Geometric Embedding Alignment via Curvature Matching in Transfer Learning

2025-06-16

AI Summary

To address the misalignment of latent-space geometric structures across pre-trained models in cross-domain transfer learning, this paper proposes the first unified transfer learning framework based on Ricci curvature alignment. Methodologically, it introduces Ricci curvature—drawn from Riemannian geometry—as a learnable geometric prior; leveraging differential-geometric tools, it estimates and aligns local curvature distributions across multiple pre-trained models’ latent spaces, enabling structured, geometry-aware collaboration rather than naive feature concatenation. The framework jointly integrates latent-space modeling, multi-source model ensembling, and molecular graph representation learning. Evaluated on 23 molecular property prediction tasks, it significantly outperforms baselines: achieving average improvements of 14.4% under random splits and 8.3% under scaffold splits. These results empirically validate the efficacy and generalizability of curvature-driven geometric alignment for cross-domain knowledge transfer.

Technology Category

• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Aligning Ricci curvature in latent spaces for transfer learning
• Integrating multiple models via Riemannian geometry concepts
• Improving performance on target tasks through geometric representation

Innovation

• Leverages Riemannian geometry for transfer learning
• Aligns Ricci curvature of latent spaces
• Improves performance via geometric representation