Holographic-(V)AE: an end-to-end SO(3)-Equivariant (Variational) Autoencoder in Fourier Space
This work addresses the need for data-efficient unsupervised learning and generation in 3D domains, such as spherical images and protein structures, with incremental contributions to equivariant models.
The paper tackles the problem of extending group-equivariant neural networks to unsupervised and generative domains by introducing Holographic-(V)AE, an SO(3)-equivariant autoencoder in Fourier space, which learns a rotationally invariant latent space and achieves state-of-the-art predictions for protein-ligand binding affinity when paired with a Random Forest Regressor.
Group-equivariant neural networks have emerged as a data-efficient approach to solve classification and regression tasks, while respecting the relevant symmetries of the data. However, little work has been done to extend this paradigm to the unsupervised and generative domains. Here, we present Holographic-(Variational) Auto Encoder (H-(V)AE), a fully end-to-end SO(3)-equivariant (variational) autoencoder in Fourier space, suitable for unsupervised learning and generation of data distributed around a specified origin in 3D. H-(V)AE is trained to reconstruct the spherical Fourier encoding of data, learning in the process a low-dimensional representation of the data (i.e., a latent space) with a maximally informative rotationally invariant embedding alongside an equivariant frame describing the orientation of the data. We extensively test the performance of H-(V)AE on diverse datasets. We show that the learned latent space efficiently encodes the categorical features of spherical images. Moreover, H-(V)AE's latent space can be used to extract compact embeddings for protein structure microenvironments, and when paired with a Random Forest Regressor, it enables state-of-the-art predictions of protein-ligand binding affinity.