interpretations of deep learning models offer insightful perspectives into their underlying mathematical structures. In this work, we introduce a novel approach that leverages differential geometry, particularly concepts from Riemannian geometry, to integrate multiple models into a unified transfer learning framework. By aligning the Ricci curvature of latent space of individual models, we construct an interrelated architecture, namely Geometric Embedding Alignment via cuRvature matching in transfer learning (GEAR), which ensures comprehensive geometric representation across datapoints. This framework enables the effective aggregation of knowledge from diverse sources, thereby improving performance on target tasks. We evaluate our model on 23 molecular task pairs and demonstrate significant performance gains over existing benchmark models—achieving improvements of at least 14.4% under random splits and 8.3% under scaffold splits.

Many AI models for molecular discovery learn useful information differently, making it difficult to combine their strengths for predicting molecular properties. We developed GEAR, a geometry-based transfer learning framework that aligns the internal latent spaces of different models using curvature from differential geometry. By connecting models through their geometric structure, GEAR improves knowledge transfer and significantly boosts performance across 23 molecular prediction tasks.