通过匹配曲率实现模型间嵌入对齐，提升跨任务迁移性能。
Geometric Embedding Alignment via Curvature Matching in Transfer Learning
- 基于黎曼几何的曲率匹配，对齐不同模型的隐空间结构。
- 在23个分子任务上，随机与骨架分割下分别提升14.4%和8.3%。
- 适合多源知识融合的迁移学习场景，尤其适用于分子性质预测。
深度学习的几何解释为理解其数学结构提供了新视角。本文提出一种新方法，利用微分几何（特别是黎曼几何）概念，将多个模型整合进统一的迁移学习框架。通过匹配各模型隐空间的里奇曲率，构建了相互关联的架构——几何嵌入对齐框架（GEAR），确保数据点在全局几何结构中具有一致表示。该框架能有效聚合多源知识，显著提升目标任务性能。我们在来自多个领域的23个分子任务对上进行评估，在随机数据划分和骨架数据划分下，相比现有基准模型分别获得14.4%和8.3%的性能提升。
原文摘要 · Abstract (English)
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.
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