# HISPO: Hierarchical Importance-Sampling Policy Optimization with Entropy-Derived Segments

arXiv: https://arxiv.org/abs/2609.15471 · HTML: https://mlsanity.com/paper/2609.15471/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 19 of its 28 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [Segment Policy Optimization: Effective Segment-Level Credit Assignment in RL for Large Language Models](https://mlsanity.com/paper/2505.23564/) (2025)
- [No Prompt Left Behind: Exploiting Zero-Variance Prompts in LLM Reinforcement Learning via Entropy-Guided Advantage Shaping](https://mlsanity.com/paper/2509.21880/) (2025)
- [Length-Unbiased Sequence Policy Optimization: Revealing and Controlling Response Length Variation in RLVR](https://mlsanity.com/paper/2602.05261/) (2026)
- [Orchestrating Tokens and Sequences: Dynamic Hybrid Policy Optimization for RLVR](https://mlsanity.com/paper/2601.05607/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) has become a central approach for improving mathematical reasoning in language models, but long-form completions introduce a difficult credit-assignment problem: different parts of a solution trace may contribute unevenly to final correctness. Existing policyoptimization objectives for RLVR commonly apply importance-sampling correction at either the token level (GRPO, DAPO) or the sequence level (GSPO), imposing different granularities for assigning credit across a response. We introduce Hierarchical Importance-Sampling Policy Optimization (HISPO), a segment-level policy-optimization method that constructs rollout-time entropy-derived contiguous segments, assigns soft entropy-based saliency weights, and applies clipped importance-sampling correction at the segment granularity. This provides an intermediate correction unit between token-level GRPO/DAPO and sequence-level GSPO. We evaluate HISPO by fine-tuning Qwen3-1.7B-Base on mathematical reasoning tasks. Across six benchmarks, HISPO improves Pass@8 over the strongest baseline on all benchmarks and matches or exceeds the strongest baseline in Acc@8 on five of them. On AIME25, HISPO improves over GRPO by +3.75 Acc@8 and +3.78 Pass@8, and over GSPO by +2.50 Acc@8 and +1.27 Pass@8. These results suggest that segment-level correction is a promising granularity for RLVR in long-form mathematical reasoning.