CE-RLVR Releases SymCE Dataset: Advancing Counterexample Generation and RL Training in Mathematical Theorem Proving

Summary:The CE-RLVR team has released SymCE, a dataset of 4,707 verified false conjectures in undergraduate algebra and real analysis, paired with executable verifiers that serve as a reward function. SymCE serves as both a dataset and a training environment for large language models (LLMs). The research demonstrates that using sparse reward reinforcement learning (RLVR) can overcome the imitation trap, significantly improving the model's performance in counterexample generation for mathematical theorem

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Core Breakthrough

The CE-RLVR team has introduced SymCE, a novel dataset comprising 4,707 false conjectures in undergraduate algebra and real analysis, each paired with executable verifiers. These verifiers serve as a reward function, guiding the model’s learning process within a reinforcement learning (RL) training environment.

Technical Highlights

1. Integrated Dataset and Training Environment: SymCE is not just a static dataset but also a dynamic training environment where verifiers act as a reward function to steer the model’s learning.
2. Overcoming the Imitation Trap: The research uncovers that models trained solely with supervised fine-tuning (SFT) fall into an 'imitation trap,' significantly degrading their ability to recognize true theorems. However, RLVR with sparse rewards effectively repairs this, boosting the true theorem recognition accuracy from 0 to 0.66.
3. Model Performance: The Qwen3-4B model, after training, outperforms all evaluated 7B open-source math-specialized models and demonstrates strong performance across benchmarks like GSM8K, MATH-500, and MMLU-college-math.
4. Human Evaluation: A human audit of 177 verifier decisions shows a 97.7% accuracy rate.

Industry Impact

The release of SymCE provides new tools and methodologies for the field of mathematical theorem proving and counterexample generation. The innovative RLVR training method offers a promising path for enhancing LLM performance in complex tasks. Furthermore, the openness of SymCE enables researchers and developers to leverage this resource for deeper research and development, driving the application and advancement of AI in mathematics.

Developer Recommendations

• Utilize SymCE for Training: Developers can use the SymCE dataset and verifiers to train models, exploring the application of RLVR methods across different models and tasks.
• Focus on RLVR Methods: It is recommended to pay attention to the potential of RLVR methods in handling complex tasks, especially in scenarios requiring high accuracy and robustness.
• Engage in Community Discussions: Join relevant communities and forums to exchange experiences and share research findings with other researchers and developers.

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Source: ArXiv NLP/LLM (cs.CL) (2026-10-05)

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Tags: #SymCE #RLVR #Math Theorem Proving #LLMs & Foundation Models #Reinforcement Learning