# PRIME: Protein Representation via Physics-Informed Multiscale Equivariant Hierarchies

arXiv: https://arxiv.org/abs/2605.01625 · HTML: https://mlsanity.com/paper/2605.01625/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 31 references that are in the map.
- First posted on arXiv 2 May 2026.

## Builds on (most cited first, 11 of 11)

- [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)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Protein Representation Learning by Geometric Structure Pretraining](https://mlsanity.com/paper/2203.06125/) (2022)
- [MeshNet: Mesh Neural Network for 3D Shape Representation](https://mlsanity.com/paper/1811.11424/) (2018)
- [DeepSF: deep convolutional neural network for mapping protein sequences to folds](https://mlsanity.com/paper/1706.01010/) (2017)
- [Multiresolution Equivariant Graph Variational Autoencoder](https://mlsanity.com/paper/2106.00967/) (2021)
- [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)
- [E(3)-Equivariant Mesh Neural Networks](https://mlsanity.com/paper/2402.04821/) (2024)

## Abstract (arXiv)

Proteins are inherently multiscale physical systems whose functional properties emerge from coordinated structural organization across multiple spatial resolutions, ranging from atomic interactions to global fold topology. However, existing protein representation learning methods typically operate at a single structural level or treat different sources of structural information as parallel modalities, without explicitly modeling their hierarchical relationships. We introduce PRIME (Protein Representation via Physics-Informed Multiscale Equivariant Hierarchies), a unified framework that models proteins as a nested family of five physically grounded structural graphs spanning surface, atomic, residue, secondary-structure, and protein levels. Adjacent levels are connected through deterministic, physics-informed assignment operators, enabling bidirectional information exchange via bottom-up aggregation and top-down contextual refinement. Experiments on standard protein representation learning benchmarks demonstrate strong and competitive performance across diverse tasks, with particularly notable gains on the Fold Classification benchmark, where PRIME outperforms the strongest geometric GNN baseline by margins of 13.80 and 18.30 points on the harder Superfamily and Fold splits, and achieves a state-of-the-art accuracy of 84.10% on Reaction Class prediction, surpassing all baseline methods, including ESM. Ablation studies confirm that each structural level contributes complementary and non-redundant information, and adaptive cross-attention analysis reveals that PRIME autonomously identifies the most task-relevant structural resolutions at prediction time. Our source code is publicly available at https://github.com/HySonLab/PRIME