DualEquiNet: A Dual-Space Hierarchical Equivariant Network for Large Biomolecules

TL;DR

DualEquiNet is a novel hierarchical neural network that combines Euclidean and Spherical Harmonics spaces to effectively model large biomolecules, capturing both local atomic details and global structural dependencies.

Contribution

It introduces a dual-space architecture with cross-space message passing and pooling, enabling multi-scale modeling of large biomolecules with improved accuracy.

Findings

Achieves state-of-the-art results on RNA and protein benchmarks.

Outperforms previous methods on new 3D structural benchmarks.

Effectively captures multi-scale features of large biomolecules.

Abstract

Geometric graph neural networks (GNNs) that respect E(3) symmetries have achieved strong performance on small molecule modeling, but they face scalability and expressiveness challenges when applied to large biomolecules such as RNA and proteins. These systems require models that can simultaneously capture fine-grained atomic interactions, long-range dependencies across spatially distant components, and biologically relevant hierarchical structure, such as atoms forming residues, which in turn form higher-order domains. Existing geometric GNNs, which typically operate exclusively in either Euclidean or Spherical Harmonics space, are limited in their ability to capture both the fine-scale atomic details and the long-range, symmetry-aware dependencies required for modeling the multi-scale structure of large biomolecules. We introduce DualEquiNet, a Dual-Space Hierarchical Equivariant Network that constructs complementary representations in both Euclidean and Spherical Harmonics spaces to capture local geometry and global symmetry-aware features. DualEquiNet employs bidirectional cross-space message passing and a novel Cross-Space Interaction Pooling mechanism to hierarchically aggregate atomic features into biologically meaningful units, such as residues, enabling efficient and expressive multi-scale modeling for large biomolecular systems. DualEquiNet achieves state-of-the-art performance on multiple existing benchmarks for RNA property prediction and protein modeling, and outperforms prior methods on two newly introduced 3D structural benchmarks demonstrating its broad effectiveness across a range of large biomolecule modeling tasks.