KTAE: A Model-Free Algorithm to Key-Tokens Advantage Estimation in Mathematical Reasoning

• URL: http://arxiv.org/abs/2505.16826v1
• Date: Thu, 22 May 2025 16:00:33 GMT
• Title: KTAE: A Model-Free Algorithm to Key-Tokens Advantage Estimation in Mathematical Reasoning
• Authors: Wei Sun, Wen Yang, Pu Jian, Qianlong Du, Fuwei Cui, Shuo Ren, Jiajun Zhang,
• Abstract summary: Key-token Advantage Estimation (KTAE) is a novel algorithm that estimates fine-grained, token-level advantages without introducing additional models.<n>We show that models trained with GRPO+KTAE and DAPO+KTAE outperform baseline methods across five mathematical reasoning benchmarks.
• Score: 19.25257653416883
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent advances have demonstrated that integrating reinforcement learning with rule-based rewards can significantly enhance the reasoning capabilities of large language models, even without supervised fine-tuning. 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 and hindering effective learning. 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.

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