Geometric Embedding Alignment via Curvature Matching in Transfer Learning

2025/06/16 by Sung Moon Ko, Ko, Sung Moon, Jaewan Lee +8
Computer Science · Engineering · #3D Shape Modeling and Analysis #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Image Processing and 3D Reconstruction #Machine Learning (cs.LG) #Medical Imaging and Analysis

paper · pdf · doi:10.48550/arxiv.2506.13015

openalex publication_date 2025/06/16 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

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.

Citations

• Counterfactual Explanations via Riemannian Latent Space Traversal
• Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifolds
• Task Addition in Multi-Task Learning by Geometrical Alignment
• Multitask Extension of Geometrically Aligned Transfer Encoder
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• Transfer Learning with Kernel Methods
• PubChem 2023 update
• Learning Multimodal Graph-to-Graph Translation for Molecular Optimization
• Geodesic Clustering in Deep Generative Models
• Geometric Deep Learning: Going beyond Euclidean data
• Convolutional Networks on Graphs for Learning Molecular Fingerprints
• Spectral Networks and Locally Connected Networks on Graphs
• The Graph Neural Network Model

Related

• Geometrically Aligned Transfer Encoder for Inductive Transfer in Regression Tasks
• The Geometry of Machine Learning Models
• Task Addition in Multi-Task Learning by Geometrical Alignment
• Geometric Deep Learning: Going beyond Euclidean data
• Connecting Neural Models Latent Geometries with Relative Geodesic Representations