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The paper introduces Sci-CoE, a two-stage co-evolutionary framework for scientific reasoning LLMs that addresses fragility issues stemming from unreliable solution evaluation and limited verification diversity. Sci-CoE first uses a small annotated dataset to establish correctness judgment anchors for the Verifier, then employs a geometric reward mechanism considering consensus, reliability, and diversity to drive self-iteration on unlabeled data. Experiments on scientific benchmarks demonstrate that Sci-CoE improves complex reasoning and scalability, leading to more robust evaluation systems.
Forget RLHF, self-play, or chain-of-thought: geometric consensus with sparse supervision unlocks scientific reasoning in LLMs.
Large language models (LLMs) have demonstrated exceptional reasoning capabilities, and co-evolving paradigms have shown promising results in domains such as code and math. However, in scientific reasoning tasks, these models remain fragile due to unreliable solution evaluation and limited diversity in verification strategies. In this work, 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. In the first stage, the model uses a small set of annotated data to establish fundamental correctness judgment anchors for the Verifier. In the second stage, we introduce a geometric reward mechanism that jointly considers consensus, reliability, and diversity, driving large-scale self-iteration on unlabeled data. Experiments on several general scientific benchmarks demonstrate that Sci-CoE enhances complex reasoning capabilities and exhibits strong scalability, facilitating the construction of more robust and diverse evaluation systems. Codes are available at https://github.com/InternScience/Sci-CoE.
