# Ophiuchus: Scalable Modeling of Protein Structures through Hierarchical Coarse-graining SO(3)-Equivariant Autoencoders

arXiv: https://arxiv.org/abs/2310.02508 · HTML: https://mlsanity.com/paper/2310.02508/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 31 of its 69 references that are in the map.
- First posted on arXiv 4 Oct 2023.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 31)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [Protein Representation Learning by Geometric Structure Pretraining](https://mlsanity.com/paper/2203.06125/) (2022)
- [Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2205.15019/) (2022)
- [ATOM3D: Tasks On Molecules in Three Dimensions](https://mlsanity.com/paper/2012.04035/) (2020)
- [Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics](https://mlsanity.com/paper/1710.11239/) (2017)
- [Generating Novel, Designable, and Diverse Protein Structures by Equivariantly Diffusing Oriented Residue Clouds](https://mlsanity.com/paper/2301.12485/) (2023)
- [Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Properties](https://mlsanity.com/paper/2008.08461/) (2020)
- [DeepSF: deep convolutional neural network for mapping protein sequences to folds](https://mlsanity.com/paper/1706.01010/) (2017)
- [DeepConv-DTI: Prediction of drug-target interactions via deep learning with convolution on protein sequences](https://mlsanity.com/paper/1811.02114/) (2018)
- [Ankh: Optimized Protein Language Model Unlocks General-Purpose Modelling](https://mlsanity.com/paper/2301.06568/) (2023)
- [Coarse-Graining Auto-Encoders for Molecular Dynamics](https://mlsanity.com/paper/1812.02706/) (2018)
- [A Latent Diffusion Model for Protein Structure Generation](https://mlsanity.com/paper/2305.04120/) (2023)
- [Generative Coarse-Graining of Molecular Conformations](https://mlsanity.com/paper/2201.12176/) (2022)
- [Chemically Transferable Generative Backmapping of Coarse-Grained Proteins](https://mlsanity.com/paper/2303.01569/) (2023)
- [Auto-Encoding Molecular Conformations](https://mlsanity.com/paper/2101.01618/) (2021)
- [SidechainNet: An All-Atom Protein Structure Dataset for Machine Learning](https://mlsanity.com/paper/2010.08162/) (2020)

## Built on by (most cited first, 3 of 3)

- [Out of Many, One: Designing and Scaffolding Proteins at the Scale of the Structural Universe with Genie 2](https://mlsanity.com/paper/2405.15489/) (2024)
- [EquiJump: Protein Dynamics Simulation via SO(3)-Equivariant Stochastic Interpolants](https://mlsanity.com/paper/2410.09667/) (2024)
- [Accelerating Protein Molecular Dynamics Simulation with DeepJump](https://mlsanity.com/paper/2509.13294/) (2025)

## Abstract (arXiv)

Three-dimensional native states of natural proteins display recurring and hierarchical patterns. Yet, traditional graph-based modeling of protein structures is often limited to operate within a single fine-grained resolution, and lacks hourglass neural architectures to learn those high-level building blocks. We narrow this gap by introducing Ophiuchus, an SO(3)-equivariant coarse-graining model that efficiently operates on all-atom protein structures. Our model departs from current approaches that employ graph modeling, instead focusing on local convolutional coarsening to model sequence-motif interactions with efficient time complexity in protein length. We measure the reconstruction capabilities of Ophiuchus across different compression rates, and compare it to existing models. We examine the learned latent space and demonstrate its utility through conformational interpolation. Finally, we leverage denoising diffusion probabilistic models (DDPM) in the latent space to efficiently sample protein structures. Our experiments demonstrate Ophiuchus to be a scalable basis for efficient protein modeling and generation.