Title: Geometric Algebra-Enhanced Bayesian Flow Network for RNA Inverse Design
Venue: NeurIPS 2025
Accepted: yes
Keywords: Geometric algebra

Bayesian flow network

RNA inverse design
Abstract: With the development of biotechnology, RNA therapies have shown great potential. 
However, different from proteins, the sequences corresponding to a single RNA three-dimensional structure are more abundant. Most of the existing RNA design methods merely take into account the secondary structure of RNA, or are only capable of generating a limited number of candidate sequences. 
To address these limitations, we propose a geometric-algebra-enhanced $\textbf{B}$ayesian $\textbf{F}$low $\textbf{N}$etwork for the inverse design of $\textbf{R}$NA, called $\textbf{RBFN}$. RBFN uses a Bayesian Flow Network to model the distribution of nucleotide sequences in RNA, enabling the generation of more reasonable RNA sequences. Meanwhile, considering the more flexible characteristics of RNA conformations, we utilize geometric algebra to enhance the modeling ability of the RNA three-dimensional structure, facilitating a better understanding of RNA structural properties. 
In addition, due to the scarcity of RNA structures and the limitation that there are only four types of nucleic acids, we propose a new time-step distribution sampling to address the scarcity of RNA structure data and the relatively small number of nucleic acid types. Evaluation on the single-state fixed-backbone re-design benchmark and multi-state fixed-backbone benchmark indicates that RBFN can outperform existing RNA design methods in various RNA design tasks, enabling effective RNA sequence design.


Peer reviews:
comments: SUMMARY:
This paper utilized geometric algebra to represent the 3D structure of RNA. Then they proposed a Geometric Algebra-Enhanced Bayesian Flow Network (RBFN) for RNA inverse design. RBFN improves RNA sequence generation by combining geometric algebra for better 3D structure modeling with a Bayesian Flow Network to sample sequences that correspond to a given RNA 3D backbone. The method outperforms existing RNA design tools in benchmarks, showing improvements in sequence recovery and structural consistency.

STRENGTHS AND WEAKNESSES:
Strengths:
- Originality: Combining geometric algebra with Bayesian Flow Networks for RNA design is novel.
- Significance: It has potential applications in RNA-based therapies and synthetic biology.
- Experimental Validation: The method shows superior performance in benchmark tests. The structure evaluation is very good, which may be ignored by previous works.
- Clarity: The paper is well-structured and clear for a technical audience.

Weaknesses:
- Complexity: The technical concepts, particularly geometric algebra and Bayesian Flow Networks, may be challenging for some readers.
- Data Scarcity: The method depends on the availability of high-quality RNA structural data.
- Limited Wet-Lab Validation: There’s no real-world experimental validation of the method.

QUESTIONS:
- Does the method work for more dynamic RNA structures?
- What are the computational costs for large-scale RNA design tasks?

LIMITATIONS:
- Computational Cost: The method could be computationally expensive for large RNA molecules.
- Data Quality Dependence: The method relies on accurate 3D RNA structural data, which may not always be available.
- Lack of Wet-Lab Testing: Without experimental validation, the real-world applicability is uncertain.
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-06-20

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces RBFN, a novel generative model for the RNA inverse design problem, which aims to generate valid nucleic acid sequences for a given 3D RNA structure. It combines a geometric-algebra-enhanced graph neural network with a Bayesian flow network (BFN) and addresses two key challenges: the \"one-to-many\" nature of the problem and the conformational flexibility of RNA. The work provides clear theories and promising experimental results.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. The paper introduces geometric algebra to encode RNA 3D backbone geometry, yielding richer structural representations than traditional coordinate or hand-crafted features.\n\n2.  The work has effective ablation studies, removing either the geometric algebra module or the custom sampling schedule degrades performance markedly. The reports with mean and standard deviations add confidence that gains aren’t due to random chance.\n\n3.  The results show gains in diversity metrics (UCR/USR). They support the major hypothesis that a generative flow-based model is better suited for exploring the vast sequence space of RNA.\n\nWeaknesses: \n\nThe paper should explain the motivation for using geometric algebra and a Bayesian Flow Network. It currently does not describe in detail the limitations of the existing RNA modeling methods used as baselines, which components those approaches lack, and why geometric algebra together with a Bayesian Flow Network can address these gaps.\n\nQUESTIONS:\n1. What is the metric used in Table 1?\n\n2. In Table 2, does AR refer to autoregression? The RBFN is only compared with the baseline gRNAde with AR. Are there additional comparisons with other models for this task, such as diffusion models or VAEs? Why not compare RBFN with the methods from Table 1?\n\n3. Is there any demonstration that the geometric algebra module provides geometric inductive bias? Why do the multiple vectors 0/1/2/3-... improve expressivity? Or the performance gain may come from the increasing parameters.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-22"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces a novel model for RNA inverse design, i.e. the generation of RNA sequences given one (or several) 3D backbone structures. The model is based on the generative framework of Bayesian Flow networks, which allow to learn the distribution of discrete RNA sequences. The network architecture uses layers from recent graph neural networks based on Clifford algebra to enhance the geometric expressiveness of the model.  The paper further employs a new distribution for the sampling of time-steps which emphasizes times near t=0. The model achieves competitive result on various metrics in single- and multi-state RNA design benchmarks.\n\nSTRENGTHS AND WEAKNESSES:\n- Strengths:\n    - The paper has a clear target in improving RNA inverse design and overcoming common problems in this task like the existence of several conformers and target sequences for a given 3D structures. The proposed methods are sensible and are proven to be helpful in the ablation studies.\n    - The paper does provide errors obtained from runs with three different random seed for most conducted experiments\n- Weaknesses:\n    - It is very hard to follow the formal presentation of methods in the paper. The main problem here is that a large number of symbols and expressions are not properly defined anywhere which makes the framework only understandable with prior knowledge in both Geometric algebra and Bayesian flow networks. Below is an incomplete list of examples:\n        - There is no clear notation for scalars, vectors and higher grade elements of Clifford algebra. Sometimes vectors are written in bold sometimes not. Sometimes they are written with an arrow on top sometimes they are not.\n        - On page 3 , G is introduced as the 3D backbone structure, but the components of the tuple are not defined until section 3.1 and they also do not reference the backbone coordinates in the previous sentence.\n        - The notation for a Clifford algebra G_{p,q,r} and the parameters p,q,r are mentioned but never properly defined\n        - In the first paragraph of page 5 the index k is reused multiple times and sometimes wrongly instead of the correct index n (for the number of graphs). Other indices like f and f’ are never defined\n        - In line 165 the initialization of geometric algebra features is unclear, the symbol q was also never defined before\n        - …\n    - It is never explicitly stated which Clifford algebra is used within the model. I assume its the Euclidean geometric algebra since this is what the reference architecture uses. In this case the interpretation of elements as points, lines, planes and solid structures is wrong. Points, lines and planes would be appropriate interpretations for projective geometric algebra, whereas the geometric interpretation of Elements of the Euclidean geometric algebra corresponds to scalars, vectors, directed area elements (pseudovectors) and directed volume elements (pseudoscalars). A discussion for why this algebra was chosen over other geometric algebras which have also found use in recent deep learning architectures is missing\n    - Overall the results of RBFN are only marginally better than the baselines. Given that inference time is probably higher due to the iterative procedure, the use cases for the model are limited.\n    - There is the related work [1] which is not cited, but seems to achieve similar results on the single-state benchmark dataset\n\n[1] Manzourolajdad, A., & Mohebbi, M. (2025). Secondary-Structure-Informed RNA Inverse Design via Relational Graph Neural Networks. Non-coding RNA, 11(2), 18.\n\nQUESTIONS:\n- I think it would be good to include a plot of the beta distribution used for the time-step distribution for better intuition on the shape of the distribution\n- On page 4 it is indicated that for the neighborhood of a node the 32 nearest neighbors are used. I wonder why a fixed number of neighbors was chosen instead of defining a cutoff radius?\n- How long does inference take for models with different numbers of steps and compared to the baseline models (in particular gRNAde)\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "CLARITY": 1, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-25"}

comments: SUMMARY:
This paper presents RBFN, a geometric-algebra-enhanced Bayesian flow network for inverse RNA design. RBFN incorporates geometric algebra to better capture 3D structural properties, generating representation for edges, planes, and higher-order substructures. In addition, to address limited RNA data and the small nucleotide alphabet, they introduce a new time-step distribution sampling strategy. The authors evaluate RBFN on RNA inverse folding benchmarks and show better performance than existing state-of-the-art models, including gRNAde.

STRENGTHS AND WEAKNESSES:
Strength:
1. The idea of incorporating geometric algebra for RNA inverse folding is interesting and novel. It can generate representation not only at node-level, but also for edges, planes, which gives a richer representation of the geometric structure.
2. The results show that RBFN achieves better performance than gRNAde, which is a well-known RNA inverse folding baseline.
3. The paper is written clearly, with intuitive figures

Weakness
1. This paper presented ablation studies to study different modeling choices, but it didn't show why BFN is beneficial. Could the model perform better with a standard diffusion model enhanced with geometric algebra? This part is unclear.
2. Comparison with additional RNA inverse folding baselines are needed, such as RiboDiffusion.

QUESTIONS:
1. Can you incorporate more RNA inverse folding baselines such as RiboDiffusion or RhoDesign? These models are available on Github (e.g., https://github.com/ml4bio/RhoDesign)
2. Can you design an experiment to validate the advantage of BFN? I can see the benefit of geometric algebra enhanced network but it's unclear BFN is the right choice. Wouldn't diffusion, GFlowNet, and other methods work as well?

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-01