LG AI Research Uses Riemannian Geometry to Solve Data Scarcity in AI for Science

LG AI Research addressed the critical challenge of data scarcity in AI for Science by introducing two new transfer learning methods, GEAR and Sim-GEAR, at ICML 2026. These methods leverage Riemannian geometry to transfer knowledge from data-rich physical properties to data-scarce ones, a common issue in materials development where measuring certain properties is time- and cost-intensive.

GEAR: Curvature-Based Transfer Learning

GEAR (Geometric Transfer Learning through Latent-Space Curvature Matching) interprets differences between latent spaces of different models as geometric variations rather than simple vector discrepancies. By calculating the Ricci scalar, which condenses curvature information, GEAR trains a data-poor target model to inherit the geometric structure of a data-rich source model. This approach allows for accurate knowledge transfer even when models use different architectures or embeddings, as curvature is invariant to coordinate transformations.

Sim-GEAR: Metric Matching for Efficiency

While GEAR demonstrated the potential of geometric transfer learning, it suffered from high computational complexity due to the need for higher-order derivatives to calculate curvature. Sim-GEAR simplifies this process by aligning the metrics of the source and target latent spaces directly, bypassing the curvature calculation. This shift reduces computational complexity from approximately the fourth order to the third order, preserving distance and angle information more directly than the Ricci scalar.

Performance and Impact

In experimental evaluations, Sim-GEAR achieved a 91.1% computational speedup and reduced memory usage by 62.6% compared to GEAR. Despite the simplified structure, Sim-GEAR maintained stable transfer learning performance across various molecular physical property datasets. These advancements enable the use of larger latent dimensions and batch sizes on existing hardware, facilitating more efficient AI-driven materials discovery.