Disposition Distillation at Small Scale: A Three-Arc Negative Result

Small instruction-tuned language models reach phones, cars, and offline assistants through knowledge distillation, and whether a distilled model is fair enough to ship is often decided by a multiple-choice bias score on a benchmark that offers an abstention option. Three mechanisms move behavior around the abstention option: refusal loss, where the student stops declining on items its pre-distillation reference declined; sampling churn, the same change observed between two runs of the reference itself; and option capture, where the student takes an abstention option whenever one is offered. Injecting each mechanism into a reference's own records shows that aggregate scores see only outright loss, per-item scores see churn and remapping, and only conditioning on committed answers stops moved refusal mass from reading as fairness. Resampling a reference across inference seeds already turns 10% to 27% of its refusals into stereotype answers, so a per-item refusal metric reported without that floor overstates damage. Option capture is what corpus repair teaches: students trained with refusal exemplars take an offered abstention option on up to 95% of science questions where abstention is never correct, and the habit carries to three further benchmarks. Free-form evaluation shows that the refusals multiple choice loses are not where free-form stereotyping occurs. We distill these findings into a per-condition report anchored to the reference, with measured floors and ceilings, and apply it to four student families against a fine-tuning control: distillation keeps fewer of the reference's refusals than fine-tuning on the same prompts where the reference's refusals are reliable, by a few points, while the common metrics report improvements whenever refusal mass moves. A bias score quoted for a distilled model should say which of these it reports.

Can post-trained large language models (LLMs) further improve themselves using only unlabeled prompts, without external teachers or feedback from tools? We study this setting starting only from unlabeled seed questions with no ground-truth solutions, across three reasoning domains: math, science, and coding. We propose Self-Verified Distillation, a simple post-training refinement algorithm in which the model generates candidate solutions to these seed questions, filters them using prompt-based self-verification, and trains on the resulting self-curated dataset. Inspired by the UQ benchmark's use of multiple validators to screen candidate answers to hard unsolved questions, we adapt this validation-based filtering idea to self-training: the model filters its own generated solutions through a three-stage cascade of cycle-consistency, factuality, and correctness checks, accepting a solution only if it passes all stages with unanimous judge votes. We find that sampling more candidate generations and using a larger verification budget during training data construction produces higher-quality self-curated data and, in turn, better reasoning models. We then train Qwen3 models at multiple scales with Self-Verified Distillation and obtain gains across all three domains. For Qwen3-4B, our method improves aggregate held-out pass@1 by +16.7 points in math (AIME26 and HMMT), +11.1 points in science (GPQA Diamond and HLE), and +8.3 points in coding (LCBv5 and LCBv6), with gains also extending to 0.6B and 8B models. Compared to our test-time-only baseline (UQ-TTC), which improves performance by spending extra compute at inference time, Self-Verified Distillation achieves better performance in most settings while requiring only a single inference call at test time.

Black-box LLM distillation is usually evaluated as an output-matching problem: a student is considered successful when its responses are semantically similar to, or task-consistent with, those of a teacher. However, output similarity does not imply that the student is behaviorally indistinguishable from the model it imitates. We introduce bounded behavioral indistinguishability, formalized as $(ε,q,t,\mathbb{A})$-behavioral indistinguishability over an explicit prompt distribution, where $ε$ bounds distinguishing advantage, $q$ bounds oracle queries, $t$ bounds computation, and $\mathbb{A}$ denotes the adversary class. We instantiate this notion on Qwen and Llama teacher-student pairs using a controlled $5,000$-prompt behavioral probe suite. For each family, we compare the teacher with both the base student and the LoRA-distilled student, measuring whether distillation reduces distinguishability rather than merely improving similarity. LoRA raises semantic similarity from $0.788$ to $0.862$ for Qwen and from $0.814$ to $0.874$ for Llama. Yet adversarial evaluation reveals remaining behavioral differences: learned discriminators retain nonzero advantage, and pairwise category analysis shows artifacts concentrated in style/format, robustness, and domain-technical prompts. A pairwise teacher-identification adversary confirms this trend. With a different-family Llama judge and A/B-swap consistency filtering, Qwen distinguishing advantage drops from $0.158$ for the base student to $0.081$ after LoRA distillation. Query-budget experiments show that disagreement-guided acquisition does not consistently outperform stratified random sampling, indicating that coverage and diversity remain strong baselines. Our results show that semantic fidelity is useful but insufficient: black-box LLM distillation requires bounded, adversarial, and category-aware evaluation.