Title: DualEqui: A Dual-Space Hierarchical Equivariant Network for Large Biomolecules
Venue: NeurIPS 2025
Accepted: yes
Keywords: Geometric deep learning

Graph Neural Networks

GNNs

RNA property prediction
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.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nIn this paper, the authors propose the DualEquiNet model to combined invariant and equivariant-based representation together. The key idea is to develop  a dual-space hierarchical equivariant network that constructs complementary representations in both Euclidean and spherical harmonics spaces to capture both invariant and equivariant properties. More importantly, the model employs bidirectional cross-space message passing and cross-space interaction pooling mechanism to hierarchically aggregate atomic features. The model has been validated based on several existing benchmarks and shows promising results.\n\nSTRENGTHS AND WEAKNESSES:\nStrength: The developed Dual-Space-based learning architecture is novel and promising.\n\nWeakness: The message-passing for spherical harmonic features is not explained clearly. The definition of neighborhood is very confusing! The importance of two difference components is unclear!\n\nQUESTIONS:\n1. The definition for SH neighborhood is confusing! From the definition, it is not the distance between the two atoms that matter, instead if they have similar local structures (with similar orientation), they will be treated as neighbors. This is very weird. For instance, if we have two benenze ring in the structure (with similar orientations), then they will be regarded as neighbors. However, if two benzene rings are oriented differently, they are no longer neighbors. Why the authors choose to do it this way? Why not just use the standard SH-based neighborhood definition? Is there any ablation study to show that the specially-design neighborhood will have better performance?\n\n2. The ablation study part is not clear. Normally SH will contain more information that standard invariant-based graph models. State differently, SH-based models, such as E3NN, will have better performance than general GNNs, as they are more complicated and consider equivariant information. For the ablation study, the authors should consider just using SH-based model (w/o CSIP/Cross/Dual) instead of removing SH-based models.\n\n3. The benchmarks are not very widely used. More interesting dataset from MolecularNet should be considered. In particular, the prediction of SARA and torsion angles seems to be not proper for this case. Note that the model input has all the geometric information, and SARA and torsion angles are just special properties that can be analytically calculated.\n\nLIMITATIONS:\nN.A.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-24"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors present DualEquiNet, a novel geometric graph neural network operating in joint Euclidean-spherical harmonics spaces for biomolecular representation learning. The authors' methodology is interesting, and their experimental results are promising. Nonetheless, a few concerns remain regarding the evaluation of their proposed methodology.\n\nSTRENGTHS AND WEAKNESSES:\n**Points of strength:**\n1. The authors' methodology is well-motivated, sound, and interesting. I particularly appreciated the authors' depth and clarity in discussing the importance of local-to-global (and vice versa) representation learning on biomolecular graphs. Using spherical harmonics to bridge this gap is a compelling idea.\n2. The authors evaluate their new method on a variety of protein and RNA datasets, and in all cases, their results are positive.\n3. The authors' writing style is clear and consistent, making it easy for readers to grasp the main takeaways from each section of the manuscript.\n\n**Points for improvement:**\n1. My main concern is that the authors' empirical results with DualEquiNet are preliminary. Tables 1-2 are compelling experiments demonstrating the method's expressiveness. However, Tables 3-4 struck me as a bit unrealistic from the perspective of how this method might be applied in a drug discovery setting. To thoroughly demonstrate how DualEquiNet compares to leading e.g., protein representation learning methods, I would highly recommend the authors report the results of their method for standardized protein and RNA representation learning benchmarks such as ProteinWorkshop [1] and rnaglib [2] in their supplementary materials.\n2. In theory, it's great to see the authors' method working well in Tables 2-4, but after considering the authors' ablation studies in Table 5, I'm left with the feeling that DualEquiNet is outperforming the baselines for reasons beyond its key architectural components, as ablating several of them doesn't change the method's average RNA performance much. I'd like the authors to discuss why the components aren't as necessary as readers may initially be led to believe and what other reasons may be leading DualEquiNet to achieve top performance for RNA property prediction (in the ablations).\n3. The authors highlight the importance of E(3) equivariance for 3D biomolecules, but they don't discuss the relationship between E(3) and SE(3) equivariance for modeling molecular chirality. As such, it's currently unclear if the authors' proposed method is truly E(3)-equivariant and therefore can't detect chirality or whether it is actually SE(3)-equivariant and can detect chirality. A discussion of this point would be helpful.\n\n**References:**\n\n[1] Jamasb, A. R., Morehead, A., Joshi, C. K., Zhang, Z., Didi, K., Mathis, S. V., ... & Blundell, T. L. Evaluating Representation Learning on the Protein Structure Universe. In The Twelfth International Conference on Learning Representations.\n\n[2] Wyss, L., Mallet, V., Karroucha, W., Borgwardt, K., & Oliver, C. (2025). A Comprehensive Benchmark for RNA 3D Structure-Function Modeling. arXiv preprint arXiv:2503.21681.\n\nQUESTIONS:\n1. What do the authors think about simpler approaches to modeling 3D biomolecules that have emerged over the last 12 months, such as vanilla Transformer encoders trained with rotation data augmentation (e.g., AlphaFold 3)? Do they think such simpler methods may hold some promise in future work as generic biomolecular representation learners, or do the authors think there are fundamental limitations to such (generic) approaches that methods such as DualEquiNet address?\n\nLIMITATIONS:\nThe authors haven't thoroughly discussed the computational complexity (time and memory) of their proposed method, so it's currently unclear how scalable it truly is.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-25"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis submission presents DualEquiNet, a graph neural network (GNN) for the simulation of macromolecules such as RNA and proteins.   This submission proposes a dual-space representation method that concurrently functions in both Euclidean space (for local atomic interactions) and Spherical Harmonics space (for global structural relationships).  The authors suggest bidirectional cross-space message transfer between these complementary representations and a Cross-Space Interaction Pooling (CSIP) method that facilitates hierarchical aggregation from atoms to residues.  These improvements enable DualEquiNet to proficiently capture both intricate atomic details and extensive connections essential for biomolecular modeling.  The authors assess their methodology across several RNA and protein property prediction tasks, using two newly established 3D structural benchmarks (SASA and torsion angle prediction), demonstrating consistent improvements over current geometric GNN baselines.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n\n1. The submission shows a cool way to make complementary representations in both Euclidean and Spherical Harmonics spaces. This fixes a problem with the current GNNs that use geometry. With two spaces, this design lets the model see both atomic interactions in a small area and structural patterns in a large area at the same time.\n2. The Cross-Space Interaction Pooling mechanism that was suggested is a great way to combine features at the atomic level into representations, without losing the natural hierarchical structure of biomolecules.\n3. Extensive experiments are conducted to verify the effectiveness of the proposed DualEquiNet. The authors also perform ablation studies to provide further insight into the method designed.\n\n**Weaknesses:**\n\n1. The submission states that the model works well, but it doesn't go into much detail about how hard it is to compute in the main text, instead putting it in the appendix. There needs to be more upfront discussion about the resources it needs compared to baselines, especially for the \"large biomolecules\" it targets.\n\n2. The main point of this submission is that it can better model long-range dependencies. But most of the experimental comparisons are only between other equivariant GNNs. To support the claims about long-range modeling, it would be more convincing to compare it to models that are made for long-range tasks and also use a dual-space representation [1,2,3]. This kind of comparison would help separate the performance gains, provide stronger evidence of the effectiveness of the proposed method.\n\n3. The proposed architecture adds several new modules (dual-neighborhood construction, bidirectional cross-space attention, CSIP projections) and new hyperparameters without clear instructions on how to set them. Without design heuristics or simpler versions, it is hard for practitioners to adapt, tune, or extend the method to new datasets. This could make it harder to reproduce and use it more widely.\n\nReferences:\n\n[1] UniIF: Unified Molecule Inverse Folding. In NeurIPS, 2024.\n\n[2] Neural atoms: Propagating long-range interaction in molecular graphs through efficient communication channel. In ICLR, 2024.\n\n[3] Ewald-based Long-Range Message Passing for Molecular Graphs. In ICML, 2023.\n\nQUESTIONS:\n1. How would DualEquiNet work with more complex biomolecular systems, like protein-RNA interactions? \n\n2. The SH-space neighborhood is implemented by a threshold $d_{SH}$ and the cosine similarity between points. Could you provide some insights on how to implement an adaptive threshold mechanism to prevent tuning hyperparameters?\n\n3. Could you provide empirical results or discussion with models specifically designed for long-range tasks, such as [1,2,3], as they also share a similar design idea?\n\nReferences:\n\n[1] UniIF: Unified Molecule Inverse Folding. In NeurIPS, 2024.\n\n[2] Neural atoms: Propagating long-range interaction in molecular graphs through efficient communication channel. In ICLR, 2024.\n\n[3] Ewald-based Long-Range Message Passing for Molecular Graphs. In ICML, 2023.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nDualEquiNet integrates both euclidean and spherical harmonic features into a message passing network and proposes a novel pooling mechanism to integrate the euclidean and spherical harmonic spaces.\n\nSTRENGTHS AND WEAKNESSES:\nSTRENGTHS \n\nThe paper is well structured and easy to follow. They clearly explain how they define the euclidean and spherical harmonic neighborhoods, the node feature and coordinate updates which utilize both euclidean and spherical harmonic features, and the novel (CISP) cross space interaction pooling mechanism which mixes the euclidean and spherical spaces through projection functions. They run experiments on a synthetic dataset N-chain task, an RNA property prediction task on three real datasets, and a surface area prediction task where they show significant improvements to many current baselines. They also demonstrate similar performance to GotenNet on an angle prediction task.   \n\nWEAKNESSES\n\nThe paper runs an ablation study on the RNA property datasets and report the performance of the model when removing various components. A current outstanding flaw is that \\textit{it is not clear where the substantial improvements against current baselines are coming from}. For context, the proposed DualEquiNet achieves $0.353 \\pm 0.006$, $0.558 \\pm 0.123$, $0.636 \\pm 0.049$ on the COVID, Ribonanza, Tc-Ribo datasets respectively, whereas the single space Euclidean model achieves $0.362 \\pm 0.010$, $0.592 \\pm 0.028$, and $0.699 \\pm 0.010$. By integrating both euclidean and spherical harmonic features there is a mean performance improvement of $\\Delta_1 = -0.009$, $\\Delta_2 = -0.034$, $\\Delta_3 = -0.063$; normalizing by the DualEquiNet standard deviations on the datasets we get $\\frac{-0.009}{0.006}=-1.5\\sigma$, $\\frac{-0.034}{0.123}=-0.27\\sigma$, $\\frac{-0.063}{0.049}=-1.28\\sigma$ which shows some improvement to the fully euclidean model. (These numbers are calculated with 5 seeds—it would be great if the authors could post ablation results with more runs if computationally feasible.) \n\nHowever, to put these numbers in context, the fully euclidean model outperforms all the current reported baselines by a much larger delta (with the exception of TC-ribo; but even GotenNet performs worse than the fully euclidean model on TC-ribo). The fully euclidean model gets $0.362 \\pm 0.010$, $0.592 \\pm 0.028$, and $0.699 \\pm 0.010$ whereas the next best benchmarked baseline gets $0.475 \\pm 0.009$ (GotenNet), $0.839 \\pm 0.020$ (FastEGNN), $0.694 \\pm 0.008$ (TFN), which lead to deltas of $\\Delta_1 = -0.113$, $\\Delta_2 = -0.247$, $\\Delta_3 = 0.005$. It is unclear why the fully euclidean model would outperform the other baselines to this extent and without further clarification it suggests that the lion's share of the improvement of the model is due to factors beyond the integration of spherical harmonic features and euclidean features. \n\nWhile it is not explicit what the fully euclidean model entails (it would be helpful if the authors could clarify this), looking at the various sections we assume that it means that we have a messaging passing framework where \n\n • The neighborhoods are defined by a threshold $N_{(i)} = \\{j | ||x_i - x_j|| \\leq d_{EU} \\}$\n\n • The message has the typical definition $m_{ij} = \\phi([h_i, h_j, ||x_i - x_j ||])$ \n\n • The update calculation uses a network which aggregates the calculation of K heads, where each head has a different message \nfunction and moreover utilizes attention to weight the messages $$\\Delta h_{EU} = \\frac{1}{K} \\sum_{k=1}^{K} \\phi_{upd} ([h_i, \\Sigma_{j \\in N(i)} \\alpha^k_{ij} \\phi^k_{h}(m_{ij})])$$ and similarly for the coordinate update $$\\Delta x_{EU} = \\frac{1}{K} \\sum_{k=1}^{K} \\sum_{j \\in N(i)} \\alpha^k_{ij} \\phi_{x}(m_{ij}) x_{ij}])$$\n\nFrom traditional message passing networks, it seems like the major differences is that attention is additionally calculated to weight the various messages and moreover that there are K many heads which each define a message network. \n\nGiven this, we do not see a clear reason why this version of the euclidean only message passing network would lead to a substantial performance improvement to current baselines (ex: a simple graph network like EGNN) beyond the additional attention calculation and the K-many heads.   \n(Thus, it would help if the authors could report the size of the different models—ablated versions and baselines—to see if there is a fair comparison in terms of model size. It also would be helpful to have the ablation experiments run for the SASA and torsion angle prediction to see if there is a similar behavior going on.)\n\nWithout further clarification, it is difficult to measure how much the integration of spherical harmonic features with euclidean features is adding to the existing body of work. Currently, the recommendation stands at 3—borderline reject—but this rating can and will change if the authors provide evidence that their integration of euclidean and spherical harmonic features leads to substantive improvement to existing work.\n\nQUESTIONS:\n1. Could you explicitly define the architecture and design choices of the “fully euclidean” model used in your ablations? Specifically, does it include multi-head attention and the same network depth/width as DualEquiNet? Additionally, how do its parameter count and training hyperparameters compare to the other baseline models such as EGNN, TFN, and GotenNet?\n\n2. Given that the fully euclidean variant already significantly outperforms established baselines, could you disentangle the performance gains attributable solely to the spherical harmonic integration? For example, can you provide ablations across tasks (especially SASA and torsion angle prediction) that isolate the effect of the cross-space interaction pooling (CISP) and the spherical message passing components?\n\n3. Have you run the ablations with a larger number of seeds to confirm the statistical significance of these improvements? If so, could you provide those results, including confidence intervals or standard errors, across all relevant tasks?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-01"}