Lorentz Group Equivariant Autoencoders

There has been significant work recently in developing machine learning models in high energy physics (HEP), for tasks such as classification, simulation, and anomaly detection. Typically, these models are adapted from those designed for datasets in computer vision or natural language processing without necessarily incorporating inductive biases suited to HEP data, such as respecting its inherent symmetries. Such inductive biases can make the model more performant and interpretable, and reduce the amount of training data needed. To that end, we develop the Lorentz group autoencoder (LGAE), an autoencoder model equivariant with respect to the proper, orthochronous Lorentz group $\mathrm{SO}^+(3,1)$, with a latent space living in the representations of the group. We present our architecture and several experimental results on jets at the LHC and find it significantly outperforms a non-Lorentz-equivariant graph neural network baseline on compression and reconstruction, and anomaly detection. We also demonstrate the advantage of such an equivariant model in analyzing the latent space of the autoencoder, which can have a significant impact on the explainability of anomalies found by such black-box machine learning models.