ICML Workshop (2026)
Sung Moon Ko, Sumin Lee
Abstract
Riemannian geometry offers a principled framework for modeling the smooth, curved latent spaces induced by deep learning models, and has shown particular promise in transfer learning. Recent approaches improve prediction performance by aligning the Ricci scalar curvature between target and source domains, thereby matching their intrinsic geometric structures. However, Ricci curvature computation is mathematically complex and computationally expensive, limiting its reproducibility. In this work, we propose a simplified metric matching approach that reduces both the algorithmic complexity and computational cost. Our method leverages an exact diffeomorphism between target and source spaces, enabling coordinate frame alignment such that, by definition of the curvature tensor, the curvature remains unchanged. Extensive experiments demonstrate that our approach achieves noticeable speed improvements while maintaining performance comparable to Ricci curvature–based methods.