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DualEqui: A Dual-Space Hierarchical Equivariant Network for Large Biomolecules
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Proposes DualEquiNet, an E(3)-equivariant GNN that runs Euclidean-space and spherical-harmonics-space message passing in parallel with cross-space exchange and a cross-space pooling step, targeting RNA and protein property prediction.
Problem
Geometric GNNs operate in only Euclidean or only spherical harmonics space, which limits their ability to jointly capture fine-grained atomic interactions, long-range dependencies, and the residue-level hierarchy of large biomolecules like RNA and proteins.
Approach
Maintain complementary Euclidean (distance-cutoff neighbors) and spherical-harmonic (feature-similarity neighbors) representations, exchange messages bidirectionally between them, and pool atoms into residues with Cross-Space Interaction Pooling that mixes features across both spaces.
Key results
- On RNA property prediction, DualEquiNet reduces RMSE by 25.7% (CovidVaccine), 33.5% (Ribonanza) and 8.4% (Tc-ribo) relative to the best baseline.
- On the TorsionAngle benchmark, DualEquiNet reaches the lowest average circular MAE of 15.87 versus 16.27 for GotenNet, best on 5 of 7 angles.
- On the N-chain expressivity task (N=10), DualEquiNet reaches near-perfect accuracy at d_SH <= 0.8 with fewer layers than the baselines, which stay at chance level.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add CSIP instead of standard mean pooling (ablation) | DualEquiNet · CovidVaccine | RMSE: 0.356 ±0.002 -> 0.353±0.006 | Helped |
| add CSIP and cross-space message passing (ablation) | DualEquiNet · CovidVaccine | RMSE: 0.356 ±0.013 -> 0.353±0.006 | Helped |
| add CSIP, cross-space message passing, and dual-space representations (ablation) | DualEquiNet · CovidVaccine | RMSE: 0.362 ±0.010 -> 0.353±0.006 | Helped |
| add CSIP instead of standard mean pooling (ablation) | DualEquiNet · Ribonanza | RMSE: 0.586 ±0.016 -> 0.558±0.123 | Helped |
| add CSIP and cross-space message passing (ablation) | DualEquiNet · Ribonanza | RMSE: 0.591 ±0.081 -> 0.558±0.123 | Helped |
| add CSIP, cross-space message passing, and dual-space representations (ablation) | DualEquiNet · Ribonanza | RMSE: 0.592 ±0.028 -> 0.558±0.123 | Helped |
| add CSIP instead of standard mean pooling (ablation) | DualEquiNet · Tc-ribo | RMSE: 0.682 ±0.026 -> 0.636±0.049 | Helped |
| add CSIP and cross-space message passing (ablation) | DualEquiNet · Tc-ribo | RMSE: 0.698 ±0.010 -> 0.636±0.049 | Helped |
| add CSIP, cross-space message passing, and dual-space representations (ablation) | DualEquiNet · Tc-ribo | RMSE: 0.699 ±0.010 -> 0.636±0.049 | Helped |
Surprising findings
- Most geometric baselines (SchNet, EGNN, TFN, HEGNN, GotenNet) stay at chance (50%) on the N-chain task even with more layers than the hop requirement.
Limitations
- Performance depends on the quality of input 3D structures, which vary across datasets (RhoFold-predicted for RNA tasks).
- Hyperparameter-dependent neighborhood thresholds d_EU and d_SH must be tuned.
Experimental setup
Datasets: CovidVaccine Ribonanza Tc-ribo mRFP protein RNASolo TorsionAngle
Benchmarks: CovidVaccine Ribonanza Tc-ribo mRFP protein SASA RNASolo SASA TorsionAngle N-chain discrimination
Metrics: RMSE circular MAE accuracy
Baselines: SchNet EGNN GVPGNN TFN FastEGNN HEGNN GotenNet
Builds on: EGNN GotenNet HEGNN e3nn
Closest papers by meaning
- Geometric Hyena Networks for Large-scale Equivariant Learning (ICML 2025 · similarity 0.89)
- Evaluating Representation Learning on the Protein Structure Universe (ICLR 2024 · similarity 0.88)
- Generalist Equivariant Transformer Towards 3D Molecular Interaction Learning (ICML 2024 · similarity 0.88)
- Towards Multiscale Graph-based Protein Learning with Geometric Secondary Structural Motifs (NeurIPS 2025 · similarity 0.87)
- Beyond Sequence: Impact of Geometric Context for RNA Property Prediction (ICLR 2025 · similarity 0.87)
- Pushing the Limits of All-Atom Geometric Graph Neural Networks: Pre-Training, Scaling, and Zero-Shot Transfer (ICLR 2025 · similarity 0.87)
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