Learning What to Learn: Stage-Specific Data Sets for SFT-then-RL in Small Language Model Reasoning
Authors: Chongyang He, Rui Zhang, Zixuan Wang, Xin Li
Organizations: 1Tsinghua University · 2National University of Singapore · 3DiDi · University of Electronic Science and Technology of China
Abstract
Post-training Small Language Models (SLMs) for reasoning typically follows an SFT-then-RL pipeline, yet existing work rarely considers what data should be learned at each stage. We argue that data strategy should be aligned with the distinct roles of SFT and RL: SFT is better suited for acquiring not-yet-mastered reasoning skills, while RL is better suited for consolidating skills that the model can already partially access. Based on this principle, we propose a difficulty-aware SFT-then-RL framework that organizes training data into stage-specific sets. For hard samples in the SFT stage, we introduce a Bridge mechanism that transforms raw teacher-generated reasoning traces into more learnable supervision for SLMs. For hard samples that remain unsolved during RL, we apply Critique Fine-Tuning by converting all-zero-reward failures into diagnostic, repair, and new reasoning trace supervision for the next SFT stage. Experiments on two SLMs across five reasoning benchmarks show that our method consistently improves over representative SFT, distillation, and RL baselines. Our results highlight the importance of coordinating data difficulty across SFT and RL for effective SLM reasoning post-training.
Supervised fine-tuning (SFT) on a small, high-quality set of long reasoning traces is an effective approach for eliciting strong reasoning capabilities in Large Language Models (LLMs). However, existing methods for curating high-quality SFT data rely heavily on strong reasoning models to filter examples based on diversity and difficulty, making the curation process costly while often yielding suboptimal data quality. In this work, we show that diverse and challenging reasoning examples can be identified using only the initial reasoning tokens. Specifically, we demonstrate that difficult problems can be reliably detected based on the loss of the first 100 reasoning tokens evaluated at a randomly perturbed checkpoint of the pretrained model. We further show that examples exhibiting similar loss patterns over their first 1k reasoning tokens across a small number of perturbed checkpoints extrapolating along the fine-tuning trajectory provably induce similar gradients. We validate our approach through extensive experiments on fine-tuning Qwen2.5-7B and Llama3.1-8B models on the M23K medical reasoning and OpenThoughts-Math datasets. Our method outperforms existing baselines by up to 1.7% while being 91% more token efficient.
Recent advances in large language models (LLMs) have demonstrated that reinforcement fine-tuning of pretrained base models can lead to significant gains in reasoning performance at inference time. In this work, we theoretically analyze why reinforcement fine-tuning induces better reasoning ability than purely supervised fine-tuning (SFT) methods. We model chain-of-thought (CoT) reasoning as a pathfinding problem on graphs and compare the popular method of reinforcement learning with verifiable rewards (RLVR) against traditional SFT. We prove that SFT, when trained on golden shortest paths without negative examples, fails to learn how to efficiently backtrack. In contrast, an RLVR-trained model can learn how to efficiently backtrack from dead ends using only outcome reward. This leads to an exponential separation in inference-time compute between the two methods, and demonstrates that RLVR leads the model to learn the location of difficult decisions in a reasoning chain, ultimately allowing for better allocation of inference-time compute. Finally, we show that the reasoning traces of an RLVR model can be distilled to train a base model to backtrack efficiently as well.
Large language models (LLMs) have achieved remarkable progress, with post-training playing a crucial role in enhancing their reasoning capabilities. Among post-training paradigms, supervised fine-tuning (SFT) is widely used: it leverages external data to provide dense supervision and enables efficient training. However, directly fine-tuning on expert data can hurt generalization when the data distribution is mismatched with the target model's own distribution. In this work, we propose Data Adaptation for Reasoning Tuning (DART), which formulates the use of a fixed, potentially distributionally misaligned SFT dataset as an optimization problem over demonstration transformations. DART trains a mapper model with reinforcement learning to convert original SFT data into model-adapted supervision that better matches the target model's distribution and learning preferences. The transformed data are then used for SFT, allowing the target model to better exploit external supervision. Experiments across multiple models and datasets show that DART improves generalization, achieves higher training efficiency than direct RL, and helps models surpass standard SFT. Our code is available at https://anonymous.4open.science/r/DART525E50D.