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TGPO uses teacher token guidance on student prefixes plus trajectory rewards to enable effective on-policy reasoning distillation under large policy divergence.

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2026-06-30 21:38 UTC pith:VPZTCO4J

load-bearing objection TGPO adds token-level teacher conditioning on student prefixes to RLVR, but the abstract gives no equations, ablations, or token metrics to show the conditioning actually helps under divergence. the 2 major comments →

arxiv 2605.13230 v2 pith:VPZTCO4J submitted 2026-05-13 cs.LG cs.AI

Teacher-Guided Policy Optimization for On-Policy Reasoning Distillation under Large Policy Divergence

Xinyu Liu , Kechen Jiao , Chunyang Xiao , Runsong Zhao , Junhao Ruan , Bei Li , Jiahao Liu , Qifan Wang
show 5 more authors
Xin Chen Jingang Wang Chenglong Wang Tong Xiao JingBo Zhu
This is my paper
classification cs.LG cs.AI
keywords on-policy distillationreasoning distillationpolicy optimizationlarge language modelsreinforcement learningteacher guidancepolicy divergencetoken-level supervision
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Existing reverse KL supervision in on-policy distillation breaks down when student exploration produces trajectories far from the teacher distribution, yielding uninformative negative signals. TGPO counters this by letting the teacher directly predict each token conditioned on the student's own generated context, then combines those signals with trajectory-level verifiable rewards to steer sampling toward better sequences. The result is distillation that stays informative even when policies diverge substantially. Experiments show consistent gains over RKL baselines and stability across teacher choices on reasoning benchmarks.

Core claim

TGPO remains effective under large teacher-student policy divergence by using the teacher to directly guide token level generation conditioning on student-generated contexts; together with RLVR-style trajectory level rewards, TGPO steers exploration toward improved continuations.

What carries the argument

Teacher token-level guidance conditioned on student-generated prefixes, paired with trajectory-level RLVR rewards.

Load-bearing premise

Conditioning the teacher's next-token predictions on prefixes sampled from the student will produce higher-quality continuations without adding new biases or shifts.

What would settle it

Run TGPO and an RKL baseline on the same reasoning task with deliberately large divergence; if the TGPO continuations show no quality or benchmark improvement over RKL, the mechanism claim does not hold.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Outperforms RKL-based OPD methods on reasoning benchmarks.
  • Maintains performance robustness when different teacher models are used.
  • Avoids uninformative feedback from trajectories outside the teacher distribution.
  • Combines token-level teacher signals with trajectory rewards to direct exploration.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same conditioning trick could be tried in other distillation settings where student sampling routinely leaves the teacher support.
  • It may reduce the need to keep teacher and student policies artificially close during training.
  • One could measure the fraction of tokens where teacher guidance actually changes the student's choice and correlate that with final gains.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 1 minor

Summary. The paper claims that existing reverse KL (RKL)-based on-policy distillation (OPD) methods for reasoning LLMs fail under large teacher-student policy divergence because RL-driven exploration produces trajectories outside the teacher distribution, yielding uninformative negative feedback. It proposes Teacher-Guided Policy Optimization (TGPO), which augments RLVR-style trajectory rewards with direct token-level teacher guidance conditioned on student-generated prefixes to steer exploration toward improved continuations, and reports that TGPO outperforms RKL-based OPD baselines while remaining robust across teacher models on reasoning benchmarks.

Significance. If the core mechanism is validated, TGPO would address a practical limitation in combining on-policy RL with distillation for LLMs, enabling more effective reasoning post-training when student policies diverge substantially. The approach is a straightforward algorithmic combination rather than a parameter-free derivation or machine-checked result, so its significance hinges on whether the reported gains are attributable to the proposed conditioning rather than RLVR alone.

major comments (2)
  1. [Abstract (mechanism description) and Experiments] The central claim that teacher token predictions conditioned on student prefixes produce higher-quality continuations (and thus better steering than RKL) under large divergence is load-bearing, yet the manuscript provides no token-level quality metrics, no measurement of divergence between the conditioned teacher distribution and optimal continuations, and no ablation that disables the conditioning while retaining RLVR-style rewards.
  2. [Experiments] End-to-end benchmark outperformance is reported, but without isolating the contribution of the student-prefix conditioning (e.g., via a controlled comparison to pure RLVR or to RKL on the same trajectories), it is impossible to determine whether the claimed advantage over RKL-based OPD collapses to standard RLVR when trajectories fall outside the teacher distribution.
minor comments (1)
  1. [Abstract] The abstract refers to 'RLVR-style trajectory level rewards' without defining the precise reward formulation or how it interacts with the token-level guidance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the major comments below and commit to revisions that strengthen the isolation of the proposed mechanism.

read point-by-point responses

  1. Referee: [Abstract (mechanism description) and Experiments] The central claim that teacher token predictions conditioned on student prefixes produce higher-quality continuations (and thus better steering than RKL) under large divergence is load-bearing, yet the manuscript provides no token-level quality metrics, no measurement of divergence between the conditioned teacher distribution and optimal continuations, and no ablation that disables the conditioning while retaining RLVR-style rewards.

    Authors: We agree that token-level metrics and an explicit ablation would strengthen the mechanistic claims. While our primary results focus on end-to-end reasoning performance (the relevant downstream metric), we will add in revision: (i) an ablation of TGPO versus RLVR without the teacher conditioning, and (ii) token-level statistics such as average teacher log-probability on tokens generated under student prefixes. Direct measurement of divergence to 'optimal' continuations is not feasible without an oracle, but the added ablation will isolate the conditioning effect. revision: yes

  2. Referee: [Experiments] End-to-end benchmark outperformance is reported, but without isolating the contribution of the student-prefix conditioning (e.g., via a controlled comparison to pure RLVR or to RKL on the same trajectories), it is impossible to determine whether the claimed advantage over RKL-based OPD collapses to standard RLVR when trajectories fall outside the teacher distribution.

    Authors: Our reported comparisons are against RKL-based OPD baselines under identical large-divergence settings and trajectories. We acknowledge that a direct head-to-head with pure RLVR (no teacher guidance) is missing and will include this controlled ablation in the revision to quantify the incremental benefit of the student-prefix conditioning. revision: yes

Circularity Check

0 steps flagged

No circularity: TGPO is a new algorithmic combination with no self-referential derivations or fitted predictions

full rationale

The paper proposes TGPO as an on-policy distillation method combining teacher token-level guidance conditioned on student-generated prefixes with RLVR trajectory rewards. No equations, parameters, or predictions are defined in terms of themselves. The abstract identifies a limitation of RKL methods and presents TGPO as an alternative without any reduction of claims to inputs by construction, self-citation load-bearing for uniqueness, or renaming of known results. Experiments are end-to-end comparisons, not internal fits. This is a standard non-circular algorithmic contribution.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only abstract available; no free parameters, axioms, or invented entities are specified or can be extracted.

pith-pipeline@v0.9.1-grok · 5742 in / 1143 out tokens · 27071 ms · 2026-06-30T21:38:22.468381+00:00 · methodology

0 comments
read the original abstract

On-policy distillation (OPD) has become a promising paradigm for reasoning-oriented post-training of large language models (LLMs), especially when combined with reinforcement learning from verifiable rewards (RLVR). Existing OPD methods rely on reverse KL (RKL)-based teacher supervision over trajectories sampled from the student policy. However, we identify a critical limitation: under large teacher--student policy divergence, RL-driven exploration often produces trajectories outside the teacher distribution, resulting in uninformative negative feedback. To address this, we propose Teacher-Guided Policy Optimization (TGPO), an on-policy reasoning distillation method that remains effective under large policy divergence settings. Rather than relying solely on evaluative supervision, TGPO uses teacher to directly guide token level generation conditioning on student-generated contexts; together with RLVR-style trajectory level rewards, TGPO steers exploration toward improved continuations. Experiments on reasoning benchmarks show that TGPO consistently outperforms existing RKL-based OPD methods and remains robust across different teacher models.

Figures

Figures reproduced from arXiv: 2605.13230 by Bei Li, Chenglong Wang, Chunyang Xiao, Jiahao Liu, Jingang Wang, Jingbo Zhu, Junhao Ruan, Kechen Jiao, Qifan Wang, Runsong Zhao, Tong Xiao, Xin Chen, Xinyu Liu.

Figure 1
Figure 1. Figure 1: RKL vs. TGPO. (a) RKL relies on scalar rewards to penalize deviation. When the policy gap is significant, these penal￾ties fail to provide directional information. (b) TGPO utilizes the teacher’s predicted distribution as guidance, explicitly informing the student what to generate next rather than what not to generate. et al., 2025), resulting in a rigid model with limited explo￾ration capabilities (Chen e… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of RKL distillation dynamics. We distill a Qwen2.5-Math-1.5B student using either an In-Family teacher (Qwen2.5-Math-7B) or a Cross-Family teacher (Qwen3-30B-A3B). While the In-Family setting converges stably, the Cross-Family setting exhibits catastrophic instability, characterized by sharp training score degradation (Left), gradient norm spikes (Middle), and unbounded response length growth (R… view at source ↗
Figure 3
Figure 3. Figure 3: Overview of the TGPO. The Policy Model generates a group of rollouts {yi} G i=1 conditioned on input x. At each step, the Teacher Model provides dynamic token-level guidance by predicting the optimal target token y T based on the student’s current prefix. This dense guidance signal (J) complements the outcome-based advantage (A) derived from the Rule-based Verifier to update the policy. with sequence yi (e… view at source ↗
Figure 3
Figure 3. Figure 3: Overview of the TGPO. The Policy Model generates a group of rollouts [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Training Dynamics Analysis. (Left) Training reward. TGPO demonstrates robust growth and convergence compared to RKL. (Middle) Response length. TGPO avoids RKL’s length explosion and aligns with GRPO++’s stability. (Right) Gradient norm. TGPO shows stable optimization compared to the high variance in RKL, KDRL and LUFFY. 5. Experimental Results 5.1. Main Results Overall Performance [PITH_FULL_IMAGE:figures… view at source ↗
Figure 5
Figure 5. Figure 5: Ablation of annealing schedules. The inset details the guidance weight (w) schedule for each setting. Our method yields the best convergence. though both strategies start similarly, the performance gap becomes evident in the later stages. This suggests that a transition to a “pure RL phase” (where wt = 0) before the end of training is essential. By removing the imitation con￾straint at step 200, Ours allow… view at source ↗
Figure 5
Figure 5. Figure 5: Training reward curves in the in-family setting. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Training Dynamics Analysis. (Left) Training reward. TGPO demonstrates robust growth and convergence compared to RKL and KDRL. (Middle) Response length. TGPO avoids RKL’s length explosion and aligns with GRPO++’s stability. (Right) Gradient norm. TGPO shows stable optimization compared to the high variance in RKL, KDRL and LUFFY. B.3. Analysis of Experiments on the 1.5B Model B.3.1. OVERALL PERFORMANCE To f… view at source ↗
Figure 6
Figure 6. Figure 6: Ablation of annealing schedules. The inset de [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Training Dynamics Analysis. (Left) Training reward. TGPO demonstrates robust growth and convergence compared to RKL and KDRL. (Middle) Response length. TGPO avoids RKL’s length explosion and aligns with GRPO++’s stability. (Right) Gradient norm. TGPO shows stable optimization compared to the high variance in RKL, KDRL and LUFFY. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages · cited by 1 Pith paper · 3 internal anchors

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    Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models

    Self-distilled reasoner: On-policy self- distillation for large language models.arXiv preprint arXiv:2601.18734. 10 A Theoretical Analysis of RKL Instability In this appendix, we provide the formal derivations referenced in Section 2.2. We analyze the gradient behavior of the Reverse KL (RKL) objective and show why optimization becomes unstable when the s...

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