Confucius3-Math demonstrates that high-performance mathematical reasoning capabilities can be achieved in lightweight 14B parameter models at extremely low cost, delivering state-of-the-art performance on Chinese K-12 mathematics benchmarks while running efficiently on consumer-grade GPUs.

Objective: The main goal of this study was to develop a lightweight, high-performance reasoning large language model specifically designed for Chinese K-12 mathematics education that could run efficiently on consumer-grade hardware while achieving state-of-the-art performance. The researchers aimed to create an affordable AI solution that could help democratize access to high-quality mathematical education and reduce educational inequality caused by economic disparities.

Methods: The study employed a comprehensive approach involving several key components:

Data Curation: The researchers collected approximately 540,000 training samples from two main sources: open-source datasets (210,000 samples) including GSM8K, MATH, NuminaMath-1.5, and various reasoning datasets, and proprietary data (330,000 samples) from Chinese K-12 educational contexts covering various problem types.

Base Model Selection: Through extensive exploration of different models (Qwen2.5-14B variants, DeepSeek-R1-Distill-Qwen-14B, and Confucius-o1-14B), they selected DeepSeek-R1-Distill-Qwen-14B based on performance metrics and policy entropy analysis.

Training Pipeline: A three-stage pure reinforcement learning (RL) approach with progressive context window expansion (4K → 8K → 16K tokens), using frameworks like Group Relative Policy Optimization (GRPO) and Dynamic sAmpling Policy Optimization (DAPO) with custom improvements.

Technical Innovations: Three key technical contributions were introduced:

• Targeted Entropy Regularization to control model output entropy and prevent language mixing issues
• Recent Sample Recovery (RSR) to improve data efficiency by reusing legitimate samples from previous batches
• Policy-Specific Hardness Weighting (PSHW) to incorporate relative difficulty into advantage estimation

Key Findings: The study achieved several significant results:

Performance Excellence: Confucius3-Math outperformed much larger models on Chinese K-12 mathematics benchmarks, achieving 96.24% on CK12-MATH (vs. 92.74% for DeepSeek-R1), 98.46% on GAOKAO-Bench Math (vs. 93.27% for DeepSeek-R1), and competitive performance on international benchmarks like MATH500 (98.44%) and AIME competitions.

Cost Effectiveness: The entire training process cost only $26,000 using 13,109 H800 GPU hours, demonstrating remarkable efficiency compared to alternative approaches requiring expensive teacher models for distillation.

Inference Efficiency: The model achieved approximately 15× faster inference speed than DeepSeek-R1 (671B parameters), with throughput reaching 31,994 tokens/second compared to R1's 1,631 tokens/second, while running on significantly fewer resources.

Technical Validation: The three proposed innovations proved highly effective - Targeted Entropy Regularization solved language mixing problems, RSR improved both data efficiency and model quality, and PSHW enhanced learning by incorporating problem difficulty relative to current model capability.

Implications: This research makes several important contributions to AI in education:

Democratization of AI Education: By demonstrating that high-performance reasoning models can be built at low cost and deployed on consumer-grade hardware, the work addresses the digital divide in educational AI access, making quality AI tutoring more accessible to students from lower socioeconomic backgrounds.

Technical Advancement: The study proves that pure reinforcement learning can elicit strong reasoning capabilities in lightweight models, providing an alternative to expensive distillation approaches that require access to powerful teacher models.

Domain-Specific Optimization: The focus on Chinese K-12 mathematics demonstrates how targeted domain optimization can achieve superior performance compared to general-purpose models, suggesting a viable path for building specialized educational AI tools.

Open Source Impact: By releasing the model and technical details, the work enables broader community development of practical reasoning models and educational applications.

Limitations: The study acknowledges several important limitations:

Scope Constraints: The model focuses specifically on Chinese K-12 mathematics, limiting generalizability to other subjects or educational contexts without additional training and adaptation.

Data Dependency: The approach requires access to high-quality, domain-specific training data, which may not be readily available for all educational domains or languages.

Infrastructure Requirements: While more efficient than alternatives, the training process still requires significant computational resources (H800 GPUs) that may not be accessible to all research groups.

Evaluation Coverage: The study primarily evaluates mathematical reasoning and may not capture other important educational aspects like pedagogical effectiveness, student engagement, or long-term learning outcomes.

Future Directions: The researchers outline several promising areas for continued development:

Expanded Subject Coverage: Extending the approach to other K-12 subjects beyond mathematics, including language learning, science, and social studies.

Enhanced Educational Features: Incorporating additional capabilities such as homework correction, personalized learning adaptation, academic evaluation, and comprehensive student progress tracking.

Technical Improvements: Further exploration of reinforcement learning techniques, including principled approaches to entropy regulation using frameworks like Bayesian multi-armed bandits.

Longitudinal Studies: Conducting real-world deployment studies to evaluate the model's actual impact on student learning outcomes and educational effectiveness.

Cross-Cultural Adaptation: Investigating how the approach can be adapted to different educational systems, curricula, and cultural contexts beyond the Chinese K-12 system.

Title and Authors: "Confucius3-Math: A Lightweight High-Performance Reasoning LLM for Chinese K-12 Mathematics Learning" by Lixin Wu, Na Cai, Qiao Cheng, Jiachen Wang, and Yitao Duan.

Published on: June 25, 2025

Published by: arXiv preprint arXiv:2506.18330v2 [cs.LG]

This work represents a significant advancement in making high-quality AI educational tools more accessible and demonstrates the potential for domain-specific optimization to achieve remarkable performance improvements at substantially reduced costs.