# Topotein: Topological Deep Learning for Protein Representation Learning

arXiv: https://arxiv.org/abs/2509.03885 · HTML: https://mlsanity.com/paper/2509.03885/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 4 Sep 2025.

## Builds on (most cited first, 20 of 20)

- [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)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Weisfeiler and Lehman Go Cellular: CW Networks](https://mlsanity.com/paper/2106.12575/) (2021)
- [Protein Representation Learning by Geometric Structure Pretraining](https://mlsanity.com/paper/2203.06125/) (2022)
- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [On the Expressive Power of Geometric Graph Neural Networks](https://mlsanity.com/paper/2301.09308/) (2023)
- [A new perspective on building efficient and expressive 3D equivariant graph neural networks](https://mlsanity.com/paper/2304.04757/) (2023)
- [Ankh: Optimized Protein Language Model Unlocks General-Purpose Modelling](https://mlsanity.com/paper/2301.06568/) (2023)
- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [TopoBench: A Framework for Benchmarking Topological Deep Learning](https://mlsanity.com/paper/2406.06642/) (2024)
- [TopoX: A Suite of Python Packages for Machine Learning on Topological Domains](https://mlsanity.com/paper/2402.02441/) (2024)
- [E(n) Equivariant Topological Neural Networks](https://mlsanity.com/paper/2405.15429/) (2024)
- [Geometry-Complete Perceptron Networks for 3D Molecular Graphs](https://mlsanity.com/paper/2211.02504/) (2022)
- [Evaluating representation learning on the protein structure universe](https://mlsanity.com/paper/2406.13864/) (2024)
- [Message Passing Neural Networks for Hypergraphs](https://mlsanity.com/paper/2203.16995/) (2022)
- [Protein Representation Learning with Sequence Information Embedding: Does it Always Lead to a Better Performance?](https://mlsanity.com/paper/2406.19755/) (2024)
- [SE3Set: Harnessing equivariant hypergraph neural networks for molecular representation learning](https://mlsanity.com/paper/2405.16511/) (2024)

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

- [From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Features](https://mlsanity.com/paper/2606.11911/) (2026)
- [Collapsed Effective Operators for Higher-order Structures](https://mlsanity.com/paper/2606.23517/) (2026)

## Abstract (arXiv)

Protein representation learning (PRL) is crucial for understanding structure-function relationships, yet current sequence- and graph-based methods fail to capture the hierarchical organization inherent in protein structures. We introduce Topotein, a comprehensive framework that applies topological deep learning to PRL through the novel Protein Combinatorial Complex (PCC) and Topology-Complete Perceptron Network (TCPNet). Our PCC represents proteins at multiple hierarchical levels -- from residues to secondary structures to complete proteins -- while preserving geometric information at each level. TCPNet employs SE(3)-equivariant message passing across these hierarchical structures, enabling more effective capture of multi-scale structural patterns. Through extensive experiments on four PRL tasks, TCPNet consistently outperforms state-of-the-art geometric graph neural networks. Our approach demonstrates particular strength in tasks such as fold classification which require understanding of secondary structure arrangements, validating the importance of hierarchical topological features for protein analysis.