REVIEW 4 major objections 6 minor 3 cited by
EDGE-GRPO: Entropy-Driven GRPO with Guided Error Correction for Advantage Diversity
T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash
Pith's one-line read EDGE-GRPO claims that injecting reference solutions into GRPO response groups and rescaling advantages by policy entropy fixes advantage collapse, with over 20% average gains from just 1K training samples.
desk verdict Real empirical gains for math RL with 1K samples, but GEC breaks GRPO's on-policy assumption and the 'advantage collapse' story needs a reframe before I'd believe it as RL. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the advantage itself. In vanilla GRPO the advantage $A_i = (r_i - \mathrm{mean}(\{r_1,\dots,r_G\}))/\mathrm{std}(\{r_1,\dots,r_G\})$ collapses to zero whenever all group rewards tie, and EDGE-GRPO replaces it with an entropy-scaled advantage $\hat{A}_i = A_i / \hat{P}_i$, where $\hat{P}_i$ is the response's average per-token policy entropy divided by the group mean entropy. The second mechanism, GEC, reshapes group composition by inserting correct answers or reference solutions into groups of model-generated responses, turning all-correct or all-incorrect groups into mixed groups so that $A_i$ is nonzero before scaling. Together these give the policy gradient a nonzero, entropy-discriminated training signal on every sampled question.
What would settle it
Run a control that removes the policy-gradient contribution of all GEC-injected responses, or equivalently trains on the same 1K data with only the reference solutions under a supervised cross-entropy loss; if the control matches EDGE-GRPO's pass@1, the advantage-scaling mechanism is not what drives the gains. A second check is to compute the importance ratio $\pi_\theta(o)/\pi_{\theta_{\mathrm{old}}}(o)$ for injected reference responses during training; if the ratios for injected tokens are extreme or the clipped objective saturates on them, the GRPO surrogate is not being applied to on-policy samples.
Extended reading notes
Core claim
On the paper's own terms, the central discovery is quantitative evidence that model self-reflection is a weak lever and that sample-level policy entropy is miscalibrated, so neither forced reflection nor unconditional entropy control fixes GRPO's advantage collapse. The proposed EDGE-GRPO algorithm instead combines Guided Error Correction (GEC) with Entropy-Driven Advantage (EDA). GEC takes each incorrect response in a group and, with probability 0.5 prompts regeneration, with probability 0.25 injects the correct answer next to a reflection prompt, and with probability 0.25 replaces the response with a reference solution, guaranteeing a mix of correct and incorrect completions in every group. EDA computes each response's per-token policy entropy $P_i$, normalizes it as $\hat{P}_i = P_i / \mathrm{mean}(\{P_1,\dots,P_G\})$, and forms $\hat{A}_i = A_i / \hat{P}_i$, so that correct-and-confident responses get higher advantage and incorrect-but-confident responses get a harsher penalty. The paper reports that this maintains higher intra-group advantage variance during training and improves pass@1 on AIME, AMC, MATH, Minerva, and OlympiadBench with one epoch on 1K DeepScaleR samples, for both Qwen2.5-Math-1.5B and Qwen2.5-Math-7B.
Load-bearing premise
GEC inserts reference solutions and answer-injected responses into the GRPO group and treats them as if the current policy generated them, without any importance correction; if those off-policy sequences are not valid on-policy samples, the reported gains could come from supervised memorization of injected answers rather than from the RL mechanism.
Editorial extensions
If this is right
- With one epoch on 1K problems, EDGE-GRPO raises average pass@1 over vanilla GRPO from 40.32 to 48.08 on Qwen2.5-Math-1.5B and from 46.47 to 49.30 on Qwen2.5-Math-7B using the random split, with larger gaps on the hard split.
- Intra-group advantage variance stays high throughout training instead of decaying toward zero, indicating that advantage collapse is being actively mitigated rather than avoided by data filtering.
- Ablations show that forced reflection alone gives small or negative gains, forced reflection plus EDA helps only when groups already contain both correct and incorrect responses, and full EDGE-GRPO is required when most groups are all incorrect.
- The method transfers to harder data: on DeepScaleR-Hard-1K, where roughly 80% of questions have no correct response within the group, the 7B model's average improves from 47.69 to 53.21.
- The approach requires reference solutions and final answers for training questions, which limits it to domains where such ground truth is available.
Reading between the lines
- Because GEC inserts off-policy sequences into a GRPO surrogate derived for old-policy samples, part of the reported gain may come from supervised imitation of the injected reference solutions; a control experiment that trains only on injected references with a standard language-modeling loss would separate the RL effect from the data effect.
- The entropy scaling treats low per-token entropy as confidence, yet the paper itself shows many low-entropy responses are wrong, so EDA is better read as a certainty-weighted advantage renormalization than as a calibrated confidence measure.
- The same two-part recipe should transfer to code generation or other verifiable-reward domains where reference solutions exist, and the hard-data version suggests that deliberately selecting problems the current policy always fails maximizes the benefit.
- The reported 1K-sample competitiveness suggests that data composition and guaranteed response mix, rather than dataset scale, may be the dominant factors in small-scale GRPO training.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. EDGE-GRPO is a training-time modification of GRPO for mathematical reasoning LLMs. The paper first reports two empirical findings: (i) 'self-reflection' tokens in model responses are usually associated with lower accuracy, and forced reflection rarely turns incorrect answers into correct ones; (ii) although models are on average more confident in correct responses, at the sample level a large fraction of incorrect responses have low policy entropy and a large fraction of correct responses have high entropy. Based on these findings, the authors modify GRPO at two levels. At the response level, Guided Error Correction (GEC) takes every incorrect response in a training group and, with fixed probabilities, either asks the model to regenerate it with a short reflection prompt, injects the correct answer after such a prompt, or replaces it with a reference solution. At the signal level, Entropy-Driven Advantage (EDA) divides the GRPO advantage of each response by its length-normalized policy entropy, so that correct low-entropy responses receive larger positive advantages and incorrect low-entropy responses receive more negative advantages. Training for one epoch on 1K DeepScaleR samples, the method is evaluated on AIME, AMC, MATH500, Minerva, and OlympiadBench with Qwen2.5-Math-1.5B and Qwen2.5-Math-7B; the full EDGE-GRPO exceeds vanilla GRPO in seven of eight model/data-set combinations, with larger gains on the hard subset.
Significance. If taken at face value, the paper offers a useful empirical contribution to small-data RL fine-tuning for reasoning: it systematically documents the limited benefit of forced reflection for the tested models, quantifies sample-level entropy/correctness miscalibration, and shows that reference-solution injection plus entropy-scaled advantages yields large accuracy gains with only 1K training samples. The comparison to SFT on the same 1K reference solutions is a meaningful control and partially mitigates the concern that the reported gains are pure memorization of the injected answers. The release of code is also a strength for reproducibility. The significance is weakened, however, by three issues: no repeated seeds or error bars are reported; the entropy-driven scaling in Eqs. (6)-(7) is not fully specified; and, most importantly, the GEC responses are trained through a GRPO surrogate that is not a valid policy-gradient objective for off-policy or reference-injected sequences unless an importance correction is added.
major comments (4)
- [Section 3.2, Response-level: GEC, and Eq. (1).] The GRPO surrogate in Eq. (1) is derived under the assumption that each response o_i is sampled from pi_theta_old(·|q). GEC introduces responses that violate this assumption: regenerations conditioned on q plus the model's own incorrect trace and a reflection prompt, answer-injected responses whose final answer is forced, and reference solutions that were never sampled from the policy. For the latter two types, the ratio pi_theta/pi_theta_old is not the correct importance weight; for reference solutions pi_theta_old can be very small, and the clipped ratio then saturates at 1±epsilon, turning the update into a supervised nudge whose sign is set by the group-normalized advantage. With high probability, GEC inserts a correct injected response into a previously all-incorrect group, so the positive advantage on that response can increase its likelihood directly. The paper reports no diagnostics (importance-ratio magnitudes, fraction of clipped updates, or gradient contribution per GEC type), and the SFT rows in Tables 1 and 2 do not by themselves rule out reward-conditioned memorization of the reference answers. Please add an importance correction or a behavior-model term, or reformulate GEC as a separate supervised term, so that the claim that EDGE-GRPO is an RL method is supported.
- [Tables 1 and 2, Experimental Setup.] No seed information or error bars are reported, so the 'consistent improvement' claim rests on single comparisons. The fragility of the ablation is visible in the tables: in Table 1, Qwen2.5-Math-7B with '+ Force-R & EDA' scores 45.71, below vanilla GRPO's 46.47, and in Table 2 the same variant scores 45.19 vs. 47.69. The differences between the full EDGE-GRPO and vanilla GRPO (e.g., 1.5B random: 48.08 vs. 40.32; 7B hard: 53.21 vs. 47.69) are large, but without repeated runs or variance estimates one cannot tell whether the smaller gains are real. Please run at least three seeds for the main comparisons and the ablation, and report means and standard deviations (or per-run results).
- [Figure 5, Signal-level: EDA.] The advantage-variance plot in Figure 5 is not independent evidence for the claim that the policy-gradient signal is healthier under EDGE-GRPO. Because GEC intentionally inserts correct responses into groups that would otherwise be all-incorrect, the intra-group reward standard deviation, and therefore the advantage variance, rises by construction even if the clipped surrogate is not functioning as a valid policy gradient. To separate diversity from supervision, please (i) plot advantage variance computed only on responses actually sampled from the policy, and (ii) include an ablation in which GEC injects a random but distinct answer or reference solution rather than the ground-truth correct answer. This would clarify whether the observed improvements come from advantage diversity or from injected labels.
- [Eqs. (6)-(7), Signal-level: EDA.] The EDA definition divides by the normalized entropy P_i without any stated lower bound or clipping. For low-entropy responses, which are exactly the ones the method most strongly rewards or penalizes, this can produce very large advantages and unstable updates. The text says the entropy is scaled to keep values in a reasonable range, but the scaling or clipping mechanism is not specified in Eqs. (6)-(7) or in the implementation details. Please define the exact transformation and report gradient-norm statistics or advantage distributions to demonstrate stability.
minor comments (6)
- [Section 3.2, Response-level: GEC.] The sentence 'These three strategies ensure that each group of responses contains positive examples with correct answers' is too strong: the prompt-and-regenerate branch (P=0.5) can still return an incorrect answer, so the guarantee is probabilistic rather than absolute.
- [Eq. (5) and the Appendix.] The notation for the relative confidence metric uses both EntropyWrong (Eq. (5)) and EntropyIncorrect (Appendix); please unify the notation.
- [Section 3.2, Signal-level: EDA.] The claim that EDA gives distinct final advantages to 'different responses' is not implied by Eq. (7): two responses with the same original advantage and the same normalized entropy receive the same EDA value.
- [Contributions, Introduction.] The contribution bullet 'consistently achieving over 20% improvement' compares with the base model; please make explicit that the gains over the vanilla GRPO baseline are smaller (e.g., 48.08 vs. 40.32 for Qwen2.5-Math-1.5B).
- [Experimental Setup.] The description 'generate one response per GPU, resulting in a total of 1K training steps' for Qwen2.5-Math-7B is ambiguous; please clarify the exact effective batch size, number of optimizer updates, and how the 1K training steps correspond to one epoch.
- [Throughout the manuscript.] Minor typographic issues: 'Qwen2.5-math-7B' appears in the experimental setup, and 'DeepSeek-R1-Di still-Qwen-1.5B' appears in Figure 2; the model names should be rendered consistently as Qwen2.5-Math-7B and DeepSeek-R1-Distill-Qwen-1.5B.
Circularity Check
No significant circularity: the method's objective modifications are transparent and its main claims rest on held-out benchmarks.
full rationale
The paper's central effectiveness claims are measured on held-out mathematical benchmarks (AIME, AMC, MATH500, Minerva, OlympiadBench), which are external to the training set and to the EDGE-GRPO construction. The Entropy-Driven Advantage of Eq. (7) is a direct, unparameterized modification of the GRPO advantage; it is not fitted to any target and does not by itself guarantee benchmark improvement. Guided Error Correction injects reference or answer-injected responses into each GRPO group, which mechanically increases intra-group reward variance; the paper explicitly presents this as the intended mechanism for mitigating advantage collapse rather than as an independent empirical discovery. That a group containing guaranteed positive and negative examples has nonzero advantage variance follows from the definition of Eq. (2), but this is the method's stated design, not a hidden circular derivation of the benchmark results. The only citation to the authors' own prior work (Zhang et al. 2025b) appears in a related-work list of rule-based reward usage and is not load-bearing. The off-policy concern about reference solutions being scored through a surrogate derived for on-policy samples is a validity and correctness issue, not a circularity. No prediction in the paper reduces by construction to its inputs, and no self-citation chain forces the conclusions.
Assumptions & free parameters
free parameters (3)
- GEC probability for prompt-and-regenerate =
0.5
- GEC probability for direct answer injection =
0.25
- GEC probability for reference solution replacement =
0.25
assumptions (4)
- ad hoc to paper The GRPO surrogate objective (Eq. 1) remains a valid training signal when applied to responses not sampled from the policy (reference solutions and answer-injected responses).
- domain assumption Rule-based rewards based solely on final answer correctness are sufficient to evaluate all responses, including injected ones.
- domain assumption KL divergence can be removed without destabilizing training.
- domain assumption Per-token policy entropy averaged over the response is a meaningful confidence signal at the sample level.
Cite this review
Pith. "Pith review of EDGE-GRPO: Entropy-Driven GRPO with Guided Error Correction for Advantage Diversity." pith.science (2026). https://pith.science/paper/P4HS375L
@misc{pith2026250721848,
author = {Pith},
title = {Pith review of: EDGE-GRPO: Entropy-Driven GRPO with Guided Error Correction for Advantage Diversity},
year = {2026},
howpublished = {\url{https://pith.science/paper/P4HS375L}},
note = {Machine review of arXiv:2507.21848}
}
read the original abstract
Large Language Models (LLMs) have made remarkable progress in enhancing step-by-step reasoning through reinforcement learning. However, the Group Relative Policy Optimization (GRPO) algorithm, which relies on sparse reward rules, often encounters the issue of identical rewards within groups, leading to the advantage collapse problem. Existing works typically address this challenge from two perspectives: enforcing model reflection to enhance response diversity, and introducing internal feedback to augment the training signal (advantage). In this work, we begin by analyzing the limitations of model reflection and investigating the policy entropy of responses at the fine-grained sample level. Based on our experimental findings, we propose the EDGE-GRPO algorithm, which adopts \textbf{E}ntropy-\textbf{D}riven Advantage and \textbf{G}uided \textbf{E}rror Correction to effectively mitigate the problem of advantage collapse. Extensive experiments on several main reasoning benchmarks demonstrate the effectiveness and superiority of our approach. It is available at https://github.com/ZhangXJ199/EDGE-GRPO.
Figures
Figures from the paper (4 more)
Forward citations
Cited by 3 Pith papers
-
Compress the Easy, Explore the Hard: Difficulty-Aware Entropy Regularization for Efficient LLM Reasoning
CEEH selectively applies entropy regularization to hard questions and a shortest-correct-length penalty to easy ones, reducing reasoning length while preserving accuracy across six math benchmarks.
-
Harnessing Uncertainty: Entropy-Modulated Policy Gradients for Long-Horizon LLM Agents
EMPG re-weights policy-gradient updates by step-level token entropy, amplifying confident correct actions and muting uncertain ones, and adds a future-clarity bonus.
-
When Correct Solutions Repeat: Rarity-Aware Credit Redistribution for GRPO
Cue-GRPO redistributes GRPO's positive rewards across clusters of correct traces defined by deterministic strategy cues, improving high-budget AIME pass@k on two 7B/8B models.
Reference graph
Works this paper leans on
-
[1]
Liu, K.; Shen, C.; Zhang, Z.; Liu, J.; Yuan, X.; et al. 2025a. Efficient Reasoning Through Suppression of Self- Affirmation Reflections in Large Reasoning Models. arXiv preprint arXiv:2506.12353. Liu, Z.; Chen, C.; Li, W.; Qi, P.; Pang, T.; Du, C.; Lee, W. S.; and Lin, M. 2025b. Understanding r1-zero-like training: A critical perspective. arXiv preprint a...
-
[2]
arXiv preprint arXiv:2506.14758
Reasoning with Exploration: An En- tropy Perspective. arXiv preprint arXiv:2506.14758. Cui, G.; Yuan, L.; Wang, Z.; Wang, H.; Li, W.; He, B.; Fan, Y .; Yu, T.; Xu, Q.; Chen, W.; et al
-
[3]
arXiv preprint arXiv:2502.01456
Process reinforcement through implicit rewards. arXiv preprint arXiv:2502.01456. Fatemi, M.; Rafiee, B.; Tang, M.; and Talamadupula, K
-
[4]
arXiv preprint arXiv:2504.05185
Concise reasoning via reinforcement learning. arXiv preprint arXiv:2504.05185. Gao, Z.; Chen, L.; Zhou, J.; and Dai, B
-
[5]
arXiv preprint arXiv:2505.20282
One-shot Entropy Minimization. arXiv preprint arXiv:2505.20282. Guo, D.; Yang, D.; Zhang, H.; Song, J.; Zhang, R.; Xu, R.; Zhu, Q.; Ma, S.; Wang, P.; Bi, X.; et al
-
[6]
arXiv preprint arXiv:2501.12948
Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning. arXiv preprint arXiv:2501.12948. He, C.; Luo, R.; Bai, Y .; Hu, S.; Thai, Z. L.; Shen, J.; Hu, J.; Han, X.; Huang, Y .; Zhang, Y .; et al
-
[9]
arXiv preprint arXiv:2503.24290
Open-reasoner-zero: An open source approach to scaling up reinforcement learning on the base model. arXiv preprint arXiv:2503.24290. Jaech, A.; Kalai, A.; Lerer, A.; Richardson, A.; El-Kishky, A.; Low, A.; Helyar, A.; Madry, A.; Beutel, A.; Carney, A.; et al
-
[10]
arXiv preprint arXiv:2412.16720
Openai o1 system card. arXiv preprint arXiv:2412.16720. Lewkowycz, A.; Andreassen, A.; Dohan, D.; Dyer, E.; Michalewski, H.; Ramasesh, V .; Slone, A.; Anil, C.; Schlag, I.; Gutman-Solo, T.; et al
Show all 23 references
-
[13]
arXiv preprint arXiv:2501.19393
s1: Simple test-time scaling. arXiv preprint arXiv:2501.19393. Schulman, J.; Wolski, F.; Dhariwal, P.; Radford, A.; and Klimov, O
-
[15]
arXiv preprint arXiv:2402.03300
Deepseekmath: Pushing the limits of mathematical reasoning in open lan- guage models. arXiv preprint arXiv:2402.03300. Su, J.; Healey, J.; Nakov, P.; and Cardie, C
-
[16]
arXiv preprint arXiv:2505.00127
Be- tween underthinking and overthinking: An empirical study of reasoning length and correctness in llms. arXiv preprint arXiv:2505.00127. Team, K.; Du, A.; Gao, B.; Xing, B.; Jiang, C.; Chen, C.; Li, C.; Xiao, C.; Du, C.; Liao, C.; et al
-
[17]
5: Scaling reinforcement learning with llms
Kimi k1. 5: Scaling reinforcement learning with llms. arXiv preprint arXiv:2501.12599. Tian, X.; Zhao, S.; Wang, H.; Chen, S.; Ji, Y .; Peng, Y .; Zhao, H.; and Li, X
-
[18]
arXiv preprint arXiv:2503.19855
Think twice: Enhancing llm reasoning by scaling multi-round test-time thinking. arXiv preprint arXiv:2503.19855. von Werra, L.; Belkada, Y .; Tunstall, L.; Beeching, E.; Thrush, T.; Lambert, N.; Huang, S.; Rasul, K.; and Gal- lou´edec, Q
-
[19]
arXiv preprint arXiv:2506.01713
Srpo: En- hancing multimodal llm reasoning via reflection-aware rein- forcement learning. arXiv preprint arXiv:2506.01713. Wang, H.; Qu, C.; Huang, Z.; Chu, W.; Lin, F.; and Chen, W. 2025a. Vl-rethinker: Incentivizing self-reflection of vision-language models with reinforcemen...
-
[20]
5-math tech- nical report: Toward mathematical expert model via self- improvement
Qwen2. 5-math tech- nical report: Toward mathematical expert model via self- improvement. arXiv preprint arXiv:2409.12122. Yu, Q.; Zhang, Z.; Zhu, R.; Yuan, Y .; Zuo, X.; Yue, Y .; Dai, W.; Fan, T.; Liu, G.; Liu, L.; et al
-
[21]
arXiv preprint arXiv:2503.14476
Dapo: An open- source llm reinforcement learning system at scale. arXiv preprint arXiv:2503.14476. Zeng, W.; Huang, Y .; Liu, Q.; Liu, W.; He, K.; Ma, Z.; and He, J
-
[22]
Zhang, Q.; Wu, H.; Zhang, C.; Zhao, P.; and Bian, Y
Simplerl-zoo: Investigating and taming zero re- inforcement learning for open base models in the wild.arXiv preprint arXiv:2503.18892. Zhang, Q.; Wu, H.; Zhang, C.; Zhao, P.; and Bian, Y . 2025a. Right question is already half the answer: Fully unsupervised llm reasoning incen...
-
[23]
arXiv preprint arXiv:2503.05132
R1-Zero’s” Aha Moment” in Visual Reasoning on a 2B Non-SFT Model. arXiv preprint arXiv:2503.05132. Appendix Reflection Keywords We determine whether a reflection phenomenon has oc- curred based on the presence of reflection-related key- words in the response. The set of 15 key...
-
[2017]
arXiv preprint arXiv:1707.06347
Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347. Shao, Z.; Wang, P.; Zhu, Q.; Xu, R.; Song, J.; Bi, X.; Zhang, H.; Zhang, M.; Li, Y .; Wu, Y .; et al
-
[2021]
arXiv preprint arXiv:2103.03874
Measuring mathematical problem solving with the math dataset. arXiv preprint arXiv:2103.03874. Hu, J.; Zhang, Y .; Han, Q.; Jiang, D.; Zhang, X.; and Shum, H.-Y
- [2022]
-
[2024]
arXiv preprint arXiv:2402.14008
Olympiad- bench: A challenging benchmark for promoting agi with olympiad-level bilingual multimodal scientific problems. arXiv preprint arXiv:2402.14008. Hendrycks, D.; Burns, C.; Kadavath, S.; Arora, A.; Basart, S.; Tang, E.; Song, D.; and Steinhardt, J
-
[2025]
arXiv preprint arXiv:2505.12346
Seed-grpo: Semantic entropy enhanced grpo for uncertainty-aware policy optimization. arXiv preprint arXiv:2505.12346. Cheng, D.; Huang, S.; Zhu, X.; Dai, B.; Zhao, W. X.; Zhang, Z.; and Wei, F
Reviewed August 6, 2026 · model on record in the stance chip above.
Discussion (0). Sign in to comment.