On-policy distillation (OPD) accelerates post-training by providing dense token-level supervision from a frozen teacher on the student's own rollouts. Vanilla OPD applies this supervision uniformly across prompts, without checking whether the teacher is reliable for each prompt. Because reverse KL is mode-seeking, a confidently wrong teacher can induce a strong yet misleading update. Distributional proxies, such as entropy or teacher-student likelihood agreement, measure uncertainty or agreement but do not directly verify outcome correctness. We introduce Teacher-Gated On-Policy Distillation (TGOPD), built on the principle that teacher reliability should be verified at the prompt level before dense supervision is admitted. TGOPD estimates reliability from a small set of verifier-scored teacher probes and routes each prompt exclusively to dense OPD when the reliability check passes or to verifier-grounded GRPO otherwise. Across 4B and 35B students in mathematics, code, and instruction following, TGOPD outperforms Vanilla OPD in all six single-domain settings and achieves higher seven-benchmark averages at both scales under multi-domain training. By using otherwise-idle teacher capacity for reliability estimation, TGOPD also reduces teacher-side compute waste in asynchronous OPD, increasing teacher-node GPU utilization from 9.8% to 78.9% in the measured 4B single-domain run.
Zewen Ding, Zezhong Wu, Zhou Tao +5cs.LG cs.AI cs.CL
On-policy self-distillation (OPSD) improves reasoning by training a problem-only student on its own rollouts using dense token-level supervision from a privileged teacher that also sees a reference solution. However, standard OPSD treats the teacher distribution as a fixed target along the student's rollout and updates only the student %, although -- even though privileged conditioning does not guarantee that the teacher always provides the most appropriate target for problem-only reasoning. This one-way supervision can therefore misdirect the student when the teacher distribution is misaligned with valid student reasoning. We therefore introduce Verifier-Informed Student-to-Teacher Adaptation (VISTA), which preserves the standard OPSD student update while using outcome-verified rollouts to adapt the teacher toward the student distribution. Within each verified rollout, VISTA further restricts this adaptation to the top-$k$ positions with the largest teacher--student KL divergence. Notably, VISTA reuses the rollout and loss function from standard OPSD, introducing no additional sampling or separate reward objective. Across AIME24, AIME25, and HMMT25 with Qwen3 models at 1.7B, 4B, and 8B, VISTA achieves the highest Avg@12 at every scale, improving over OPSD by $0.6$, $0.7$, and $2.1$ points, respectively. These results demonstrate the value of student supervision from outcome-verified rollouts and highlight student-to-teacher adaptation as a promising direction for OPSD.
Test-time collaboration, including self-consistency, best-of-N selection, critic models, and verifier pipelines, is often credited with broadly improving LLM reasoning, yet its gains are uneven and sometimes negative. We ask when training-free collaboration should be expected to help. For a fixed candidate pool, we decompose a selector or verifier's net gain into measurable factors: recoverable mass, verification-signal coverage, conditional selection quality, and harm to already-correct outputs. This reframes collaboration as a candidate-selection problem rather than as an intrinsic property of a multi-agent topology. Across LiveCodeBench, MATH Level-5 hard subjects, and GPQA-Diamond, gains are bounded first by the oracle gap and then by signal fidelity, which we measure directly as candidate-level agreement between verifier verdicts and official labels. On LiveCodeBench, a public-test verifier (MCC 0.825) gains +8.14 percentage points (pp) over a first-sample baseline; a generated-test verifier (MCC 0.248) improves by +2.70pp and is not statistically distinguishable from an LLM selector, but operates at near-zero harm versus the selector's 4.69% harm rate. On MATH, a symbolic answer-equivalence selector beats self-consistency by +4.67pp, while LLM selectors are negative. On GPQA-Diamond, recoverable mass is only 3.03% and 87.54% of candidate pools are answer-identical; a weaker model's pools shrink both further, suggesting that oracle gap is a joint property of task, model, and sampling configuration. Our framework yields a practical pre-deployment diagnostic: estimate the oracle gap, then measure coverage, signal fidelity, and harm before investing in collaboration.
For the development of Large language models (LLMs), recent approaches to generating pseudo intermediate reasoning have shown remarkable progress. But they typically rely on large numbers of correctly annotated answers to assess reasoning quality. This paper presents a semi-supervised framework that scales reasoning learning from minimal supervision, turning reasoning verification itself into a data creation mechanism. We train a lightweight reasoning-correctness classifier on only a few labeled samples, which judges whether intermediate reasoning traces generated by an LLM are valid. Furthermore, an entropy-based confidence threshold filters out unreliable samples, and the remaining high-confidence reasoning traces are used to fine-tune the model. Experiments on Verifiable Math Problems (Orca-Math subset) and Question Answering on Image Scene Graphs (GQA) with Visual Programming show that our method achieves accuracy comparable to using 10-15x more labeled data. Ablation analyses confirm that both the classifier and entropy filtering are essential for scalable and noise-resistant pseudo-labeling. By replacing expensive answer-level supervision with lightweight reasoning verification, our method provides a practical path toward constructing large-scale reasoning resources and paves the way for future autonomous reasoning systems that learn from minimal human input.
When a language model trains on its own verified outputs, does it acquire capability beyond its base, or merely get better at expressing capability the base already had? We make the question decidable with a teacher-free "constellation" -- a generator, a learned critic, and a free exact verifier -- on a FlashFill-style "trapdoor" DSL, where verified (problem, solution) pairs are cheap to synthesize, hard to invert, and free to check exactly. Everything runs on one 4-bit Qwen3-4B on a single 24 GB GPU, with no model in the loop larger than the base. We report three findings. (i) Critic-guided selection beats verifier-filtered best-of-$k$ by $+9.1$ pp ($6/6$ seeds), with the entire gain localized to tasks where candidates disagree on held-out inputs. (ii) Per-round STaR self-training raises the ceiling but never accelerates -- the gain tracks remaining headroom and decelerates across $K=4$ independent training trajectories. (iii) The domain has no clean zero-capability frontier, so the usual "$0\% \to$ climb $=$ emergence" test is invalid here. A measured pass@$K$ crossover settles the diagnosis: the trained model wins at the operating budget (pass@$8$) but the base overtakes it at a large budget (pass@$64$) on every trajectory, so self-training concentrates probability mass rather than expanding reach. This is amplification, not compounding. ($K=4$ is indicative, not yet a robust across-trajectory CI.)