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arxiv: 2510.08141 · v7 · pith:HWNOVPQOnew · submitted 2025-10-09 · 💻 cs.LG

SCOPE-RL: Stable and Quantitative Control of Policy Entropy in RL Post-Training

Chen Wang , Zhaochun Li , Jionghao Bai , Hexuan Deng , Ge Lan , Yue Wang This is my paper

Pith reviewed 2026-05-21 20:26 UTC · model grok-4.3

classification 💻 cs.LG
keywords entropy controlpolicy optimizationreinforcement learninglarge language modelsGRPOentropy collapsepost-trainingreasoning models
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The pith

High-temperature positive samples increase policy entropy and can reverse its collapse in RL post-training of LLMs.

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

The paper identifies an asymmetry in how samples affect policy entropy under high-temperature sampling during reinforcement learning updates for large language models. Positive samples drawn at high temperature increase entropy while negative samples decrease it, and the authors derive that the derivative of entropy with respect to temperature is strictly positive precisely when entropy is falling under positive-sample updates. From this they build SCOPE-RL, which adds a regularization term built from temperature-adaptive positive samples to hold entropy inside a stable exploration range. Experiments show the method raises both Pass@1 and Pass@k scores over strong GRPO baselines without the oscillations or reward drops seen in earlier entropy bonuses. The work therefore supplies both a mechanism to escape premature convergence and evidence that a moderate, controllable level of exploration improves reasoning performance.

Core claim

Under high-temperature sampling, positive samples promote entropy growth while negative samples suppress it; when entropy is decreasing during policy updates its partial derivative with respect to temperature is strictly positive for positive-sample updates, so high-temperature positive samples can slow or reverse entropy collapse. SCOPE-RL therefore introduces a regularization term constructed from temperature-adaptive positive samples that achieves stable, quantitative entropy control and consistently improves Pass@1 and Pass@k.

What carries the argument

Regularization term built from temperature-adaptive positive samples that exploits the positive derivative of entropy with respect to temperature under positive-sample updates.

If this is right

  • SCOPE-RL keeps entropy inside a stable regime without introducing oscillatory behavior or reward degradation.
  • Escaping entropy collapse improves reasoning performance on Pass@1 and Pass@k metrics.
  • The benefit of higher entropy is non-monotonic, so an optimal intermediate level of exploration exists for RL post-training of reasoning LLMs.
  • The method supplies a concrete lever for quantitative entropy control that earlier bonuses and clipping approaches lack.

Where Pith is reading between the lines

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

  • The same temperature-adaptive positive-sample construction could be inserted into other policy-gradient algorithms that currently suffer rapid entropy decay.
  • If the derivative sign flips under negative samples, one could also design a complementary term that selectively damps entropy when it becomes too high.
  • The non-monotonic performance curve suggests that future work should search for the entropy target that maximizes downstream reasoning accuracy rather than simply maximizing or minimizing entropy.

Load-bearing premise

The observed asymmetry between positive and negative samples at high temperature generalizes beyond the tested models, tasks, and sampling temperatures, and the added regularization does not create new instabilities or reward degradation.

What would settle it

Apply SCOPE-RL to a new reasoning task or model family at the same temperature schedule and measure whether policy entropy still collapses to near-zero while Pass@1 and Pass@k remain no better than the GRPO baseline.

Figures

Figures reproduced from arXiv: 2510.08141 by Chen Wang, Ge Lan, Hexuan Deng, Jionghao Bai, Yue Wang, Zhaochun Li.

Figure 1
Figure 1. Figure 1: Entropy across five runs of AEPO. By adjusting [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Entropy dynamics under temperature-controlled [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Entropy trajectories of AEPO compared with [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

Reinforcement learning (RL) is a key paradigm for post-training large language models (LLMs), but the widely used Group Relative Policy Optimization (GRPO) often suffers from entropy collapse: exploration quickly disappears, policies converge prematurely, and sample diversity declines, ultimately harming training effectiveness. Existing remedies, including entropy bonuses and clip-based methods, rarely keep entropy within a stable exploration regime and often introduce oscillatory entropy or reward degradation. In this work, we identify a previously overlooked asymmetry in entropy dynamics: under high-temperature sampling, positive and negative samples have opposite effects on policy entropy. Specifically, high-temperature positive samples promote entropy growth, whereas negative samples suppress it. We provide a theoretical explanation for this phenomenon: when entropy decreases during policy updates, its derivative with respect to temperature is strictly positive under positive-sample updates, indicating that high-temperature positive samples can counteract entropy decay, thereby slowing entropy collapse and potentially reversing it. Motivated by this insight, we propose SCOPE-RL, a stable and quantitative entropy control framework through a regularization term constructed from temperature-adaptive positive samples. Extensive experiments show that SCOPE-RL consistently outperforms strong RL baselines on both Pass@1 and Pass@$k$. Our results provide evidence that escaping entropy collapse can improve reasoning performance, while also showing that the benefit is non-monotonic, with an optimal level of exploration for RL post-training in reasoning LLMs.

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 / 2 minor

Summary. The paper claims that GRPO-based RL post-training of LLMs suffers from entropy collapse, identifies an asymmetry in entropy dynamics under high-temperature sampling (positive samples promote entropy growth, negative samples suppress it), and provides a theoretical explanation that the derivative of entropy w.r.t. temperature is strictly positive under positive-sample updates when entropy is decreasing. Motivated by this, it introduces SCOPE-RL, a regularization framework using temperature-adaptive positive samples for stable quantitative entropy control, and reports consistent outperformance over baselines on Pass@1 and Pass@k with evidence of non-monotonic benefits from controlled exploration.

Significance. If the theoretical derivative result and empirical findings hold, the work supplies a principled mechanism for maintaining exploration in LLM RL post-training without the oscillations or reward degradation seen in prior entropy bonuses or clipping methods. The observation of an optimal (non-monotonic) exploration level for reasoning performance is a useful empirical contribution, and the quantitative control via temperature-adaptive regularization directly targets a load-bearing failure mode in current GRPO pipelines.

major comments (2)
  1. [Theoretical explanation (abstract and §3/§4)] Abstract and theoretical section: the central claim that 'its derivative with respect to temperature is strictly positive under positive-sample updates' is stated without any derivation steps, full equations, or proof. It is therefore impossible to verify independence from the regularization coefficient or to check whether the sign remains positive when positive/negative labels are assigned under the temperature-altered distribution produced by GRPO.
  2. [Experimental results] Experiments: the reported consistent outperformance on Pass@1 and Pass@k lacks error bars, ablation results on the regularization coefficient, and any analysis of how data exclusions or fitting choices affect the entropy-control claim. This weakens the assertion of 'quantitative' and 'stable' control.
minor comments (2)
  1. [Method] Clarify the exact form of the regularization term and its dependence on the temperature schedule; the current description leaves open whether the term introduces new instabilities outside the tested regime.
  2. [Abstract and experiments] Notation: Pass@$k$ should be written consistently as Pass@k throughout.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Theoretical explanation (abstract and §3/§4)] Abstract and theoretical section: the central claim that 'its derivative with respect to temperature is strictly positive under positive-sample updates' is stated without any derivation steps, full equations, or proof. It is therefore impossible to verify independence from the regularization coefficient or to check whether the sign remains positive when positive/negative labels are assigned under the temperature-altered distribution produced by GRPO.

    Authors: We agree that the theoretical claim in the abstract and §3 requires explicit derivation steps for verifiability. In the revised manuscript we will expand the theoretical section to include the full step-by-step derivation of the entropy derivative with respect to temperature under positive-sample updates. The added material will show all intermediate equations, state the assumptions clearly, demonstrate independence from the regularization coefficient, and address the sign of the derivative when labels are assigned under the temperature-altered GRPO distribution. revision: yes

  2. Referee: [Experimental results] Experiments: the reported consistent outperformance on Pass@1 and Pass@k lacks error bars, ablation results on the regularization coefficient, and any analysis of how data exclusions or fitting choices affect the entropy-control claim. This weakens the assertion of 'quantitative' and 'stable' control.

    Authors: We acknowledge that the experimental section would be strengthened by additional reporting. In the revision we will add error bars computed over multiple independent runs for all Pass@1 and Pass@k results. We will also include ablations over a range of regularization coefficients to illustrate the stability of entropy control. Finally, we will add a short analysis subsection discussing data exclusions and fitting choices and their influence on the entropy-control observations. revision: yes

Circularity Check

0 steps flagged

No significant circularity; theoretical claim presented as independent derivation without reduction to inputs by construction.

full rationale

The abstract presents a theoretical explanation that the derivative of entropy w.r.t. temperature is strictly positive under positive-sample updates when entropy is decreasing. No equations, proofs, or self-citations are provided in the given text that would allow exhibiting a specific reduction (e.g., the claimed derivative equaling a fitted parameter or input by definition). The regularization term is motivated by the insight rather than defined in terms of it. No fitted-input-called-prediction, self-definitional, or uniqueness-imported patterns are identifiable. The derivation chain appears self-contained against external benchmarks in the abstract.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on an unproven generalization of the entropy-temperature derivative and on the effectiveness of the constructed regularization term; no explicit free parameters or invented entities are named in the abstract.

free parameters (1)
  • regularization coefficient
    Likely introduced to scale the temperature-adaptive positive-sample term; value would be chosen or fitted during experiments.
axioms (1)
  • domain assumption When entropy decreases during policy updates, its derivative with respect to temperature is strictly positive under positive-sample updates.
    This is the load-bearing theoretical statement invoked to justify the regularization construction.

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discussion (0)

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Forward citations

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  2. Understanding and Preventing Entropy Collapse in RLVR with On-Policy Entropy Flow Optimization

    cs.LG 2026-05 unverdicted novelty 6.0

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  3. Advantage Collapse in Group Relative Policy Optimization: Diagnosis and Mitigation

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