Date
Publisher
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.
Study at a glance
- Question: Can a lightweight AI model achieve high performance in Chinese K-12 mathematics reasoning at low cost using reinforcement learning?
- Setting and data: 540,000 Chinese and English math problems from open-source datasets and proprietary Chinese K-12 queries; evaluated on multiple national and competition benchmarks.
- Method: Model training and benchmark evaluation using reinforcement learning post-training.
Why it matters
High-performing reasoning AI models remain too expensive for many low-income students to access, potentially worsening educational inequality. Powerful models also frequently make errors on K-12 math tasks, which can negatively affect student learning.
Key findings
- Confucius3-Math achieved higher accuracy on Chinese K-12 benchmarks than larger models, scoring 96.24% on CK12-MATH and 98.46% on GAOKAO-Bench.
- The 14-billion-parameter model delivered inference throughput up to 15.8 times faster than DeepSeek-R1 and functioned effectively on a single consumer-grade graphics processing unit.
- Entire post-training reinforcement learning required 13,109 graphics processing unit hours and cost approximately $26,000, with inference costing $0.15 per million tokens.
Summary drafted with AI from the full paper and may contain errors. See the full paper for details.
What is the application?
Why use AI?
Study design
