Reflect, Rewrite, Repeat: How Simple Arithmetic Enables Advanced Reasoning in Small Language Models

摘要

Contemporary advancements in language model reasoning typically require computationally intensive reinforcement learning (RL) and massive datasets, creating barriers for resource-constrained teams. In this work, we demonstrate that high-quality, iterative training on minimal data can rival modern RL approaches. We introduce a resource-efficient framework that combines Direct Preference Optimization (DPO) and Supervised Fine-Tuning (SFT) with selective guidance from larger models, iteratively refining solutions through a “reflect, rewrite, repeat” cycle (R^3). Using Qwen 2.5 7B and Qwen 2.5 Math 7B as base models, our method shows meaningful performance improvements across arithmetic, symbolic and cognitive reasoning benchmarks—including GSM8K (83.1% → 88.6%), AIME’25@10 (20.0% → 30.0%) and LastLetterConcat (40.7% → 53.3%) problems. The model-agnostic nature of our R^3 framework is further demonstrated through substantial improvements when applied to Mistral and LLaMA-based models. Remarkably, these gains are achieved using mere 700 basic arithmetic training samples, in stark contrast to the hundreds of thousands of examples typically required by RL-based systems. Our results suggest that reasoning improvements need not strictly depend on large-scale data. By emphasizing strategically curated training grounded in foundational principles, we achieve competitive generalization with minimal resource overhead. Our R^3 pipeline also generates high-quality SFT data with high-fidelity reasoning traces as byproduct, further enabling scalable and annotation-free fine-tuning. Code is available.[https://github.com/aws-samples/sample-for-reflect-rewrite-repeat]