Phi-4-Mini-Reasoning: Exploring the Limits of Small Reasoning Language
  Models in Math
Authors: name: Haoran Xu, name: Baolin Peng, name: Hany Awadalla, name: Dongdong Chen, name: Yen-Chun Chen, name: Mei Gao, name: Young Jin Kim, name: Yunsheng Li, name: Liliang Ren, name: Yelong Shen, name: Shuohang Wang, name: Weijian Xu, name: Jianfeng Gao, name: Weizhu Chen

Chain-of-Thought (CoT) significantly enhances formal reasoning capabilities
in Large Language Models (LLMs) by training them to explicitly generate
intermediate reasoning steps. While LLMs readily benefit from such techniques,
improving reasoning in Small Language Models (SLMs) remains challenging due to
their limited model capacity. Recent work by Deepseek-R1 demonstrates that
distillation from LLM-generated synthetic data can substantially improve the
reasoning ability of SLM. However, the detailed modeling recipe is not
disclosed. In this work, we present a systematic training recipe for SLMs that
consists of four steps: (1) large-scale mid-training on diverse distilled
long-CoT data, (2) supervised fine-tuning on high-quality long-CoT data, (3)
Rollout DPO leveraging a carefully curated preference dataset, and (4)
Reinforcement Learning (RL) with Verifiable Reward. We apply our method on
Phi-4-Mini, a compact 3.8B-parameter model. The resulting Phi-4-Mini-Reasoning
model exceeds, on math reasoning tasks, much larger reasoning models, e.g.,
outperforming DeepSeek-R1-Distill-Qwen-7B by 3.2 points and
DeepSeek-R1-Distill-Llama-8B by 7.7 points on Math-500. Our results validate
that a carefully designed training recipe, with large-scale high-quality CoT
data, is effective to unlock strong reasoning capabilities even in
resource-constrained small models.