# GTPO and GRPO-S: Token and Sequence-Level Reward Shaping with Policy Entropy

arXiv: https://arxiv.org/abs/2508.04349 · HTML: https://mlsanity.com/paper/2508.04349/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 33 of its 38 references that are in the map.
- First posted on arXiv 6 Aug 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 33)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Dueling Network Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1511.06581/) (2015)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [R1-VL: Learning to Reason with Multimodal Large Language Models via Step-wise Group Relative Policy Optimization](https://mlsanity.com/paper/2503.12937/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [From r to Q^*: Your Language Model is Secretly a Q-Function](https://mlsanity.com/paper/2404.12358/) (2024)

## Built on by (most cited first, 18 of 18)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [From Code Foundation Models to Agents and Applications: A Comprehensive Survey and Practical Guide to Code Intelligence](https://mlsanity.com/paper/2511.18538/) (2025)
- [WS-GRPO: Weakly-Supervised Group-Relative Policy Optimization for Rollout-Efficient Reasoning](https://mlsanity.com/paper/2602.17025/) (2026)
- [HERO: Hierarchical Evidential Reasoning Optimization for Radiology Report Generation via Reason-then-Summarize](https://mlsanity.com/paper/2601.03321/) (2026)
- [Comparative Analysis and Parametric Tuning of PPO, GRPO, and DAPO for LLM Reasoning Enhancement](https://mlsanity.com/paper/2512.07611/) (2025)
- [How You Begin is How You Reason: Driving Exploration in RLVR via Prefix-Tuned Priors](https://mlsanity.com/paper/2605.08817/) (2026)
- [Breaking Failure Cascades: Step-Aware Reinforcement Learning for Medical Multimodal Reasoning](https://mlsanity.com/paper/2606.31825/) (2026)
- [Boosting LLM Reasoning via Human-Inspired Reward Shaping](https://mlsanity.com/paper/2602.04265/) (2026)
- [Towards Generalizable Reasoning: Group Causal Counterfactual Policy Optimization for LLM Reasoning](https://mlsanity.com/paper/2602.06475/) (2026)
- [SHAPE: Stage-aware Hierarchical Advantage via Potential Estimation for LLM Reasoning](https://mlsanity.com/paper/2604.06636/) (2026)
- [Adapting Reinforcement Learning with Chain-of-Thought Supervision for Explainable Detection of Hateful and Propagandistic Memes](https://mlsanity.com/paper/2606.15307/) (2026)
- [A First-Principles Derivation of LLM Policy Optimization: From Expected Reward to GRPO and Its Structural Extensions](https://mlsanity.com/paper/2606.16733/) (2026)
- [Know When to Stop: Segment-Level Credit Assignment for Reducing Overthinking](https://mlsanity.com/paper/2607.00482/) (2026)
- [GMTS: Gradient Magnitude-based Token Selection Improves RLVR Training for LLM Reasoning](https://mlsanity.com/paper/2608.30632/) (2026)
- [Rethinking Reinforcement fine-tuning of LLMs: A Multi-armed Bandit Learning Perspective](https://mlsanity.com/paper/2601.14599/) (2026)
- [Less Noise, More Voice: Reinforcement Learning for Reasoning via Instruction Purification](https://mlsanity.com/paper/2601.21244/) (2026)
- [Momentum for Reasoning: Dense Intrinsic Signals in Policy Optimization](https://mlsanity.com/paper/2606.08815/) (2026)
- [BoT-GRPO: Efficient Process-Reward RL for Reasoning via Bag-of-Token Aggregation](https://mlsanity.com/paper/2610.09804/) (2026)

## Abstract (arXiv)

Reinforcement Learning (RL) is pivotal for enhancing Large Language Model (LLM) reasoning, yet mainstream algorithms such as GRPO and DAPO remain constrained by a coarse-grained credit assignment paradigm, where all tokens within the same response receive the identical reward. In this paper, we propose Dynamic Entropy Weighting, systematically define entropy-based weight ratios fracHi,tsumk=1n Hk,t and similar variants to redistribute rewards and get fine-grained rewards through two new algorithms: Group Token Policy Optimization (GTPO), which assigns an entropy-weighted reward to each token and synthesizes token-specific advantage function to drive the model toward optimal path, and the analogous algorithm Sequence-Level GRPO (GRPO-S), which extends this design to the sequence level and exhibits superior stability in long Chain-of-Thought (CoT) reasoning tasks.