arXiv 2005.078522020-05stat.MLcs.LGmath.DGq-bio.GN

纤维潜在空间中的测地线：学习条件之间对应关系的几何方法

Geodesics in fibered latent spaces: A geometric approach to learning correspondences between conditions

Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）；Broad Institute（博德研究所）；Université Paul Sabatier, Toulouse 3（图卢兹第三大学保罗·萨巴蒂埃大学）；Institut de mathématiques de Toulouse（图卢兹数学研究所）；InvivoAI（InvivoAI公司）；Université Laval（拉瓦尔大学）

Tariq Daouda, Reda Chhaibi, Prudencio Tossou, Alexandra-Chloé Villani

备注：: 36 pages, many figures. v1: Preliminary version. v2: Minor ref fix. v3: Submitted version with enhanced presentation

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摘要：

这项工作介绍了一个几何框架和一种新的网络架构，用于创建不同条件下的样本之间的对应关系。在这种形式下，潜在空间是一个纤维丛分层成一个基本空间编码条件，和纤维空间编码的条件内的变化。此外，该潜在空间被赋予了自然的拉回度量。条件之间的对应关系通过最小化能量泛函得到，从而导致纤维之间的同构流。我们使用MNIST和Olivetti说明了这种方法，并在批量校正任务上对其性能进行了基准测试，这是将多个生物数据集集成在一起的问题。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。