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.
Abstract (translated)
深度学习模型的几何解释为理解其数学结构提供了深刻的视角。在这项工作中，我们提出了一种新颖的方法，利用微分几何（特别是黎曼几何的概念）将多个模型整合到一个统一的迁移学习框架中。通过使单个模型潜在空间的里奇曲率对齐，我们构建了一个相互关联的架构，即通过曲率匹配进行转移学习的几何嵌入对齐（GEAR），确保了数据点之间的全面几何表示。该框架能够有效地汇总来自不同来源的知识，从而提高目标任务上的性能。我们在23个分子任务配对（源自不同的领域）上评估了我们的模型，并在随机和支架数据拆分下均表现出显著的性能提升（分别提高了14.4%和8.3%）。
URL
https://arxiv.org/abs/2506.13015
