Sci-CoE: Co-evolving Scientific Reasoning LLMs via Geometric Consensus with Sparse Supervision

🌟 Introduction

We tackle a key challenge in RL for LLMs: 🧩 how to train models when there is no explicit final answer and no reliable outcome reward, such as unit tests or exact matching. This is common in 🔬 scientific reasoning and 📐 mathematical proofs, where solutions are non-unique and expressed in natural language. In these settings, traditional reward signals ❌ fail, making standard RL ineffective.

To address this challenge, we propose Sci-CoE, a two-stage scientific co-evolving framework that enables models to self-evolve as both 🧠 solver and 🔍 verifier through a transition from sparse supervision to unsupervised learning.

• Stage 1: Using a small set of annotated data 🏷️, the model establishes fundamental correctness judgment anchors for the Verifier.
• Stage 2: We introduce a geometric reward mechanism 📐 that jointly models ✅ consensus, 🔒 reliability, and 🌱 diversity, enabling stable and scalable self-iteration on unlabeled data without relying on explicit ground-truth answers.

Sci-CoE thus transforms the absence of outcome rewards into a structured self-evolving learning signal. 🚀

🔧 Training

To start training, simply set the configurations in ./optimization/optimization_config.py, run the following command.

python run.py

🧪 Evaluation

The accuracy of generated solutions, verification strategies, and Best-of-N (BoN) performance during the training process can be evaluated using the following script:

cd evaluation
python eval.py

You can modify the model path and evaluation configurations in ./evaluation/evaluation_config.py.

📊 Benchmarks and Results

For final benchmark evaluation, we use the official evaluation scripts provided by each dataset. The evaluation scripts for MMLU-Pro, GPQA-Diamond and UGPhysics are provided in ./benchmarks.

The results of Sci-CoE on the above three benchmarks are as follows:

Model	MMLU-Pro	Bio.	Bus.	Che.	C.S.	Eco.	Eng.	Hea.	His.	Law	Math	Phi.	Phy.	Psy.	Oth.
Qwen2.5-7B-Instruct
Base Model	57.39	72.11	64.89	57.16	60.49	68.84	39.94	56.85	48.29	32.52	71.87	49.90	58.35	65.91	54.33
Sci-CoE-Stage 1	57.68	74.34	67.17	56.89	60.73	68.72	40.04	56.60	47.77	33.33	72.09	48.50	59.05	65.54	53.90
Sci-CoE-Stage 2-18k	58.05	73.50	68.69	57.16	61.22	68.01	40.04	58.07	49.08	32.61	72.54	50.50	58.97	66.67	54.65
Sci-CoE-Stage 2-30k	58.51	73.92	68.19	55.39	61.71	70.62	42.31	58.19	48.82	34.06	72.76	50.50	59.35	67.17	54.87
Qwen3-8B
Base Model	63.19	78.80	69.71	68.02	66.10	72.27	53.04	62.47	51.97	31.52	78.53	51.50	67.67	69.30	55.95
Sci-CoE-Stage 1	63.27	78.94	69.20	66.78	65.85	72.63	53.77	63.08	50.92	32.61	78.09	52.51	68.44	69.42	55.41
Sci-CoE-Stage 2-18k	63.56	79.22	70.85	68.02	66.34	72.87	53.35	62.71	51.44	32.52	79.42	52.91	67.74	69.17	55.19
Sci-CoE-Stage 2-30k	64.34	80.20	70.72	68.20	68.05	73.93	54.59	63.33	54.07	33.42	79.79	53.51	68.36	70.30	56.06

Model	Data Scale	UGPhysics	Mec. and Ther.	Elec.	Modern Physics
Qwen2.5-7B-Instruct
Base Model	--	20.67	18.88	18.52	23.34
Sci-CoE-Stage 1	4k	21.07	20.14	19.81	22.51
Sci-CoE-Stage 2	18k	21.92	20.92	21.31	23.17
Sci-CoE-Stage 2	30k	22.64	21.84	23.13	24.91
Qwen3-8B
Base Model	--	31.76	30.73	29.98	33.51
Sci-CoE-Stage 1	4k	32.03	30.25	30.62	34.38
Sci-CoE-Stage 2	18k	32.46	30.21	33.30	34.38
Sci-CoE-Stage 2	30k	33.10	30.51	34.80	34.99

Model	Data Scale	GPQA-Diamond	Physics	Chemistry	Biology
Qwen2.5-7B-Instruct
Base Model	--	30.81	33.73	24.73	47.37
Sci-CoE-Stage 1	4k	31.31	34.88	24.73	47.37
Sci-CoE-Stage 2	18k	33.33	41.86	23.66	42.11
Sci-CoE-Stage 2	30k	35.35	41.86	26.88	47.37
Qwen3-8B
Base Model	--	36.87	39.53	33.33	42.11
Sci-CoE-Stage 1	4k	37.88	45.35	29.03	47.37
Sci-CoE-Stage 2	18k	38.89	41.86	33.33	52.63
Sci-CoE-Stage 2	30k	40.91	43.02	35.48	57.89

🤝 Citation

@misc{he2026scicoecoevolvingscientificreasoning,
      title={Sci-CoE: Co-evolving Scientific Reasoning LLMs via Geometric Consensus with Sparse Supervision}, 
      author={Xiaohan He and Shiyang Feng and Songtao Huang and Lei Bai and Bin Wang and Bo Zhang},
      year={2026},
      eprint={2602.12164},
      archivePrefix={arXiv},
      primaryClass={cs.AI},
      url={https://arxiv.org/abs/2602.12164}, 
}

🤝 Acknowledgement

We sincerely thank the CURE for laying the foundation in Co-evolving mechanism. Sci-CoE is developed on top of the CURE framework, inheriting its training pipeline while adapting it to scientific reasoning settings.