Curriculum-Augmented GFlowNets For mRNA Sequence Generation

Aya Laajil; Abduragim Shtanchaev; Sajan Muhammad; Aya El Mir; Eric Moulines; Tiago Silva; Salem Lahlou

cs.LGOct 4, 2025

Curriculum-Augmented GFlowNets For mRNA Sequence Generation

Authors: Aya Laajil, Abduragim Shtanchaev, Sajan Muhammad, Aya El Mir, Eric Moulines, Tiago Silva, Salem Lahlou

Organizations: Mohamed Bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE

Abstract

We develop an approach for the de novo synthesis of messenger RNA (mRNA) sequences encoding target proteins. This requires optimizing multiple biological objectives over large combinatorial spaces defined by synonymous codon sequences, a setting where Reinforcement Learning (RL) methods suffer from mode collapse and Generative Flow Networks (GFlowNets) face sparse rewards over long horizons. To address these challenges, we propose Curriculum-Augmented GFlowNets (CAGFNs), a multi-objective GFlowNet trained with an adaptive length-based curriculum driven by learning progress. In a nutshell, CAGFNs learn from progressively harder tasks corresponding to longer target proteins. We evaluate CAGFNs on CodonDesignEnv, a novel codon-level environment that preserves protein identity via dynamic action masking. Our experiments show that CAGFNs achieve competitive or stronger Pareto-front coverage and diversity while converging up to 4 times faster than non-curriculum GFlowNets, and maintaining 100% sequence uniqueness compared to RL baselines.

Figures & tables

Figure 1: Codon redundancy in the mRNA design space. Each amino acid in Magainin 2 (23 amino acids) admits multiple synonymous codons; the product of choices across all positions yields $\approx 3.8\times 10^{10}$ distinct mRNA sequences encoding the same protein. Two example sequences are highlighted. All candidates produce the same protein but differ in biological properties such as stability, translation efficiency, and nucleotide composition.

Figure 2: Tree representation of the mRNA sequence design process for the illustrative protein Met–Met–Ile–Asn. Each node corresponds to a codon selection step, and edges represent possible transitions. For this example, Met has 1 codon (AUG), Ile has 3 (AUU, AUC, AUA), and Asn has 2 (AAU, AAC). Terminal states correspond to mRNA sequences encoding this protein, each with unique biological properties. This DAG (tree in this case) forms the basis for the GFlowNet to explore diverse and high-quality sequences. In particular, notice that each target protein induces a distinct DAG.

Panel of Figure 3 — Figure 3: Quality-efficiency frontier. Each point plots the relative training time versus a combined quality score $Q=\tfrac{1}{2}\left(\overline{\mathrm{TopKReward}}+\overline{\mathrm{TopKDiversity}}/41\right)$ , ( $K=50$ ). The diversity term is normalized by 41, which corresponds to the maximum achievable TopK diversity in our setting. Relative training time is reported with respect to SGFN. Averages are taken over all tasks in Table 2 .

Method	Reward ( $\uparrow$ )	Uniqueness (%, $\uparrow$ )	Diversity ( $\uparrow$ )
MOReinforce	0.69 ( $\pm$ 0.05)	1	19
PPO	0.51 ( $\pm$ 0.02)	12	30
CAGFN	0.59 ( $\pm$ 0.066)	100	31

Table 1: CAGFN maintains 100% uniqueness and greater diversity (measured as the average edit distance between the generated sequences) while achieving competitive reward. Metrics are averaged over 100 generated sequences. While MOReinforce achieves the highest scalar reward, it collapses to a single unique sequence (1% uniqueness), making it unsuitable for practical mRNA design where diversity is important.

(25–60 AA)
	TopK Reward ( $\uparrow$ )					TopK Diversity ( $\uparrow$ )					Pareto Performance ( $\uparrow$ )
Model	0	1	2	3	4	0	1	2	3	4	0	1	2	3	4
SGFN	0.58 (±0.01)	0.52 (±0.05)	0.55 (±0.02)	0.64 (±0.02)	0.67 (±0.02)	24 (±3.2)	32 (±3.1)	37 (±3.0)	40 (±3.5)	36 (±3.3)	0.08	0.06	0.09	0.16	0.19
ROGFN	0.58 (±0.02)	0.53 (±0.02)	0.55 (±0.02)	0.67 (±0.02)	0.70 (±0.02)	25 (±3.3)	32 (±3.4)	38 (±3.2)	40 (±3.5)	37 (±3.3)	0.13	0.15	0.17	0.17	0.21
CAGFN	0.61 (±0.06)	0.58 (±0.05)	0.62 (±0.05)	0.69 (±0.06)	0.73 (±0.01)	25 (±3.3)	32 (±3.2)	38 (±3.8)	41 (±3.6)	37 (±4.0)	0.07	0.12	0.21	0.21	0.22
LGFN	0.62 (±0.03)	0.57 (±0.03)	0.61 (±0.02)	0.70 (±0.03)	0.73 (±0.03)	24 (±3.1)	30 (±3.2)	36 (±3.3)	38 (±3.5)	35 (±3.3)	0.05	0.13	0.21	0.21	0.20

Table 2: Comparison of generation quality across models and protein lengths. We report TopK Reward and TopK Diversity (with

K=50

), as well as Pareto Performance, computed over 50 generated sequences per protein. Results are shown for five distinct protein targets (indexed 0–4) within each length range. Standard deviations across runs are reported in parentheses when available. Higher values indicate better performance for all metrics.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Hyperparameter	Value
curriculum_tasks	[25,40], [45,60], [65,80],
	[85,120], [125,180]
n_iterations	100
eval_every	5
train_steps_per_task	200

Appendix

Table 3: Curriculum learning hyperparameters

Hyperparameter	Value
lr_logz	1e-1
lr	5e-3
lr_patience	10
n_samples	100
top_n	50
batch_size	64

Appendix

Table 4: Optimization and sampling hyperparameters

Hyperparameter	Value
lpe (learning-progress estimator)	Online
acp (progress metric)	LP
a2d (action-to-difficulty)	GreedyProp
a2d_eps	0.15
lpe_alpha	0.05
acp_MR_K	25

Appendix

Table 5: Teacher / curriculum selection hyperparameters

Panel of Figure 4 — Figure 4: Conditional vs. unconditional mRNA generation results. Metrics distribution across mRNA sequences for a small target protein ( $\sim$ 35 AA). GC percentage: higher is better, MFE: lower is better, CAI: higher is better.

Panel of Figure 5 — Figure 5: Distribution of reward and objectives for the medium-protein task, contrasting the curriculum-augmented GFlowNet (CAGFN) with a baseline GFlowNet trained without curriculum (ROGFN). Panels show empirical distributions of (a) Reward, (b) CAI, (c) MFE (lower is better), and (d) GC content. CAGFN shifts distributions toward higher reward and CAI, lower MFE, and GC content closer to the desired range.

Panel of Figure 6 — Figure 6: Metrics distribution for the OAZ2 protein

Panel of Figure 7 — Figure 7: Sub-Trajectory Balance (SubTB) loss on 75AA sequences. Unlike TB, SubTB converges smoothly and remains numerically stable.

Panel of Figure 8 — Figure 8: Loss dynamics and curriculum progression. (a) Training loss for Short-Only , Long-Only , Random-Order , and Curriculum-Augmented GFN (ours) . (b) Corresponding progression of protein sequence lengths shown to the model during training.

Panel of Figure 9 — Figure 9: Curriculum learning dynamics. (a) We report the protein length progression of the four GFN variants. The comparison shows how the curriculum adapts the sequence length during training compared to alternative strategies. This curriculum schedule reduces the difficulty gap between tasks and allows the model to build competence over time without compromising simple tasks. (b) Indicates how often tasks of different lengths are sampled during curriculum, it shows the balance between exploration across easy and hard tasks, ensuring that the training process remains stable while covering the full range of sequence lengths. (c) CAGFN Loss. Brief spikes or oscillations may occur around curriculum tasks transitions.

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ProMORNA: An End-to-End Generative Framework for Full-Length mRNA Design

Zixi Shao, Tao Wang, Ye Shen, Tianyi Huang+1

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Multi-Objective Reinforcement Learning Molecular Generation RL for Generative Models

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Designing therapeutic messenger RNA (mRNA) requires generating full-length transcripts that optimally balance intracellular stability and translation efficiency. While generative models have advanced mRNA design, existing approaches rely on region-wise generation, expensive inference-time search, or target-specific model updates. To overcome these limitations, we introduce ProMORNA, a zero-shot, end-to-end generative framework for full-length mRNA design. ProMORNA aligns the design process with modern Large Language Model training pipelines: it utilizes a BART-style architecture pre-trained on over 6 million natural protein-mRNA pairs, followed by a two-stage post-training process comprising cold-start supervised fine-tuning and multi-objective reinforcement learning. By standardizing and aggregating relative advantages at the individual metric level with domain-specific stabilization, our post-training stage directly aligns the generative policy with conflicting biological constraints while avoiding direct scalarization of raw objective scores. In silico evaluations demonstrate that ProMORNA pushes the Pareto frontier of predicted stability and translation efficiency beyond standard baselines and GEMORNA, a leading state-of-the-art method. In three independent in vitro Fluc2P experiments, Candidate 2 achieved a 12-72h reporter-activity AUC 3.33 times that of the conventional Benchmark (Holm-adjusted

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