Abstract: We develop the Lorentz group autoencoder (LGAE), an autoencoder that is 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 data at the Large Hadron Collider and find it outperforms a graph neural network baseline model on several compression, reconstruction, and anomaly detection tasks. The PyTorch code for our models is provided in Hao et al. (2022a).