Probing to Refine: Reinforcement Distillation of LLMs via Explanatory Inversion

Knowledge distillation from large language models (LLMs) assumes that the teacher's output distribution is a high-quality training signal. On reasoning tasks, this assumption is frequently violated. A model's intermediate representations may encode the correct answer, yet this information is lost or distorted through the vocabulary projection, where prompt formatting and answer-token choices creates brittle, noisy outputs. We introduce \method{}, a distillation framework that bypasses this bottleneck by training lightweight probes on frozen teacher hidden states and using the probe's predictions, rather than output logits, as supervision for student training. This simple change yields consistent improvements across four reasoning benchmarks (AQuA-RAT, ARC Easy/Challenge, and MMLU), with gains most pronounced under limited data. Probes trained on intermediate representations provide cleaner labels than the teacher's own outputs, effectively denoising the distillation signal. \method{} requires no architectural changes to student or teacher, is architecture-agnostic, and adds minimal compute since probe training is cheap and teacher representations can be cached. By exploiting internal representations, \method{} enables practitioners to extract more value from large teacher models without additional training data or architectural complexity.

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.

When distilling reasoning from large language models (LLMs) into smaller ones, teacher rationales for similar problems often vary wildly in structure and strategy. Like a chef who makes the same dish differently each time, this inconsistency burdens the student with noisy supervision that is hard to internalize. We propose Distillation through Reasoning Path Compression (D-RPC), which constrains the teacher to follow a compact, dynamically maintained bank of reusable high-level reasoning paths. For each training question, D-RPC retrieves the most relevant path and conditions the teacher to follow it, producing rationales that are consistent across similar problems yet diverse enough to cover different problem types. A PAC-Bayes analysis formalizes the resulting trade-off between bank size and coverage: smaller banks reduce supervision entropy but risk coverage gaps, and the generalization bound identifies an optimal intermediate size confirmed by our ablations. Across five math and commonsense reasoning benchmarks with two student models, D-RPC consistently outperforms chain-of-thought distillation, freeform rationale generation, direct distillation, and structured-supervision baselines, while using fewer tokens than template-heavy alternatives.