论文标题
纤维潜在空间中的测量学：条件之间学习对应关系的几何方法
Geodesics in fibered latent spaces: A geometric approach to learning correspondences between conditions
论文作者
论文摘要
这项工作介绍了一个几何框架和一种新颖的网络体系结构，用于在不同条件的样本之间创建对应关系。在这种形式主义下，潜在空间是一个分层为基本空间编码条件的光纤束，以及在条件下编码变化的光纤空间。此外，这个潜在空间具有天然的下拉度度量。条件之间的对应关系是通过最小化能量功能来获得的，从而导致纤维之间的差异流。 我们使用MNIST和OLIVETTI进行了说明这种方法，并基准了其在批次校正任务上的性能，这是将多个生物数据集整合在一起的问题。
This work introduces a geometric framework and a novel network architecture for creating correspondences between samples of different conditions. Under this formalism, the latent space is a fiber bundle stratified into a base space encoding conditions, and a fiber space encoding the variations within conditions. Furthermore, this latent space is endowed with a natural pull-back metric. The correspondences between conditions are obtained by minimizing an energy functional, resulting in diffeomorphism flows between fibers. We illustrate this approach using MNIST and Olivetti and benchmark its performances on the task of batch correction, which is the problem of integrating multiple biological datasets together.
