Title: KTAE: A Model-Free Algorithm to Key-Tokens Advantage Estimation in Mathematical Reasoning
Venue: NeurIPS 2025
Accepted: yes
Keywords: Large language model;Reinforcement learning;Mathematical reasoning
Abstract: Recent advances have demonstrated that integrating reinforcement learning with rule-based rewards can significantly enhance the reasoning capabilities of large language models (LLMs), even without supervised fine-tuning (SFT). However, prevalent reinforcement learning algorithms such as GRPO and its variants like DAPO, suffer from a coarse granularity issue when computing the advantage. Specifically, they compute rollout-level advantages that assign identical values to every token within a sequence, failing to capture token-specific contributions. To address this limitation, we propose Key-token Advantage Estimation (KTAE)—a novel algorithm that estimates fine-grained, token-level advantages without introducing additional models. KTAE leverages the correctness of sampled rollouts and applies statistical analysis to quantify the importance of individual tokens within a sequence to the final outcome. This quantified token-level importance is then combined with the rollout-level advantage to obtain a more fine-grained token-level advantage estimation. Empirical results show that models trained with GRPO+KTAE and DAPO+KTAE outperform baseline methods across five mathematical reasoning benchmarks. Notably, they achieve higher accuracy with shorter responses and even surpass R1-Distill-Qwen-1.5B using the same base model.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nKey-Token Advantage Estimation (KTAE) tackles the coarse-granularity problem of existing RLHF variants (e.g., GRPO, DAPO) by computing fine-grained, token-level advantages instead of assigning a single rollout-level value to every token. The method statistically infers each token’s contribution to the final correctness signal and blends this with the rollout-level advantage, remaining model-free and easy to plug into standard policy-gradient pipelines. Empirically, GRPO+KTAE and DAPO+KTAE outperform their baselines on five mathematical-reasoning benchmarks, achieving higher accuracy with shorter answers and even surpassing R1-Distill-Qwen-1.5B when using the same backbone.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n- **Fine-grained, token-level credit assignment:** Existing RLHF-style methods propagate a single rollout-level advantage to every token, so they cannot tell which parts of the answer actually “earned” the reward. KTAE attacks this long-standing credit-assignment bottleneck by statistically estimating each token’s marginal contribution to the final correctness signal, giving the optimizer far more informative gradients. \n- **Model-free and compute-efficient:** Unlike token-reward approaches that bolt on an auxiliary critic or a learned reward network, KTAE is purely analytical; it re-weights the existing rollout advantage with a closed-form importance estimate. That means no extra parameters, no new forward passes, and no critic-training instability, making it easy to drop into any policy-gradient pipeline. This lightweight property will appeal to practitioners who already find RLHF training expensive.\n- **Consistent empirical gains on math-reasoning suites:** Across five benchmark datasets for mathematical reasoning, GRPO+KTAE and DAPO+KTAE deliver higher exact-answer accuracy while also shortening the generated solutions. \n\n## Weaknesses\n- **Heuristic, non-learned composition of statistics:** KTAE sidesteps a learned critic by multiplying four hand-selected statistics—Fisher’s test score, information gain, token frequency, and the rollout-level advantage—to obtain a key-token value. While this model-free choice keeps computation cheap, the paper offers no theoretical rationale for using a product, nor does it explore alternative compositions or automatic ways to learn the combination. The ablation study shows each component matters in isolation, but I am left unsure whether such composition structure is robust when ported to new domains.\n- **Surrounding contexts are ignored when scoring tokens:** A token’s value can depend on where it appears (e.g., a numeral “2” inside a denominator vs. as a final answer). Because KTAE treats each token independently, it may mis-attribute credit when the semantic payoff arises only from multi-token spans or long-range dependencies. That limitation becomes more glaring in text-rich domains (dialogue, code) where meaning is rarely confined to a single token.\n- **Sparse diagnosis of performance regressions:** Although KTAE generally boosts accuracy, it drops on two of the five benchmarks (AIME24 for GRPO+KTAE and OlympiadBench for DAPO+KTAE). The paper merely remarks that this is “one fewer correct answer” in a small test set, offering no deeper probe into why the estimator hurt — for instance, whether token-level weighting mis-fires on very short proofs, whether the length-penalty interacts with Olympiad-style solutions, or whether sampling variance alone explains the loss. A concise error taxonomy (e.g., mis-tagged key tokens vs. over-shortened outputs) plus a couple of annotated examples would clarify whether the regression stems from KTAE itself or dataset. \n- **Domain scope is narrow:** All experiments revolve around deterministic, auto-gradable math problems. It is unknown whether KTAE remains effective in open-ended generation where rewards are noisy, delayed, or reference-based (e.g., ChatGPT-style helpfulness RLHF). A broader evaluation—or at least a discussion of potential adaptations—would strengthen claims of generality.\n\nQUESTIONS:\nPlease consider the weaknesses outlined above; if subsequent responses offer convincing clarifications, I will be happy to revisit and potentially raise my score.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work studies the problem of doing reinforcement learning finetuning for large language models. It has been observed that many existing methods (e.g., GRPO and DAPO) typically assigns a uniform advantage function for the entire rollout, lacking more fine-grained granularity. This work proposes the KATE framework, which can be directly leveraged within GRPO and DAPO to provide fine-grained, token-level advantages without introducing additional models. In particular, KATE builds a contingency table and uses hypothesis testing for estimating the association between tokens and the final correctness, which is further complemented with the information-theory-based method using conditional entropy. Also, to determine the direction of the association, the idea of term frequency is also incorporated. With all these approaches combined, a final importance score is computed, which is used as the token-level advantage. The effectiveness of KATE is demonstrated via experiments through its combination with GRPO and DAPO on training models with different sizes.\n\nSTRENGTHS AND WEAKNESSES:\nI have a very mixed feeling about the proposed method, which are listed in the following.\n\n\nStrength:\n\n- It is indeed an interesting and important problem of how to assign more fine-grained training signals for the tokens in the rollout during RL finetuning of LLM. I appreciate the authors' valuable efforts in this direction.\n\n- Many different ideas are incorporated and nicely combined. The final score handles both the strength of the association and the direction of the association.\n\n- There is no additional model training required, and the proposed method can be easily incorporated with GRPO, DAPO, and other similar methods.\n\nWeakness:\n-  From one perspective, as mentioned above, it is carefully crafted with many different ideas incorporated. On the other hand, it is slightly against my intuition that \"directly counting\" the token occurrence and the conditional entropy can be a strong indication of the association of the token with the response correctiveness. In particular, it seems that the method ignores the order of the tokens and the connection between tokens, which may be important.\n\n- Also, the constructed method is largely heuristic without many theoretical insights. In particular, the score will be served as an advantage function while its connection with the advantage function is unclear to me, which seems to be more of an artifact created based on intuitions.\n\n- Furthermore, the proposed method seems to be mostly suitable for algorithms like GRPO and DAPO, which performs multiple rollouts from one prompt. It does not really apply for PPO and others (which uses value networks to estimate advantages). This may limit the usefulness of the proposed method. In particular, from a higher-perspective, to obtain a more fine-grained advantage estimation, it essentially (based on my understanding) viewing the problem from the single-step one (bandits) to a multiple-step one (MDP), and algorithms like PPO are well-desighed for the later case (although the current LLM training are mostly treated in a single-step manner)\n\nQUESTIONS:\nI would appreciate the authors' thoughts on the concerns that I raised in the weakness section, in particular, regarding whether the current method simplifies the token-correctness association too much (i.e., ignoring some potentially important factors), how the final score is connected to the advantage, and how the proposed method can be positioned beyond GRPO and DAPO.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes KtAE, a model-free algorithm to estimate token-level advantage of model rollouts to provide finer-grained supervision signals in LLM reinforcement learning. \n\nSpecifically, KtAE constructs contingency tables based on the correctness of sampled rollouts and uses statistical methods (Fisher's exact test and Information Gain) to quantify each token's association with correct outcomes. \n\nThe proposed method can be empirically deployed on existing algorithms GRPO and DAPO to further improve model performance. Interestingly, the proposed method can not only improve the accuracy, but also speed up the inference by generating shorter responses.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n* The idea of using statistical association measures to identify key tokens is innovative and economic. The empirical performance is also surprisingly appealing. The case study of \"aha moment\" as a result of KtAE provides the insight that such token-level advantage helps to elicit the self-reflection behaviors of LLMs.\n* Given the improvement in both performance and efficiency (reduced response length), the proposed method demonstrates strong empirical results with reasonable cost, showing potential to be applied at scale.\n* The detailed mathematical formulations and implementation details show technical maturity.\n\n### Weaknesses\n* While the empirical results are strong, KtAE is mainly a combination of statistical measures. Given the sparsity of token-level supervision signals (especially when rollout budget is limited), it is hard to quantify the quality and stability of the token-level advantages. The authors could either (i) provide detailed convergence analysis or theoretical guarantees about the quality of the token-level advantages; or (ii) conduct further ablation study to probe the sensitivity of KtAE to the statistical hyperparameters such as the number of rollouts and length of responses.\n* The token-level advantages are mainly determined by the binary rewards and statistical estimation. This makes KtAE a bit limited to mathematical reasoning (which has determined final answers). \n* KtAE introduces some additional hyperparameters (h1, h2, h3, k1, b) which may need to be adjusted on different datasets. It would be better to include some sensitivity analysis to help understand the generalizability and stability of the method.\n* While the token-level advantage calculation does not require additional model calls, it would still be helpful to discuss the computational overhead from this process to understand the complexity of the method.\n\nQUESTIONS:\n* How could KtAE be compared and combined with fine-grained reinforcement learning methods? For example, what if we have multiple reward models for different features and different granularities?\n* The relationship between BM25-inspired frequency calculation and token importance is unclear. Could you elaborate further on this?\n* What if some tokens appear rarely across rollouts? How often would such corner cases occur and impact the final performance?\n* Could you provide timing comparisons between KtAE and corresponding baseline to discuss its scalability to larger models and batch sizes?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

comments: SUMMARY:
This paper proposes KTAE: A Model-Free Algorithm to Key-Tokens Advantage Estimation in Mathematical Reasoning | OpenReview, a novel algorithm that estimates fine-grained, token-level advantages without introducing additional models. KTAE leverages the correctness of sampled rollouts and applies statistical analysis to quantify the importance of individual tokens within a sequence to the final outcome. Empirical results show that model trained with GRPO+KTAE and DAPO+KTAE outperform baseline methods across five mathematical reasoning benchmarks.

STRENGTHS AND WEAKNESSES:
Pros:
- This paper is well-written and easy-to-understand. The idea is intuitive, reasonable, and effective.
- The importance of individual tokens within a sequence to the final outcome is a very important problem in reinforcement learning.
- Experiments are conducted based on GRPO and DAPO, two recent popular RL approaches for LLMs, proving the effectiveness of KTAE.
- Solid motivations and illustrations in Section 3.
- Clear visualization examples to show the important tokens found by KTAE.

Cons:
- Experiments are conducted on 1.54B/7B models. It is not clear whether this method also have the scaling law.
- It would be better if the paper can also analyze the training efficiency (comparing with baselines).

QUESTIONS:
- Can this approach generalize to tasks beyond mathematical reasoning?

LIMITATIONS:
YES
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-04