Holographic-(V)AE: An end-to-end SO(3)-equivariant (variational) autoencoder in Fourier space

Area of Science:

• Artificial Intelligence
• Machine Learning
• Computational Science

Background:

• Group-equivariant neural networks utilize generalized convolutions to model symmetric data.
• Advances have been made in supervised and unsupervised learning tasks, but symmetry-aware representations are underexplored.

Purpose of the Study:

• Introduce the holographic (variational) autoencoder (H-(V)AE) for end-to-end SO(3)-equivariant unsupervised learning in 3D.
• Develop a method to extract informative, low-dimensional representations from data with specified origin and symmetries.

Main Methods:

• H-(V)AE is an SO(3)-equivariant autoencoder operating in Fourier space.
• It reconstructs spherical Fourier encodings, learning a latent space with rotationally invariant embeddings and equivariant orientation frames.

Main Results:

• H-(V)AE efficiently encodes categorical features of spherical images.
• Learned latent spaces provide compact embeddings for protein structure microenvironments.
• State-of-the-art protein-ligand binding affinity predictions achieved when H-VAE embeddings are paired with random forest regressors.

Conclusions:

• H-(V)AE offers a powerful framework for unsupervised learning and data generation with symmetries.
• The extracted low-dimensional representations are valuable for data-scarce downstream applications, particularly in computational biology.