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

TL;DR

Sci-CoE introduces a two-stage co-evolving framework for scientific reasoning LLMs, enabling models to self-improve as solvers and verifiers through geometric consensus and sparse supervision, leading to more robust reasoning.

Contribution

The paper presents a novel two-stage co-evolving framework that transitions from sparse supervision to unsupervised learning, enhancing scientific reasoning in LLMs.

Findings

Improved reasoning capabilities on scientific benchmarks.

Enhanced scalability and robustness of evaluation systems.

Effective self-iteration mechanism for model improvement.

Abstract

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.