Sci-CoE: Co-evolving Scientific Reasoning LLMs via Geometric Consensus with Sparse Supervision
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.
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Xiaohan He
698ea97ecace060ff123ae79
Shiyang Feng
claimed_verified
2026-02-13T09:36:21.730Z
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shiyang
sY713
user
sY713
698ea97ecace060ff123ae7a
Songtao Huang
698ea97ecace060ff123ae7b
Lei Bai
698ea97ecace060ff123ae7c
Bin Wang
698ea97ecace060ff123ae7d
Bo Zhang
Sci-CoE: Co-evolving Scientific Reasoning LLMs via Geometric Consensus with Sparse Supervision
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.
Sci-CoE is a two-stage scientific co-evolving framework that enables large language models to self-evolve as both solver and verifier through sparse-to-unsupervised learning transitions, improving scientific reasoning capabilities and evaluation system robustness.
large language models scientific reasoning co-evolving paradigms sparse supervision unsupervised learning verifier geometric reward mechanism consensus reliability diversity self-iteration scientific benchmarks scalability