ReAD: Reinforcement-Guided Capability Distillation for Large Language Models

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.

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.

Self-distillation bootstraps large language models (LLMs) by training on their own generations. However, existing methods either rely on external signals to curate self-generated outputs (e.g., correctness filtering, execution feedback, and reward search), which are costly and unavailable for the best-performing frontier models, or skip curation entirely and train on all raw outputs, an approach that is often domain-specific and hard to generalize. Both also share a deeper weakness that self-generated outputs entangle task-relevant capability with others, such as stylistic patterns, formatting artifacts, and model-specific errors, diluting the signal for the specific capability one aims to improve. In this paper, we propose Self-Policy Distillation (SPD), which achieves generalizable, capability selective without any external signal. Specifically, SPD extracts a low-rank capability subspace from the model's own gradients on correctness-defining tokens, projects key-value (KV) activations into this subspace during self-generation, and fine-tunes on the resulting raw outputs with standard next-token prediction loss. Through extensive experiments across code generation, mathematical reasoning, and multiple-choice QA, we show that SPD achieves up to 13% improvement over state-of-the-art self-distillation methods without external signals and up to 16% improvement over pre-trained baselines. Notably, SPD demonstrates superior generalizability, achieving 15% better performance under out-of-domain generalization settings.