Knowledge distillation is a key technique for transferring the capabilities of large language models (LLMs) into smaller, more efficient student models. Existing distillation approaches often overlook two critical factors: the learning order of training data and the capacity mismatch between teacher and student models. This oversight limits distillation performance, as manifested by the counter-intuitive phenomenon where stronger teachers fail to produce better students. In this work, we propose Curriculum Learning-Guided Progressive Distillation (CLPD), a unified framework that explicitly accounts for both factors by aligning data difficulty with teacher strength. CLPD constructs an explicit curriculum by organizing training examples from easy to hard, while simultaneously applying an implicit curriculum over supervision signals by progressively scheduling teachers of increasing capacity. Our framework is modular and can be integrated into standard distillation algorithms with minimal overhead. Empirical results on the reasoning benchmarks demonstrate that CLPD consistently outperforms standard distillation, data ordering alone, and teacher scheduling alone across multiple settings. These findings highlight the importance of jointly considering data ordering and teacher capacity when distilling reasoning abilities into small language models.
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.
Large language models (LLMs) demonstrate remarkable reasoning capabilities in tasks such as algorithmic coding and mathematical problem-solving. Recent methods have improved reasoning through expanded corpus and multistage training combining reinforcement learning and supervised fine-tuning. Although some methods suggest that small but targeted dataset can incentivize reasoning via only distillation, a reasoning scaling laws is still taking shape, increasing computational costs. To address this, we propose a data-efficient distillation framework (DED) that optimizes the Pareto frontier of reasoning distillation. Inspired by the on-policy learning and diverse roll-out strategies of reinforcement learning, the key idea of our approach is threefold: (1) We identify that benchmark scores alone do not determine an effective teacher model. Through comprehensive comparisons of leading reasoning LLMs, we develop a method to select an optimal teacher model. (2) While scaling distillation can enhance reasoning, it often degrades out-of-domain performance. A carefully curated, smaller corpus achieves a balanced trade-off between in-domain and out-of-domain capabilities. (3) Diverse reasoning trajectories encourage the student model to develop robust reasoning skills. We validate our method through evaluations on mathematical reasoning (AIME 2024/2025, MATH-500) and code generation (LiveCodeBench), achieving state-of-the-art results with only 0.8k carefully curated examples, bypassing the need for extensive scaling. Our systematic analysis demonstrates that DED outperforms existing methods by considering factors beyond superficial hardness, token length, or teacher model capability. This work offers a practical and efficient pathway to advanced reasoning while preserving general capabilities.
Large language model (LLM) post-training is essential for improving reasoning, adaptation, and alignment. Existing methods mainly follow two paradigms: reinforcement learning (RL) and on-policy distillation (OPD). However, RL relies on coarse-grained outcome supervision, resulting in difficult credit assignment and limited capability to acquire new knowledge. OPD, meanwhile, unconditionally matches teacher logits through KL divergence, which creates a dilemma: similar teachers provide little new knowledge, while substantially different teachers often yield ineffective guidance, largely restricting OPD to within-family distillation. We propose Distilled Reinforcement Learning (Distilled RL), which integrates teacher supervision into the RL objective to provide fine-grained guidance, selectively transfer new knowledge and avoid unconditional imitation. Distilled RL contains three components: reverse importance sampling with clipping, negative sample reset, and sequence-level geometric normalization. Through a concise and interpretable case study, we demonstrate that Distilled RL can effectively transfer previously unavailable knowledge from a teacher model to a student model. Extensive experiments across both within-family and cross-family distillation settings show that Distilled RL substantially outperforms standard RL and OPD in terms of both pass@1 and pass@k. Our code is available at https://github.com/597358816/Distilled-RL.