I present a Variational Autoencoder (VAE) trained on collider physics data
(specifically boosted $W$ jets), with reconstruction error given by an
approximation to the Earth Movers Distance (EMD) between input and output jets.
This VAE learns a concrete representation of the data manifold, with
semantically meaningful and interpretable latent space directions which are
hierarchically organized in terms of their relation to physical EMD scales in
the underlying physical generative process. The variation of the latent space
structure with a resolution hyperparameter provides insight into scale
dependent structure of the dataset and its information complexity. I introduce
two measures of the dimensionality of the learnt representation that are
calculated from this scaling.

本文提出基于变分自编码器模型的碰撞物理学数据训练方法，使用地球移动距离的近似值作为输入和输出喷注的重构误差指标。得到的模型学习到了一个数据流形的具体表示，具有语义上有意义和可解释的潜在空间方向。这些方向是按照它们与基础物理生成过程中物理 EMD 尺度的关系进行层次化组织的。随着分辨率超参数的变化，我们可以了解数据集的比例依赖性结构和信息复杂性。本文介绍了两个利用这种比例尺度计算学习表示维数的度量方法。