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

arXiv: https://arxiv.org/abs/2602.12164 · HTML: https://mlsanity.com/paper/2602.12164/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 24 of its 31 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 24 of 24)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [Yi: Open Foundation Models by 01.AI](https://mlsanity.com/paper/2403.04652/) (2024)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [When Does Pretraining Help? Assessing Self-Supervised Learning for Law and the CaseHOLD Dataset](https://mlsanity.com/paper/2104.08671/) (2021)
- [Med-R1: Reinforcement Learning for Generalizable Medical Reasoning in Vision-Language Models](https://mlsanity.com/paper/2503.13939/) (2025)
- [ChemVLM: Exploring the Power of Multimodal Large Language Models in Chemistry Area](https://mlsanity.com/paper/2408.07246/) (2024)
- [MegaScience: Pushing the Frontiers of Post-Training Datasets for Science Reasoning](https://mlsanity.com/paper/2507.16812/) (2025)
- [Co-Evolving LLM Coder and Unit Tester via Reinforcement Learning](https://mlsanity.com/paper/2506.03136/) (2025)
- [SeRL: Self-Play Reinforcement Learning for Large Language Models with Limited Data](https://mlsanity.com/paper/2505.20347/) (2025)
- [UGPhysics: A Comprehensive Benchmark for Undergraduate Physics Reasoning with Large Language Models](https://mlsanity.com/paper/2502.00334/) (2025)
- [BioReason: Incentivizing Multimodal Biological Reasoning within a DNA-LLM Model](https://mlsanity.com/paper/2505.23579/) (2025)
- [A Survey of Scientific Large Language Models: From Data Foundations to Agent Frontiers](https://mlsanity.com/paper/2508.21148/) (2025)
- [Learning to Solve and Verify: A Self-Play Framework for Code and Test Generation](https://mlsanity.com/paper/2502.14948/) (2025)
- [Guided Self-Evolving LLMs with Minimal Human Supervision](https://mlsanity.com/paper/2512.02472/) (2025)
- [ChemMLLM: Chemical Multimodal Large Language Model](https://mlsanity.com/paper/2505.16326/) (2025)
- [MindLLM: A Subject-Agnostic and Versatile Model for fMRI-to-Text Decoding](https://mlsanity.com/paper/2502.15786/) (2025)
- [Loong: Synthesize Long Chain-of-Thoughts at Scale through Verifiers](https://mlsanity.com/paper/2509.03059/) (2025)
- [SciReasoner: Laying the Scientific Reasoning Ground Across Disciplines](https://mlsanity.com/paper/2509.21320/) (2025)

## Abstract (arXiv)

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.