Holographic-(V)AE: an end-to-end SO(3)-Equivariant (Variational) Autoencoder in Fourier Space

TL;DR

Holographic-(V)AE is an end-to-end SO(3)-equivariant autoencoder in Fourier space that effectively learns rotationally invariant features for 3D data, enabling unsupervised representation learning and accurate predictions in complex biological datasets.

Contribution

This work introduces H-(V)AE, a novel SO(3)-equivariant autoencoder that operates in Fourier space for unsupervised learning and data generation of 3D structures.

Findings

Efficient encoding of categorical features in spherical images.

Extraction of compact protein structure embeddings.

State-of-the-art protein-ligand binding affinity prediction.

Abstract

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.