Knowledge distillation often supervises smaller models with raw trajectories from large reasoning models (LRMs), but this creates a gap between the distillation goal and the nature of teacher trajectories. Advanced LRMs improve their reasoning via reward‑driven post‑training such as RLHF, which optimizes them as strong solvers rather than teachers that produce reasoning steps easy for smaller models to absorb. Because students have different cognitive capacities, directly copying raw trajectories can be ineffective and demands many high‑quality examples.
To bridge this gap we introduce Cognition‑Aligned Reasoning Distillation (CARD), an RL‑based framework that directly transforms solver trajectories into teaching trajectories aligned with the student’s cognition, eliminating costly resampling. CARD is optimized with two reward signals: a Distribution Alignment Reward that matches the student’s predictive distribution to the teacher’s target, and a Logical Coherence Reward that suppresses misleading failed reasoning steps.
Extensive experiments across various student models and settings show that CARD outperforms raw‑trajectory distillation on in‑domain tasks and yields substantial gains on out‑of‑distribution data. Code is available at https://github.com/LiteSSLHub/CARD.
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