One of the biggest challenges in the research of generative adversarial
networks (GANs) is assessing the quality of generated samples and detecting
various levels of mode collapse. In this work, we construct a novel measure of
performance of a GAN by comparing geometrical properties of the underlying data
manifold and the generated one, which provides both qualitative and
quantitative means for evaluation. Our algorithm can be applied to datasets of
an arbitrary nature and is not limited to visual data. We test the obtained
metric on various real-life models and datasets and demonstrate that our method
provides new insights into properties of GANs.

本文提出了一种新的基于几何学性质的 GAN 模型性能度量方法，可以定量和定性地评估生成样本的质量和模式崩溃的程度。该算法适用于各种类型的数据集，并不仅限于视觉数据。我们在多种真实模型和数据集上测试了该方法，并展示了其提供的 GANs 特性新洞察。

几何分数：一种比较生成对抗网络的方法

Geometry Score: A Method For Comparing Generative Adversarial Networks

We develop a framework for studying the statistical properties of current
sheets in numerical simulations of 3D magnetohydrodynamic (MHD) turbulence. We
describe an algorithm that identifies current sheets in a simulation snapshot
and then determines their geometrical properties (including length, width, and
thickness) and intensities (peak current density and total energy dissipation
rate). We then apply this procedure to simulations of reduced MHD turbulence
and perform a statistical analysis on the obtained population of current
sheets. We evaluate the role of reconnection by separately studying the
populations of current sheets which contain magnetic X-points and those which
do not. We find that the statistical properties of the two populations are
different in general. We compare the scaling of these properties to
phenomenological predictions obtained for the inertial range of MHD turbulence.
Finally, we test whether the reconnecting current sheets are consistent with
the Sweet-Parker model.

通过一种算法鉴别了数值模拟中的电流片并测量了它们的几何特征和强度，统计分析由具有磁性 X 点和没有磁性 X 点组成的电流片的互作用，比较其与 MHD 涡旋惯性区域的现象学预测，最后测试了这些重连电流片是否与 Sweet-Parker 模型吻合。