Geometric Embedding Alignment via Curvature Matching in Transfer Learning

TL;DR

This paper introduces GEAR, a novel transfer learning framework that aligns models' latent space curvature using Riemannian geometry to improve performance across diverse tasks.

Contribution

It proposes a new geometric approach leveraging Ricci curvature matching for integrating multiple models in transfer learning.

Findings

Achieved 14.4% performance improvement on random splits.

Achieved 8.3% performance improvement on scaffold splits.

Validated on 23 molecular task pairs from various domains.

Abstract

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 sourced from various domains and demonstrate significant performance gains over existing benchmark model under both random (14.4%) and scaffold (8.3%) data splits.