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arxiv: 2606.18810 · v1 · pith:22ET46VHnew · submitted 2026-06-17 · 💻 cs.LG · cs.AI

Learning from Own Solutions: Self-Conditioned Credit Assignment for Reinforcement Learning with Verifiable Rewards

Yingyu Shan , Yuhang Guo , Zihao Cheng , Zeming Liu , Xiangrong Zhu , Xinyi Wang , Jiashu Yao , Wei Lin
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Hongru Wang Heyan Huang
This is my paper

Pith reviewed 2026-06-26 21:50 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords reinforcement learning with verifiable rewardscredit assignmentGRPOself-conditioningKL divergencelarge language modelsreasoning taskstoken-level weighting
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The pith

Conditioning LLMs on their own verified trajectories creates per-token KL divergences that improve credit assignment in GRPO.

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

The paper seeks to solve the problem of uniform token credit in GRPO for RL with verifiable rewards, where all tokens get the same weight despite some being more important for reasoning. It observes that conditioning the model on its verified correct outputs induces per-token KL divergence, which can be used to weight the gradients. This allows self-supervised credit assignment without external process reward models or teachers. The resulting SC-GRPO method delivers measurable gains on math, code, and agent benchmarks.

Core claim

The authors prove that distilling from a self-teacher of verified trajectories leads to infeasible weighted-average solutions when multiple verified trajectories exist, and propose using the induced per-token KL divergence as a multiplicative weight on the GRPO objective to achieve effective token-level credit assignment in the pure RLVR setting.

What carries the argument

Self-conditioned per-token KL divergence used as multiplicative weight on GRPO gradients.

If this is right

  • SC-GRPO outperforms GRPO by 8.1% and DAPO by 5.9% across five benchmarks.
  • SC-GRPO exhibits stronger out-of-distribution performance than baselines.
  • SC-GRPO achieves higher performance than On-Policy Distillation.
  • It operates without requiring external resources beyond the model's own rollouts.

Where Pith is reading between the lines

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

  • The weighting mechanism might extend to other policy gradient methods in RLVR.
  • Self-generated conditioning signals could reduce reliance on human-annotated or model-trained reward models in reasoning tasks.
  • Testing on larger models or different verifiable reward structures would reveal if the KL weighting scales.

Load-bearing premise

The per-token KL divergence from conditioning on verified trajectories provides an unbiased and effective multiplicative weight without introducing new optimization problems.

What would settle it

If experiments show that SC-GRPO performs no better than or worse than standard GRPO, or if the weighting leads to unstable training, the central claim would be falsified.

Figures

Figures reproduced from arXiv: 2606.18810 by Heyan Huang, Hongru Wang, Jiashu Yao, Wei Lin, Xiangrong Zhu, Xinyi Wang, Yingyu Shan, Yuhang Guo, Zeming Liu, Zihao Cheng.

Figure 1
Figure 1. Figure 1: Overview of SC-GRPO. Top: positioning of SC-GRPO among existing methods. Bottom: core mechanism illustrated on a LiveCodeBench example. 2025; Wang et al., 2025c) assign a single scalar re￾ward per rollout, so every token shares the same ad￾vantage. This uniform credit cannot identify which tokens caused success or failure, diluting gradient across routine tokens while under-crediting pivotal reasoning step… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of SC-GRPO. We construct a self-conditioned teacher by conditioning the model on a reference trajectory, compute token-level KL divergence, and use it to weight the GRPO gradient. KL from teacher to student: Di,t = KL(πeθ(· | si,t, τ ) ∥ πθ(· | si,t)). KL weighting We map each Di,t to a bounded weight f(Di,t) ∈ [0, 1) to modulate the GRPO gradient: tokens with small KL are downweighted, while toke… view at source ↗
Figure 3
Figure 3. Figure 3: Timing overhead of SC-GRPO vs. GRPO. Mean per-step wall-clock time (seconds) across training steps. 5.2 Computational Overhead SC-GRPO adds a single new operation compared to GRPO: a teacher forward pass for per-token KL weighting. As shown in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: In-Domain vs. OOD performance. Models trained on LiveCodeBench are evaluated on Codeforces. prevents collapse when the entire batch has near￾zero KL. A fixed constant achieves comparable performance but requires per-task calibration; p75 with floor is adaptive and hyperparameter-free. A3 Diversity coefficient The diversity signal re￾wards exploration rather than correctness, so it should serve as a weak ex… view at source ↗
Figure 6
Figure 6. Figure 6: Training dynamics on AIME 24 & 25. We compare validation performance of SC-GRPO (blue) and DAPO (red) throughout training. SC-GRPO consistently outperforms DAPO on both Avg@8 and Pass@8 metrics across both test sets. 0 100 200 300 400 500 Training Step 0.05 0.10 0.15 0.20 0.25 0.30 Entropy Policy Entropy During Training DAPO SC-GRPO [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Policy entropy during training. We com￾pare the entropy of SC-GRPO (blue) and DAPO (red) throughout training on DAPO-Math-17k. SC-GRPO maintains consistently higher entropy, indicating better exploration and diversity preservation. C.4 KL Distribution Evolution [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: Evolution of KL distribution during train￾ing. We track the percentiles of token-level KL diver￾gence throughout training. The shaded regions show the interquartile range (p25-p75, dark blue) and the p75- p90 range (light blue). The p75 line (blue) serves as our adaptive threshold, while p95 (red dashed) marks the upper tail. The distribution remains stable throughout training, with p75 consistently separa… view at source ↗
Figure 10
Figure 10. Figure 10: Token-level KL heatmap on a LiveCodeBench rollout. Each rollout token is shaded by its KL weight ft, which measures the shift in the student’s next-token distribution induced by inserting the verified trajectory τ into the teacher’s context [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
read the original abstract

Reinforcement learning with verifiable rewards (RLVR) has driven substantial progress in training LLMs for reasoning tasks, but representative methods such as GRPO assign uniform credit across all tokens, wasting gradient on routine tokens while under-crediting pivotal reasoning steps. Existing token-level credit assignment methods require resources beyond the model's own rollouts. GRPO variants rely on process reward models or ground-truth answers. Knowledge distillation assigns credit through per-token divergence but requires external teachers (On-Policy Distillation) or privileged information (On-Policy Self Distillation). However, these dependencies limit applicability in the pure RLVR setting. We observe that conditioning the model on its own verified trajectories induces a measurable per-token KL divergence between the original and conditioned distributions, and prove that distilling from a self-teacher constructed by verified trajectories leads to infeasible weighted-average solutions when multiple verified trajectories exist. We propose SC-GRPO (Self-Conditioned GRPO), which uses KL divergence mentioned before as a multiplicative weight on GRPO gradients. Across five benchmarks spanning math, code, and agentic tasks, SC-GRPO consistently outperforms 8.1% over GRPO and 5.9% over DAPO with stronger OOD performance. Moreover, SC-GRPO achieves higher performance than OPD.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper claims that conditioning an LLM on its own verified trajectories induces a per-token KL divergence that can be used as a multiplicative weight in the GRPO objective to achieve token-level credit assignment in RLVR without external teachers. It proves that self-distillation from verified trajectories yields infeasible weighted-average solutions when multiple trajectories exist, proposes SC-GRPO using this KL weight, and reports consistent gains of 8.1% over GRPO and 5.9% over DAPO across five benchmarks with stronger OOD performance.

Significance. If the KL weighting is shown to be theoretically justified and free of the averaging pathology identified in the self-distillation proof, the result would be significant: it would supply a purely internal mechanism for non-uniform credit assignment in verifiable-reward RL that outperforms uniform baselines and external-distillation methods while remaining applicable in the pure RLVR setting. The explicit infeasibility proof for self-distillation is a positive contribution that clarifies limitations of related approaches.

major comments (2)
  1. [Abstract and SC-GRPO description] Abstract / method proposal: the manuscript proves that distilling from a self-teacher on verified trajectories produces infeasible weighted-average solutions when multiple verified trajectories exist, yet introduces the induced per-token KL as a multiplicative weight on GRPO gradients without a derivation showing why this weighting avoids the same infeasibility or constitutes an unbiased estimator of token importance. This assumption is load-bearing for the central claim that SC-GRPO supplies effective credit assignment.
  2. [Results and benchmarks] Empirical section: the reported 8.1% and 5.9% gains are presented without accompanying details on the number of independent runs, statistical significance tests, or controls for trajectory-length variation that could systematically affect the magnitude of the per-token KL weights.
minor comments (1)
  1. The abstract states that SC-GRPO 'achieves higher performance than OPD' but does not specify whether OPD results are re-implemented under identical conditions or taken from prior work; clarify the comparison protocol.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and for recognizing the value of the infeasibility proof. We address each major comment below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract and SC-GRPO description] Abstract / method proposal: the manuscript proves that distilling from a self-teacher on verified trajectories produces infeasible weighted-average solutions when multiple verified trajectories exist, yet introduces the induced per-token KL as a multiplicative weight on GRPO gradients without a derivation showing why this weighting avoids the same infeasibility or constitutes an unbiased estimator of token importance. This assumption is load-bearing for the central claim that SC-GRPO supplies effective credit assignment.

    Authors: The infeasibility result applies specifically to self-distillation methods that construct a target distribution via weighted averaging across multiple verified trajectories, which can fall outside the support of the base model. SC-GRPO does not perform distillation or construct such an averaged target; the per-token KL is instead used solely as a multiplicative scalar on the existing GRPO policy gradient. This modulates credit without altering the optimization target. We agree that the current manuscript would benefit from an explicit derivation or expanded motivation section clarifying this distinction and the rationale for the weighting. We will add this material in revision. revision: partial

  2. Referee: [Results and benchmarks] Empirical section: the reported 8.1% and 5.9% gains are presented without accompanying details on the number of independent runs, statistical significance tests, or controls for trajectory-length variation that could systematically affect the magnitude of the per-token KL weights.

    Authors: We will expand the experimental section to report all results as means and standard deviations over three independent random seeds, include paired statistical significance tests against the baselines, and add a dedicated analysis of trajectory-length effects. This analysis will either normalize the KL weights by sequence length or evaluate performance on length-matched trajectory subsets to confirm that reported gains are not driven by length variation. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; derivation remains self-contained.

full rationale

The paper generates the per-token KL divergence directly from conditioning on its own verified rollouts inside each training iteration and applies it as a multiplier inside the existing GRPO objective. No equation is presented in which this multiplier is defined in terms of the target performance metric or fitted to the same data it is later claimed to predict. The separate mathematical observation that self-distillation yields infeasible averages when multiple verified trajectories exist is not used to justify the weighting scheme via self-citation; the weighting is introduced as an independent design choice whose effectiveness is evaluated empirically on external benchmarks. No self-citation chain, ansatz smuggling, or renaming of a known result is required for the central claim. The reported gains over GRPO and DAPO therefore rest on independent experimental outcomes rather than reducing to the inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The method rests on the domain assumption that self-induced KL divergence serves as a valid credit signal; no free parameters or invented entities are described in the abstract.

axioms (1)
  • domain assumption Conditioning the model on its own verified trajectories induces a per-token KL divergence that can be used as a credit weight.
    This observation is the foundation for constructing the multiplicative weight in SC-GRPO.

pith-pipeline@v0.9.1-grok · 5795 in / 1302 out tokens · 26141 ms · 2026-06-26T21:50:33.127136+00:00 · methodology

discussion (0)

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Reference graph

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