Better Accuracies, Worse Reasoning: A Step-Level Audit of Medical Chain-of-Thought Distillation

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.

A Regime Theory of Controller Class Selection for LLM Action Decisions

Deployed language and vision-language models must decide, on each input, whether to answer directly, retrieve evidence, defer to a stronger model, or abstain. Contrary to the common monotonicity intuition, greater per-input expressivity is not uniformly beneficial in finite samples: under identical strict cross-validation, different benchmarks prefer different controller classes. This reflects a finite-sample limitation of instance-level uncertainty signals, which can be exhausted at a distribution-dependent scale. We organize controllers into a nested lattice of four classes: fixed actions, partition routers, instance-level controllers, and prior-gated controllers, ordered by complexity. We prove a regime theory that turns three data-estimable bottlenecks into a class choice: how much improvement is possible beyond the best fixed action, whether there are enough samples for instance-level controllers to make reliable decisions, and how much improvement a coarse partition router can recover when instance-level signal is unreliable. The resulting Bernstein-tight threshold has a matching information-theoretic lower bound, and strict nested cross-validation provably selects a near-best class. Across SMS-Spam, HallusionBench, A-OKVQA, and FOLIO, the predicted class matches the empirical winner; the prior-gated controller wins on TextVQA when OCR tokens supply a label-free prediction-time prior. Code is available at https://github.com/Anonymous-Awesome-Submissions/Regime-Theory.