Teacher top-K distillation drops the low-probability <tool call> token from the response teacher's support, creating a one-sided gradient that causally raises tool over-calling.
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Entropy-aware on-policy distillation of language models
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abstract
On-policy distillation is a promising approach for transferring knowledge between language models, where a student learns from dense token-level signals along its own trajectories. This framework typically uses reverse KL divergence, encouraging the student to match the teacher's high-confidence predictions. However, we show that the mode-seeking property of reverse KL reduces generation diversity and yields unstable learning signals when the teacher distribution has high entropy. To address this, we introduce Entropy-Aware On-Policy Distillation. Our key idea is augmenting the standard reverse KL objective with forward KL when teacher entropy is high, capturing the full range of plausible outputs while retaining precise imitation elsewhere. It balances mode-seeking precision with mode-covering robustness without sacrificing on-policy training efficiency. Experiments show that our method maintains generation diversity (sustained token-level entropy) and improves student-teacher alignment (lower forward KL on high-entropy tokens). Across six math reasoning benchmarks, this yields Pass@8 accuracy gains of +1.37 for Qwen3-0.6B-Base, +2.39 for Qwen3-1.7B-Base, and +5.05 for Qwen3-4B-Base compared to baseline on-policy distillation methods. These results demonstrate that accounting for teacher uncertainty is essential for maintaining diversity and achieving effective knowledge transfer.
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SAGE-OPD improves multi-turn OPD via turn-level selective intervention, teacher-confidence weighting, and loss normalization, reporting up to 13.3% relative gain in ALFWorld unseen success rate over standard OPD.
PowerOPD applies the Box-Cox power transformation to create natively bounded, sign-consistent rewards for on-policy distillation, delivering up to +6.37 Avg@8 gains over vanilla OPD on math reasoning benchmarks while cutting compute costs.
AR-OPD disentangles privileged supervision via anchored residual guidance to reduce hindsight leakage in on-policy distillation, reporting gains of 2.3 points over full privileged OPD and 7.9 over SFT on reasoning tasks.
KAT detects persistent low-KL agreement traps in on-policy distillation via a dynamic threshold to filter weak supervision, improving avg@k by 2.66% and pass@k by 3.43% on four math benchmarks while shortening rollouts by 59.73%.
OPRD performs distillation in hidden-state space on on-policy data for deterministic gradients and better math benchmark performance, plus OPRD-Bridge for cross-architecture transfer via low-rank projectors.
VA-OPD improves VLM performance over standard on-policy distillation by reweighting rollouts and separating KL terms according to token-level visual advantage on math and visual benchmarks.
Decoupling prefix source from token-level KL direction in autoregressive sequence KL yields four objectives unifying SFT, DAgger, offline RL and OPD, with KL mixing and entropy-gated curriculum improving math reasoning accuracy and shortening responses.
EGRSD and CL-EGRSD advance the accuracy-length frontier in LLM reasoning by entropy-guided weighting of token-level distillation signals from the teacher.
On-policy distillation has an extrapolation cliff at closed-form lambda*(p,b,c) set by teacher modal probability, warm-start mass, and clip strength, past which training shifts from format-preserving to format-collapsing.
vOPD stabilizes on-policy distillation gradients by subtracting a closed-form per-token negative reverse KL baseline as a detached control variate, preserving unbiasedness while lowering variance and matching expensive full-vocabulary methods.
Rubric-based on-policy distillation allows training student models using only teacher responses by generating scoring rubrics from contrasts and using them for on-policy optimization, achieving superior performance and up to 10x better sample efficiency than logit-based approaches.
MAD-OPD recasts on-policy distillation teachers as a debating collective to supply better supervision, lifting agentic and code performance over single-teacher OPD across multiple model sizes.
TCOD stabilizes on-policy distillation for multi-turn agents via temporal curriculum on trajectory depth, improving performance up to 18 points over vanilla OPD and sometimes surpassing the teacher.
Transferring a weak model’s RL-induced log-ratio policy shift on a strong student’s own rollouts raises AIME accuracy more cheaply than imitating the weak teacher or running matched-step RL on the student.
ARKD uses an RL policy network to adaptively balance FKL and RKL in LLM distillation, claiming gains of 0.4-0.6 points on Rouge-L and BertScore over baselines.
SEAD applies entropy-guided token selection, KL annealing, and easy-to-hard curriculum to on-policy distillation and reports +4.8 average accuracy gain over vanilla OPD on six math benchmarks with OLMo-3 models.
ReNIO reweights negative student-generated trajectories in LLM on-policy distillation using probability ratios, reporting relative gains up to 10% on reasoning benchmarks.
DEAR identifies decision tokens via entropy and evidence tokens via cosine similarity plus divergence to improve on-policy reasoning distillation over standard methods.
ViCuR introduces recoverable visual cues as teacher privilege in multimodal on-policy distillation, yielding +1.19 to +1.24 average gains over answer-based baselines across seven benchmarks with Qwen3-VL students.
Including temperature scaling makes forward KL divergence outperform reverse KL in LLM distillation on instruction benchmarks, overturning the τ=1 preference for reverse KL.
DASD improves math reasoning in LLMs by adaptively directing self-distillation based on per-token entropy to balance exploration and step accuracy, outperforming prior self-distillation and RLVR baselines on six benchmarks.
On-Policy Consistency Training (OPCT) improves LLM safety metrics over supervised fine-tuning while largely preserving capabilities across three model families.
Position-Weighted On-Policy Self-Distillation (PW-OPSD) weights later tokens more heavily after a diagnostic shows position predicts teacher reliability better than entropy, yielding +1.0 and +1.1 Avg@12 gains on AIME 2024/2025.
citing papers explorer
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When Top-K Misses the Decision: Tool-Call Drift in Multi-Teacher On-Policy Distillation
Teacher top-K distillation drops the low-probability <tool call> token from the response teacher's support, creating a one-sided gradient that causally raises tool over-calling.
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SAGE-OPD: Selective Agent-Guided Intervention for Multi-Turn On-Policy Distillation
SAGE-OPD improves multi-turn OPD via turn-level selective intervention, teacher-confidence weighting, and loss normalization, reporting up to 13.3% relative gain in ALFWorld unseen success rate over standard OPD.
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PowerOPD: Stabilizing On-Policy Distillation with Bounded Power Transformation
PowerOPD applies the Box-Cox power transformation to create natively bounded, sign-consistent rewards for on-policy distillation, delivering up to +6.37 Avg@8 gains over vanilla OPD on math reasoning benchmarks while cutting compute costs.
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Beyond Absolute Imitation: Anchored Residual Guidance for Privileged On-Policy Distillation
AR-OPD disentangles privileged supervision via anchored residual guidance to reduce hindsight leakage in on-policy distillation, reporting gains of 2.3 points over full privileged OPD and 7.9 over SFT on reasoning tasks.
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Escaping the KL Agreement Trap in On-Policy Distillation
KAT detects persistent low-KL agreement traps in on-policy distillation via a dynamic threshold to filter weak supervision, improving avg@k by 2.66% and pass@k by 3.43% on four math benchmarks while shortening rollouts by 59.73%.
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OPRD: On-Policy Representation Distillation
OPRD performs distillation in hidden-state space on on-policy data for deterministic gradients and better math benchmark performance, plus OPRD-Bridge for cross-architecture transfer via low-rank projectors.
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Visual-Advantage On-Policy Distillation for Vision-Language Models
VA-OPD improves VLM performance over standard on-policy distillation by reweighting rollouts and separating KL terms according to token-level visual advantage on math and visual benchmarks.
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Decoupling KL and Trajectories: A Unified Perspective for SFT, DAgger, Offline RL, and OPD in LLM Distillation
Decoupling prefix source from token-level KL direction in autoregressive sequence KL yields four objectives unifying SFT, DAgger, offline RL and OPD, with KL mixing and entropy-gated curriculum improving math reasoning accuracy and shortening responses.
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Respecting Self-Uncertainty in On-Policy Self-Distillation for Efficient LLM Reasoning
EGRSD and CL-EGRSD advance the accuracy-length frontier in LLM reasoning by entropy-guided weighting of token-level distillation signals from the teacher.
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The Extrapolation Cliff in On-Policy Distillation of Near-Deterministic Structured Outputs
On-policy distillation has an extrapolation cliff at closed-form lambda*(p,b,c) set by teacher modal probability, warm-start mass, and clip strength, past which training shifts from format-preserving to format-collapsing.
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KL for a KL: On-Policy Distillation with Control Variate Baseline
vOPD stabilizes on-policy distillation gradients by subtracting a closed-form per-token negative reverse KL baseline as a detached control variate, preserving unbiasedness while lowering variance and matching expensive full-vocabulary methods.
-
Rubric-based On-policy Distillation
Rubric-based on-policy distillation allows training student models using only teacher responses by generating scoring rubrics from contrasts and using them for on-policy optimization, achieving superior performance and up to 10x better sample efficiency than logit-based approaches.
-
MAD-OPD: Breaking the Ceiling in On-Policy Distillation via Multi-Agent Debate
MAD-OPD recasts on-policy distillation teachers as a debating collective to supply better supervision, lifting agentic and code performance over single-teacher OPD across multiple model sizes.
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TCOD: Exploring Temporal Curriculum in On-Policy Distillation for Multi-turn Autonomous Agents
TCOD stabilizes on-policy distillation for multi-turn agents via temporal curriculum on trajectory depth, improving performance up to 18 points over vanilla OPD and sometimes surpassing the teacher.
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Weak-to-Strong Generalization via Direct On-Policy Distillation
Transferring a weak model’s RL-induced log-ratio policy shift on a strong student’s own rollouts raises AIME accuracy more cheaply than imitating the weak teacher or running matched-step RL on the student.
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ARKD: Adaptive Reinforcement Learning-Guided Bidirectional KL Divergence Distillation for Text Generation
ARKD uses an RL policy network to adaptively balance FKL and RKL in LLM distillation, claiming gains of 0.4-0.6 points on Rouge-L and BertScore over baselines.
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SEAD: Competence-Aware On-Policy Distillation via Entropy-Guided Supervision
SEAD applies entropy-guided token selection, KL annealing, and easy-to-hard curriculum to on-policy distillation and reports +4.8 average accuracy gain over vanilla OPD on six math benchmarks with OLMo-3 models.
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ReNIO: Reweighting Negative Trajectory Importance for LLM On-Policy Distillation
ReNIO reweights negative student-generated trajectories in LLM on-policy distillation using probability ratios, reporting relative gains up to 10% on reasoning benchmarks.
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Finding the Evidence: Discovering Decision-Supporting Tokens for On-Policy Reasoning Distillation
DEAR identifies decision tokens via entropy and evidence tokens via cosine similarity plus divergence to improve on-policy reasoning distillation over standard methods.
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ViCuR: Visual Cues as Recoverable Privilege for Multimodal On-Policy Distillation
ViCuR introduces recoverable visual cues as teacher privilege in multimodal on-policy distillation, yielding +1.19 to +1.24 average gains over answer-based baselines across seven benchmarks with Qwen3-VL students.
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Rethinking the Role of Temperature in Large Language Model Distillation
Including temperature scaling makes forward KL divergence outperform reverse KL in LLM distillation on instruction benchmarks, overturning the τ=1 preference for reverse KL.
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Tailoring Teaching to Aptitude: Direction-Adaptive Self-Distillation for LLM Reasoning
DASD improves math reasoning in LLMs by adaptively directing self-distillation based on per-token entropy to balance exploration and step accuracy, outperforming prior self-distillation and RLVR baselines on six benchmarks.
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On-Policy Consistency Training Improves LLM Safety with Minimal Capability Degradation
On-Policy Consistency Training (OPCT) improves LLM safety metrics over supervised fine-tuning while largely preserving capabilities across three model families.
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When Are Teacher Tokens Reliable? Position-Weighted On-Policy Self-Distillation for Reasoning
Position-Weighted On-Policy Self-Distillation (PW-OPSD) weights later tokens more heavily after a diagnostic shows position predicts teacher reliability better than entropy, yielding +1.0 and +1.1 Avg@12 gains on AIME 2024/2025.
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Prefix Teach, Suffix Fade: Local Teachability Collapse in Strong-to-Weak On-Policy Distillation
Local teachability collapse occurs in later trajectory segments during strong-to-weak OPD; a margin-based release rule using top-K teacher advantage and BIC change-point detection on sentence segments outperforms full-trajectory supervision on five in-domain benchmarks and preserves out-of-domain pe
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Multi-Rollout On-Policy Distillation via Peer Successes and Failures
MOPD improves on-policy distillation by using peer successes and failures from multiple rollouts to construct more informative teacher signals, yielding consistent gains over baselines on reasoning benchmarks.
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Flow-OPD: On-Policy Distillation for Flow Matching Models
Flow-OPD is a two-stage on-policy distillation method for flow matching models that lifts GenEval from 63 to 92 and OCR from 59 to 94 on SD 3.5 Medium while preserving fidelity.
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SimCT: Recovering Lost Supervision for Cross-Tokenizer On-Policy Distillation
SimCT enlarges the supervision space in cross-tokenizer on-policy distillation using short jointly tokenizable multi-token continuations, producing consistent gains over shared-token baselines on math and code benchmarks.
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UniSD: Towards a Unified Self-Distillation Framework for Large Language Models
UniSD unifies self-distillation components for autoregressive LLMs and its full integrated version improves base models by 5.4 points and baselines by 2.8 points across six benchmarks.
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Uni-OPD: Unifying On-Policy Distillation with a Dual-Perspective Recipe
Uni-OPD improves on-policy distillation via student-side data balancing for informative rollouts and teacher-side outcome-guided margin calibration that restores order consistency with rewards.
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Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe
On-policy distillation works when student and teacher models share thinking patterns and the teacher adds new capabilities, with success tied to alignment on a small set of high-probability tokens.
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DOPD: Dual On-policy Distillation
DOPD is an advantage-aware dual distillation method that dynamically assigns token supervision from either privileged teacher or student to transfer capability while mitigating non-replicable information asymmetry in on-policy distillation.
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Blockwise Policy-Drift Gating for On-Policy Distillation
Blockwise policy-drift gating raises mean pass@8 from 0.4978 to 0.5160 on four math benchmarks by reweighting OPD losses with detached mean-normalized gates from student policy drift over 64-token blocks.
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Filter, Then Reweight: Rethinking Optimization Granularity in On-Policy Distillation
FiRe-OPD introduces a two-stage filter-then-soft-reweight procedure for trajectory- and token-level supervision in on-policy distillation, claiming gains over prior token-level methods.
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$\boldsymbol{f}$-OPD: Stabilizing Long-Horizon On-Policy Distillation with Freshness-Aware Control
f-OPD decomposes on-policy distillation drift into rollout and supervision components, then applies a sample-level freshness score to adaptively limit stale data influence and stabilize long-horizon agent training.
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SOD: Step-wise On-policy Distillation for Small Language Model Agents
A step-wise reweighting of on-policy distillation, based on per-step student-teacher divergence, improves tool-integrated reasoning in 0.6B and 1.7B language models.
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A Formula-Driven Survey and Research Agenda for On-Policy Distillation
A survey creates a taxonomy for on-policy distillation in LLMs that separates temporal credit assignment from vocabulary-level probability routing.
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Internalize the Temperature: On-Policy Self-Distillation as Policy Reheater for Reinforcement Learning
TS-OPSD internalizes temperature via on-policy self-distillation to reheat entropy-collapsed RL policies in LLMs, providing stronger initialization for further training than continued RL or rollout temperature adjustment.
- DRIFT: Difficulty Routing Self-DIstillation with Rhythm-Gated Exploration and Success BuFfer Training
- ATOD: Annealed Turn-Aware On-Policy Distillation for Multi-Turn Agentic Tasks
- On-Policy Distillation with Best-of-N Teacher Rollout Selection