From Solver Trajectories to Teaching Trajectories: Cognition-Aligned Reasoning Distillation

Reasoning distillation from powerful teacher models to smaller students faces the Gap Curse: as teachers grow more sophisticated, their complex distributions increasingly diverge from what students can approximate, causing performance degradation. Existing mitigation strategies either filter out challenging examples through data selection or introduce weaker intermediate assistant models, inherently compromising supervision coverage or quality. We propose Teacher Alignment, which directly adapts the teacher toward the student's distribution without discarding data or degrading reasoning quality. However, naive alignment through standard knowledge distillation triggers catastrophic collapse of the teacher's reasoning capabilities. To address this, we reformulate teacher alignment as reinforcement learning and introduce TeacherGRPO, built on Group Relative Policy Optimization with two key innovations: (i) Curriculum Selective Alignment applies dual token- and distribution-level curricula to focus rewards on high-signal reasoning gaps while filtering noise from trivial tokens and uncertain tail distributions, and (ii) Importance-Adaptive Length Regularization selectively penalizes verbose redundancy while preserving pedagogically critical reasoning steps. The aligned teacher then distills knowledge to students via standard pipelines. Extensive experiments show TeacherGRPO significantly outperforms baselines across diverse reasoning benchmarks and distillation methods. Our code is available at https://github.com/LzyFischer/TeacherGRPO.

Distilling reasoning capabilities from Large Reasoning Models (LRMs) into smaller models is typically constrained by the limitations of rejection sampling. Standard methods treat the teacher as a static filter, discarding complex "corner-case" problems where the teacher fails to explore valid solutions independently, thereby creating an artificial "Teacher Ceiling" for the student. In this work, we propose Hindsight Entropy-Assisted Learning (HEAL), an RL-free framework designed to bridge this reasoning gap. Drawing on the educational theory of the Zone of Proximal Development (ZPD), HEAL synergizes three core modules: (1) Guided Entropy-Assisted Repair (GEAR), an active intervention mechanism that detects critical reasoning breakpoints via entropy dynamics and injects targeted hindsight hints to repair broken trajectories; (2) Perplexity-Uncertainty Ratio Estimator (PURE), a ratio-based filtering heuristic that reduces high-anomaly shortcut-like rationales; and (3) Progressive Answer-guided Curriculum Evolution (PACE), a three-stage distillation strategy that organizes training from foundational alignment to hard-case adaptation. Extensive experiments on multiple benchmarks demonstrate that HEAL significantly outperforms traditional SFT distillation and other 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.