Large reasoning models exhibit long chain-of-thought reasoning with complex strategies such as backtracking and self-verification. Yet, these capabilities typically require resource-intensive post-training. We investigate whether such behaviors can be elicited in large models without any gradient updates. To this end, we propose a decoding-time approach, ThinkLogit, which utilizes logit arithmetic to transfer these capabilities from a substantially smaller reasoning guider to a large non-reasoning target. We further show that we can boost performance by training the guider to correct the target’s errors using preference optimization over mixed model outputs, a setup we refer to as ThinkLogit-DPO. We evaluate these methods across six reasoning benchmarks spanning math, science, and coding domains using the Qwen2.5-32B guided by R1-Distill-Qwen-1.5B, a model 21x smaller. Our experiments demonstrate that ThinkLogit and ThinkLogit-DPO achieve a relative improvement of 21.5% and 24.2%, respectively, over the target model. Moreover, ThinkLogit remains effective even when the guider and target come from different model families.Crucially, our method requires zero training for the large model and would incur minimal inference overhead when logits are computed in parallel, presenting a practical solution for enabling long reasoning at scale.

Large reasoning models such as DeepSeek-R1 and their distilled variants achieve strong performance on complex reasoning tasks. Yet, distilling these models often demands large-scale data for supervised fine-tuning (SFT), motivating the pursuit of data-efficient training methods. To address this, we propose a skill-centric distillation framework that efficiently transfers reasoning ability to weaker models with two components: (1) Skill-based data selection, which prioritizes examples targeting the student model’s weaker skills, and (2) Skill-aware fine-tuning, which encourages explicit skill decomposition during problem solving. With only 1,000 training examples selected from a 100K teacher-generated corpus, our method surpasses random SFT baselines by +1.6% on Qwen3-4B and +1.4% on Qwen3-8B across five mathematical reasoning benchmarks. Further analysis confirms that these gains concentrate on skills emphasized during training, highlighting the effectiveness of skill-centric training for efficient reasoning distillation.