# Confucius3-Math: A Lightweight High-Performance Reasoning LLM for Chinese K-12 Mathematics Learning

arXiv: https://arxiv.org/abs/2506.18330 · HTML: https://mlsanity.com/paper/2506.18330/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 34 references that are in the map.
- First posted on arXiv 23 Jun 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 25 of 25)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Evaluating the Performance of Large Language Models on GAOKAO Benchmark](https://mlsanity.com/paper/2305.12474/) (2023)
- [Understanding the impact of entropy on policy optimization](https://mlsanity.com/paper/1811.11214/) (2018)
- [Skywork Open Reasoner 1 Technical Report](https://mlsanity.com/paper/2505.22312/) (2025)
- [O1 Replication Journey: A Strategic Progress Report -- Part 1](https://mlsanity.com/paper/2410.18982/) (2024)
- [LIMR: Less is More for RL Scaling](https://mlsanity.com/paper/2502.11886/) (2025)
- [MathBench: Evaluating the Theory and Application Proficiency of LLMs with a Hierarchical Mathematics Benchmark](https://mlsanity.com/paper/2405.12209/) (2024)
- [To Repeat or Not To Repeat: Insights from Scaling LLM under Token-Crisis](https://mlsanity.com/paper/2305.13230/) (2023)
- [Scaling Scaling Laws with Board Games](https://mlsanity.com/paper/2104.03113/) (2021)
- [DUMP: Automated Distribution-Level Curriculum Learning for RL-based LLM Post-training](https://mlsanity.com/paper/2504.09710/) (2025)
- [Safe and Nested Subgame Solving for Imperfect-Information Games](https://mlsanity.com/paper/1705.02955/) (2017)
- [Mitigating the Language Mismatch and Repetition Issues in LLM-based Machine Translation via Model Editing](https://mlsanity.com/paper/2410.07054/) (2024)
- [Revisiting Maximum Entropy Inverse Reinforcement Learning: New Perspectives and Algorithms](https://mlsanity.com/paper/2012.00889/) (2020)
- [Embracing AI in Education: Understanding the Surge in Large Language Model Use by Secondary Students](https://mlsanity.com/paper/2411.18708/) (2024)
- [Shaping AI's Impact on Billions of Lives](https://mlsanity.com/paper/2412.02730/) (2024)

## Built on by (most cited first, 5 of 5)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [UloRL:An Ultra-Long Output Reinforcement Learning Approach for Advancing Large Language Models' Reasoning Abilities](https://mlsanity.com/paper/2507.19766/) (2025)
- [GanitLLM: Difficulty-Aware Bengali Mathematical Reasoning through Curriculum-GRPO](https://mlsanity.com/paper/2601.06767/) (2026)
- [PA3: Policy-Aware Agent Alignment through Chain-of-Thought](https://mlsanity.com/paper/2603.14602/) (2026)
- [OmniEdu: Open Foundation Models for Learning and Teaching](https://mlsanity.com/paper/2609.23088/) (2026)

## Abstract (arXiv)

We introduce Confucius3-Math, an open-source large language model with 14B parameters that (1) runs efficiently on a single consumer-grade GPU; (2) achieves SOTA performances on a range of mathematical reasoning tasks, outperforming many models with significantly larger sizes. In particular, as part of our mission to enhancing education and knowledge dissemination with AI, Confucius3-Math is specifically committed to mathematics learning for Chinese K-12 students and educators. Built via post-training with large-scale reinforcement learning (RL), Confucius3-Math aligns with national curriculum and excels at solving main-stream Chinese K-12 mathematical problems with low cost. In this report we share our development recipe, the challenges we encounter and the techniques we develop to overcome them. In particular, we introduce three technical innovations: Targeted Entropy Regularization, Recent Sample Recovery and Policy-Specific Hardness Weighting. These innovations encompass a new entropy regularization, a novel data scheduling policy, and an improved group-relative advantage estimator. Collectively, they significantly stabilize the RL training, improve data efficiency, and boost performance. Our work demonstrates the feasibility of building strong reasoning models in a particular domain at low cost. We open-source our model and code at https://github.com/netease-youdao/Confucius3-Math.