On-policy distillation (OPD) supervises the student exclusively in the output space by matching next-token distributions. This paradigm suffers from two limitations: (i) a high-variance gradient estimator whose signal-to-noise ratio collapses as the student approaches the teacher, and (ii) an LM-head information bottleneck that discards the teacher's intermediate hidden states. We propose On-Policy Representation Distillation (OPRD), the first method to lift on-policy distillation into the hidden-state space. OPRD aligns student and teacher representations across selected layers on the same on-policy rollouts, providing dense, deterministic, per-layer supervision while bypassing the LM head entirely. Theoretically, OPRD provides a deterministic per-sample gradient, removing the token-level estimation variance that plagues OPD, and exposes structural information that any output-space objective necessarily discards. Empirically, OPRD closes the student-teacher gap on competition mathematics benchmarks (AIME 2024, AIME 2025, and AIMO), where every output-space baseline plateaus below the teacher, while training 1.44x faster and using up to 54% less memory. We further extend OPRD to the cross-architecture setting via OPRD-Bridge. By exploiting the observation that heterogeneous models share a low-rank representational structure, we construct a frozen projector pair that aligns representations across arbitrary depth and width mismatches, shifting the alignment from the output space (which depends on a shared vocabulary) to the representation space. We validate OPRD-Bridge on both cross-architecture (Qwen3-4B -> Qwen3-1.7B-Base) and cross-tokenizer (Phi-4-mini-reasoning -> Qwen3-1.7B-Base) settings, demonstrating successful knowledge transfer even when the vocabulary-based alignment channel is unavailable. Code: https://github.com/ShenzhiYang2000/OPRD.
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.
On-policy distillation (OPD) grounds token-level supervision in the student's own trajectory, yet suffers from prefix failure: once the student commits to a wrong reasoning direction, all subsequent generation builds on this deviation, producing misdirected continuations that elicit unreliable supervision and waste compute. We identify a teacher-student continuation asymmetry on failed prefixes, where the teacher tends to redirect while the student continues along the original direction, and convert it into a label-free handoff trigger in Relay On-Policy Distillation (Relay-OPD). During training, Relay-OPD constructs relay trajectories by letting the teacher briefly take over at detected trigger points to produce a teacher leg, after which the student resumes and is optimized on the resulting trajectory. A limited relay budget concentrates intervention on critical early positions while limiting departure from the student policy. With a Qwen3-4B-Instruct-2507 teacher and Qwen3-0.6B/1.7B-Non-Thinking students on eight mathematical reasoning benchmarks, Relay-OPD achieves the best or second-best results on every benchmark, outperforming standard OPD by +5.73% and the strongest baseline FastOPD by +1.49% on average for 1.7B, with consistent gains at 0.6B. Training trajectory length is reduced by over 50%.
On-policy distillation transfers reasoning capabilities by training a student model on its own generated trajectories using token-level feedback from a teacher. However, we identify a critical bottleneck, \textbf{Supervision Fidelity Decay (SFD)}: as student-generated prefixes lengthen, the teacher's next-token distribution becomes less confident and less discriminative. Consequently, the teacher-dependent corrective signal in reverse-KL distillation weakens, causing student drift to compound across long reasoning chains. To mitigate SFD, we introduce \textbf{Lookahead Group Reward (\ours{})}. Building on the insight that next-step teacher confidence reflects the discriminative strength of future reverse-KL supervision, \ours{} evaluates the student's top-K candidate tokens by the teacher confidence they induce at the subsequent step and assigns a group-normalized reward. To maintain computational efficiency, we further design an entropy-triggered tree-attention mechanism. Across six math and code benchmarks, \ours{} improves mean@8 by \textbf{2.57} points over OPD for a 7B student, with gains increasing in longer-generation and reaching +\textbf{4.92} points on AIME-26 at 39k tokens.