  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.
