Unauthorized distillation turns reasoning traces into a conduit for transferring proprietary models’ reasoning behavior to smaller students. Antidistillation Sampling (ADS) perturbs decoding to preserve task utility for legitimate users while obstructing student imitation. Our token-level Metropolis–Hastings diagnosis reveals that current ADS-style defenses leave the trace’s intrinsic learnability largely intact: most tokens still follow the original teacher, while a few teacher-uncertain positions induce extreme loss and dominate optimization. ADS hides learnable reasoning behind a sparse high-loss tail instead of eliminating it. We therefore reformulate reasoning distillation as offline reinforcement learning from imperfect demonstrations, with credit assignment that reinforces high-quality reasoning behavior while suppressing disruptive segments. Across two teachers, six students, and six datasets, the resulting learner extracts reasoning from current anti-distillation traces, outperforming vanilla maximum-likelihood training and eight supervised fine-tuning baselines by up to 21%. We then turn the same principle into an adaptive defense that directly targets high-value reasoning behaviors, exploiting the perceptual gap between humans and models to preserve readability while disrupting model-visible Unicode sequences. This strategy sharply degrades both classical distillation and the adaptive learner, and scales to protect GPT-5.5 traces. These results suggest that robust anti-distillation should optimize for low intrinsic learnability, not merely high token-level surprise.

Medical question answering fundamentally relies on accurate clinical knowledge. The dominant paradigm, Retrieval-Augmented Generation (RAG), acquires expertise conceptual knowledge from large-scale medical corpus to guide general-purpose large language models (LLMs) in generating trustworthy answers. However, existing retrieval approaches often overlook the patient-specific factual knowledge embedded in Electronic Health Records (EHRs), which limits the contextual relevance of retrieved conceptual knowledge and hinders its effectiveness in vital clinical decision-making. This paper introduces RGAR, a recurrence generation-augmented retrieval framework that synergistically retrieves both factual and conceptual knowledge from dual sources (i.e., EHRs and the corpus), allowing mutual refinement through iterative interaction. Across three factual-aware medical QA benchmarks, RGAR establishes new state-of-the-art performance among medical RAG systems. Notably, RGAR enables the Llama-3.1-8B-Instruct model to surpass the considerably larger GPT-3.5 augmented with traditional RAG. Our findings demonstrate the benefit of explicitly mining patient-specific factual knowledge during retrieval, consistently improving generation quality and clinical relevance.