# G-VAE, a Geometric Convolutional VAE for ProteinStructure Generation

arXiv: https://arxiv.org/abs/2106.11920 · HTML: https://mlsanity.com/paper/2106.11920/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 22 Jun 2021.

## Builds on (most cited first, 10 of 10)

- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Variational Lossy Autoencoder](https://mlsanity.com/paper/1611.02731/) (2016)
- [NeVAE: A Deep Generative Model for Molecular Graphs](https://mlsanity.com/paper/1802.05283/) (2018)
- [Spherical Latent Spaces for Stable Variational Autoencoders](https://mlsanity.com/paper/1808.10805/) (2018)
- [Accurate De Novo Prediction of Protein Contact Map by Ultra-Deep Learning Model](https://mlsanity.com/paper/1609.00680/) (2016)
- [Deep Learning in Protein Structural Modeling and Design](https://mlsanity.com/paper/2007.08383/) (2020)
- [Generating Tertiary Protein Structures via an Interpretative Variational Autoencoder](https://mlsanity.com/paper/2004.07119/) (2020)

## Built on by (most cited first, 2 of 2)

- [Towards Understanding the Shape of Representations in Protein Language Models](https://mlsanity.com/paper/2509.24895/) (2025)
- [A shape-similarity latent space for fluid interfaces: invertible reduced-order modelling of droplet morphology](https://mlsanity.com/paper/2609.37947/) (2026)

## Abstract (arXiv)

Analyzing the structure of proteins is a key part of understanding their functions and thus their role in biology at the molecular level. In addition, design new proteins in a methodical way is a major engineering challenge. In this work, we introduce a joint geometric-neural networks approach for comparing, deforming and generating 3D protein structures. Viewing protein structures as 3D open curves, we adopt the Square Root Velocity Function (SRVF) representation and leverage its suitable geometric properties along with Deep Residual Networks (ResNets) for a joint registration and comparison. Our ResNets handle better large protein deformations while being more computationally efficient. On top of the mathematical framework, we further design a Geometric Variational Auto-Encoder (G-VAE), that once trained, maps original, previously unseen structures, into a low-dimensional (latent) hyper-sphere. Motivated by the spherical structure of the pre-shape space, we naturally adopt the von Mises-Fisher (vMF) distribution to model our hidden variables. We test the effectiveness of our models by generating novel protein structures and predicting completions of corrupted protein structures. Experimental results show that our method is able to generate plausible structures, different from the structures in the training data.