  There has been significant work recently in developing machine learning (ML)
models in high energy physics (HEP) for tasks such as classification,
simulation, and anomaly detection. Often these models are adapted from those
designed for datasets in computer vision or natural language processing, which
lack inductive biases suited to HEP data, such as equivariance to its inherent
symmetries. Such biases have been shown to make models 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
outperforms graph and convolutional neural network baseline models on several
compression, reconstruction, and anomaly detection metrics. We also demonstrate
the advantage of such an equivariant model in analyzing the latent space of the
autoencoder, which can improve the explainability of potential anomalies
discovered by such ML models.
