Audit Before You Distill: A Controlled Workflow for Reasoning Transfer into Compact Medical Language Models

Chain-of-thought (CoT) distillation trains a smaller model to imitate a teacher's reasoning trace, but it is typically evaluated by final-answer metrics including accuracy. We ask whether gains in answer quality are accompanied by improvements in the trace. In medical QA, where short answer options can leave a richer clinical justification under-specified, a Qwen3-8B student distilled from a DeepSeek-V3-family teacher improves on MedQA-USMLE answer metrics (SC@64 74.7% to 84.4%; expected calibration error (ECE) 0.096 to 0.034). Yet under a Kimi-K2.6 style-blind LLM-judge audit, its error rate over non-abstained steps rises from 30.6% to 50.3%. In this primary medical setting, answer quality and trace factuality move in opposite directions. This before--after pattern persists across evaluators, teacher strengths, student scales and families, medical benchmarks, and style, segmentation, and answer-correctness controls. A 150-step blinded audit by a clinical expert reproduces the same ordering. Boundary checks narrow the scope of the claim: the risk appears when a compact answer under-constrains the rationale and a capable student can imitate expert-like form without reliably grounding each local claim. Standard answer metrics and aggregate hedging rates do not reveal the shift. When such traces are released or reused, answer-level metrics alone are insufficient.

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.

Medical question-answering datasets often contain answer labels, whereas high-quality rationales remain scarce, noisy, or costly to validate. This changes the acquisition question: rather than asking which questions should be labeled, we ask which already-labeled questions should receive rationale supervision under a fixed token budget. We study an offline version of this problem in which candidate rationales are visible to the selector but withheld from downstream training unless selected. We propose root-mean-square Robustness-based Sample Prioritization (RMS-RSP), which perturbs hidden states only at rationale tokens and measures the resulting shift in the gold-versus-best-distractor margin. Across five medical QA datasets, MedGemma-4B-IT, three training seeds, ten budgeted non-RSP selectors, and an unbudgeted full-supervision reference, RMS-RSP provides a deliberately qualified result. Its locked-budget accuracy is 60.61% on average versus 60.08% for Random, with a statistically resolved gain only on AfriMed-QA (+1.44 points). Its full-budget accuracy area is not better than Random. However, after three answer-option reorderings, RMS-RSP improves robust accuracy and semantic consistency by 1.91 and 2.85 points on average, respectively, with the same direction on all five datasets. Training on every pool rationale raises macro accuracy to 63.74%, but consumes 29--254 times more rationale tokens and does not uniformly improve robustness. These findings do not establish universal accuracy gains; they instead suggest that rationale-local boundary sensitivity can identify supervision that improves invariance to semantically equivalent formatting changes.