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

2026-02-12

AI Summary

This work addresses the fragility of large language models in scientific reasoning tasks, which stems from unreliable evaluation and overly simplistic verification strategies. To overcome this limitation, the authors propose a two-stage co-evolutionary framework: first, a base verifier is constructed using a small amount of annotated data; subsequently, on unlabeled data, a geometric reward mechanism drives the joint self-evolution of both solver and verifier. This reward mechanism integrates consensus, reliability, and diversity to enable efficient co-training that transitions smoothly from sparse supervision to fully unsupervised learning. Experimental results demonstrate that the approach significantly enhances complex reasoning performance across multiple scientific reasoning benchmarks, exhibits strong scalability, and establishes a more robust and diverse evaluation paradigm.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Natural Language Processing: (Large) Language Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

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.

Problem

• scientific reasoning
• large language models
• solution evaluation
• verification diversity
• model robustness

Innovation

• co-evolving
• geometric consensus
• sparse supervision
• scientific reasoning
• self-iteration