流形拓扑散度：一种用于比较数据流形的框架
Manifold Topology Divergence: a Framework for Comparing Data Manifolds
AI总结：
该研究提出基于Cross-Barcode的流形拓扑散度MTop-Divergence框架，用于比较数据流形、评估深度生成模型，可检测多种生成缺陷，扩展性好且领域无关。
摘要：
我们开发了一个用于比较数据流形的框架，尤其面向深度生成模型的评估。我们提出了一种名为Cross-Barcode(P,Q)的新型工具，给定高维空间中的一对分布，它可追踪分布所集中的流形之间的多尺度拓扑空间差异。基于Cross-Barcode，我们引入了流形拓扑散度得分（MTop-Divergence），并将其应用于评估多个领域的深度生成模型性能：图像、3D形状、时间序列，覆盖多个数据集：MNIST、Fashion MNIST、SVHN、CIFAR10、FFHQ、胸部X光图像、股市数据、ShapeNet。我们证明MTop-Divergence可准确检测不同程度的模式丢失、模式内崩塌、模式生成以及图像扰动。我们的算法随环境高维空间维度增加具备良好的可扩展性（基本呈线性）。它是首批基于拓扑数据分析（TDA）的实用方法之一，可普遍应用于不同规模和维度的数据集，包括视觉领域最新GAN所训练的数据集。所提方法具备领域无关性，且不依赖预训练网络。
英文摘要：
We develop a framework for comparing data manifolds, aimed, in particular, towards the evaluation of deep generative models. We describe a novel tool, Cross-Barcode(P,Q), that, given a pair of distributions in a high-dimensional space, tracks multiscale topology spacial discrepancies between manifolds on which the distributions are concentrated. Based on the Cross-Barcode, we introduce the Manifold Topology Divergence score (MTop-Divergence) and apply it to assess the performance of deep generative models in various domains: images, 3D-shapes, time-series, and on different datasets: MNIST, Fashion MNIST, SVHN, CIFAR10, FFHQ, chest X-ray images, market stock data, ShapeNet. We demonstrate that the MTop-Divergence accurately detects various degrees of mode-dropping, intra-mode collapse, mode invention, and image disturbance. Our algorithm scales well (essentially linearly) with the increase of the dimension of the ambient high-dimensional space. It is one of the first TDA-based practical methodologies that can be applied universally to datasets of different sizes and dimensions, including the ones on which the most recent GANs in the visual domain are trained. The proposed method is domain agnostic and does not rely on pre-trained networks.
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。
