Transfer learning is a crucial technique for handling a small amount of data that is potentially related to other abundant data. However, most of the existing methods are focused on classification tasks using images and language datasets. Therefore, in order to expand the transfer learning scheme to regression tasks, we propose a novel transfer technique based on differential geometry, namely the Geometrically Aligned Transfer Encoder (GATE). In this method, we interpret the latent vectors from the model to exist on a Riemannian curved manifold. We find a proper diffeomorphism between pairs of tasks to ensure that every arbitrary point maps to a locally flat coordinate in the overlapping region, allowing the transfer of knowledge from the source to the target data. This also serves as an effective regularizer for the model to behave in extrapolation regions. In this article, we demonstrate that GATE outperforms conventional methods and exhibits stable behavior in both the latent space and extrapolation regions for various molecular graph datasets.

翻译：迁移学习是一种关键技术，用于处理与大量潜在关联数据相比数量较少的数据。然而，现有方法大多聚焦于图像和语言数据集的分类任务。为了将迁移学习框架扩展至回归任务，我们提出了一种基于微分几何的新型迁移技术，即几何对齐迁移编码器（GATE）。在该方法中，我们将模型中的潜在向量解释为存在于黎曼弯曲流形上。我们找到任务对之间的恰当微分同胚，确保任意点映射到重叠区域的局部平坦坐标，从而允许知识从源数据迁移到目标数据。同时，这也可作为模型在外推区域表现的有效正则化器。本文在多种分子图数据集上证明，GATE 优于传统方法，并在潜在空间和外推区域中展现出稳定行为。