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

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.