An Exploration of Learnt Representations of W Jets

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. A hyperparameter $\beta$ controls the resolution at which the VAE is sensitive to structures in the data manifold. The variation of the latent space structure with $\beta$, and the scaling of some VAE properties, provide 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.