Student-in-the-Loop Chain-of-Thought Distillation via Generation-Time Selection

Recent advances in large reasoning models (LRMs) have shown strong performance on complex problems through long chain-of-thought (Long CoT) reasoning. However, distilling such trajectories into smaller student models remains challenging: direct Long CoT supervision often provides limited gains and can be less effective than concise Short CoT rationales. In this work, we investigate this phenomenon from a gradient-centric perspective. Our analysis shows that Long CoT induces larger gradient magnitudes and more concentrated update directions than Short CoT, with this effect becoming more pronounced as student model capacity increases. These findings suggest that effective Long CoT distillation requires balancing the reasoning information density of reasoning trajectories with their distributional alignment to the student model. Motivated by this insight, we propose Model Interporlation Distillation (MI-Distillation), a framework that constructs a continuous Instruct-Reasoning data spectrum through model interpolation. To select suitable trajectories from this spectrum, we further introduce Sequential Learnable Surprisal Score (SeqLSS), which favors reasoning paths that are both informative and learnable for the student. Extensive experiments on reasoning benchmarks show that MI-Distillation consistently improves small model CoT distillation over strong Long CoT baselines.

Knowledge Distillation (KD) can transfer the reasoning abilities of large models to smaller ones, which can reduce the costs to generate Chain-of-Thoughts for reasoning tasks. KD methods typically ask the student to mimic the teacher's distribution over the entire output. However, a student with limited capacity can be overwhelmed by such extensive supervision causing a distribution mismatch, especially in complex reasoning tasks. We propose Token-Selective Dual Knowledge Distillation (TSD-KD), a framework for student-centric distillation. TSD-KD focuses on distilling important tokens for reasoning and encourages the student to explain reasoning in its own words. TSD-KD combines indirect and direct distillation. Indirect distillation uses a weak form of feedback based on preference ranking. The student proposes candidate responses generated on its own; the teacher re-ranks those candidates as indirect feedback without enforcing its entire distribution. Direct distillation uses distribution matching; however, it selectively distills tokens based on the relative confidence between teacher and student. Finally, we add entropy regularization to maintain the student's confidence during distillation. Overall, our method provides the student with targeted and indirect feedback to support its own reasoning process and to facilitate self-improvement. The experiments show the state-of-the-art performance of TSD-KD on 10 challenging reasoning benchmarks, outperforming the baseline and runner-up in accuracy by up to 54.4% and 40.3%, respectively. Notably, a student trained by TSD-KD even outperformed its own teacher model in four cases by up to 20.3%. The source code is available at https://github.com/kmswin1/TSD-KD.

Knowledge distillation from large reasoning models (LRMs) often uses raw teacher trajectories as supervision. However, this practice creates a mismatch between the goal of distillation and the nature of teacher trajectories. Advanced LRMs typically improve their reasoning capabilities through reward-driven post-training, such as RLHF. This training optimizes them as strong solvers, rather than as teachers that produce reasoning processes smaller models can easily learn. Since smaller models have different "cognitive capacities" compared to their larger teachers, directly imitating raw teacher trajectories can sometimes be ineffective and often requires a substantial number of high-quality samples. To bridge this mismatch, we propose Cognition-Aligned Reasoning Distillation (CARD), an RL-based framework that transforms solver trajectories into teaching trajectories aligned with the student's cognition. Avoiding expensive resampling, our framework directly transforms existing trajectories. We optimize CARD with two reward signals: (1) a Distribution Alignment Reward that matches the student's predictive distribution, and (2) a Logical Coherence Reward that reduces misleading failed reasoning steps. Comprehensive evaluations across multiple student models and settings demonstrate that CARD outperforms distillation from raw teacher trajectories in in-domain settings while achieving substantial gains in out-of-distribution performance. Code is available at https://github.com/LiteSSLHub/CARD.