A Practical Two-Stage Recipe for Mathematical LLMs: Maximizing Accuracy
  with SFT and Efficiency with Reinforcement Learning
Authors: name: Hiroshi Yoshihara, name: Taiki Yamaguchi, name: Yuichi Inoue

Enhancing the mathematical reasoning of Large Language Models (LLMs) is a
pivotal challenge in advancing AI capabilities. While Supervised Fine-Tuning
(SFT) and Reinforcement Learning (RL) are the dominant training paradigms, a
systematic methodology for combining them to maximize both accuracy and
efficiency remains largely unexplored. This paper introduces a practical and
effective training recipe that strategically integrates extended SFT with RL
from online inference (GRPO). We posit that these methods play complementary,
not competing, roles: a prolonged SFT phase first pushes the model's accuracy
to its limits, after which a GRPO phase dramatically improves token efficiency
while preserving this peak performance. Our experiments reveal that extending
SFT for as many as 10 epochs is crucial for performance breakthroughs, and that
the primary role of GRPO in this framework is to optimize solution length. The
efficacy of our recipe is rigorously validated through top-tier performance on
challenging benchmarks, including a high rank among over 2,200 teams in the
strictly leak-free AI Mathematical Olympiad (AIMO). This work provides the
community with a battle-tested blueprint for developing state-of-the-art
mathematical reasoners that are both exceptionally accurate and practically
efficient. To ensure full reproducibility and empower future research, we will
open-source our entire framework, including all code, model checkpoints, and
training configurations at
https://github.com/analokmaus/kaggle-aimo2-fast-math-r1.