Revisiting the Capacity Gap in Chain-of-Thought Distillation from a Practical Perspective

Chain-of-Thought (CoT) distillation transfers multi-step reasoning from large reasoning models to smaller students, but verbose teacher traces inflate both training and inference cost. Existing CoT compression methods fall into two families, selective pruning and generative rewriting, yet prior studies have left key factors entangled: granularity is confounded with importance criteria in pruning, restructuring level is rarely isolated in rewriting, and compression budgets are not systematically evaluated across domains or regimes. We recast CoT compression along three dimensions: importance criterion, restructuring level, and compression budget. Sweeping these across two model families, Math and General domains, and Long-/Short-CoT regimes, we find that (i) importance criterion utility is strictly governed by granularity: step-level criteria converge on a shared reasoning backbone, while token-level pruning requires symbol-aware signals to preserve the logical core; (ii) restructuring level inverts across domains: Math degrades monotonically with structural disruption, while aggressive rewriting acts as a denoiser on General tasks; (iii) training-time compression does not necessarily translate to inference-time savings: Long-CoT students retain verbose habits despite concise supervision, making the training ratio an optimistic lower bound on deployment cost. These findings yield condition-aware guidelines for matching compression to deployment context.

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.

Chain-of-Thought (CoT) reasoning has significantly improved LLMs' mathematical problem-solving capabilities, but distilling such capabilities into smaller models remains challenging due to the capacity mismatch between verbose teachers and compact students. Directly copying teachers' lengthy reasoning chains causes capacity overload, resulting in truncated outputs or repetitive failure. Existing remedies each sacrifice a critical property of CoT: implicit reasoning methods (e.g., compressing reasoning into hidden states) trade away interpretability and verifiability, while heuristic compression strategies (e.g., random step pruning) destroy logical integrity. To address this, we propose BRIDGE, a curriculum framework that first establishes structural understanding via masked reconstruction, then uses GRPO-based reinforcement learning to guide students in self-discovering the optimal balance between accuracy and brevity, and finally internalizes complex reasoning through teacher-guided rewriting on failure cases. On GSM8K, BRIDGE enables Qwen2.5-3B to achieve 11.29% accuracy improvement and 27.4% token reduction over the original model, outperforming instruction-tuned variants and distillation baselines. Zero-shot transfer experiments on SVAMP and MATH-500 further confirm the generalization of internalized reasoning. Our code and model checkpoints are publicly available at https://github.com/Applied-Machine-Learning-Lab/SDM2026_BRIDGE and https://huggingface.co/bowen0815/BRIDGE.