The ability to represent and compare machine learning models is crucial in
order to quantify subtle model changes, evaluate generative models, and gather
insights on neural network architectures. Existing techniques for comparing
data distributions focus on global data properties such as mean and covariance;
in that sense, they are extrinsic and uni-scale. We develop a first-of-its-kind
intrinsic and multi-scale method for characterizing and comparing data
manifolds, using a lower-bound of the spectral variant of the
Gromov-Wasserstein inter-manifold distance, which compares all data moments. In
a thorough experimental study, we demonstrate that our method effectively
discerns the structure of data manifolds even on unaligned data of different
dimensionalities; moreover, we showcase its efficacy in evaluating the quality
of generative models.

用 Gromov-Wasserstein 距离的下界，通过对所有数据矩计算，基于内在和多尺度的方法对比数据流形。实验证明，该方法能够有效地识别不同维度未对齐数据的结构，并展示了在评估生成模型质量方面的功效。