mlsanityData to 7 Oct 2026

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

arXiv 2209.15567 ↗First posted 30 Sep 2022cs.LG physics.bio-phcited by 3

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Abstract (arXiv)

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.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 39 of its 99 references that are in the map. First posted on arXiv 30 Sep 2022.

Builds on

39 of 99 references.

References · 39

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27 more
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Cited by year

Citing papers per year: 2023: 1; 2024: 2.

3 papers.

  1. 2023H-Packer: Holographic Rotationally Equivariant Convolutional Neural Network for Protein Side-Chain Packingcited by 6
  2. 2024Categorical data clustering: 25 years beyond K-modescited by 2
  3. 2024HERMES: Holographic Equivariant neuRal network model for Mutational Effect and Stability predictioncited by 1