# SPS: Steering Probability Squeezing for Better Exploration in Reinforcement Learning for Large Language Models

arXiv: https://arxiv.org/abs/2604.16995 · HTML: https://mlsanity.com/paper/2604.16995/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 39 references that are in the map.
- First posted on arXiv 18 Apr 2026.

## Builds on (most cited first, 25 of 25)

- [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)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Statistical Rejection Sampling Improves Preference Optimization](https://mlsanity.com/paper/2309.06657/) (2023)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [S*: Test Time Scaling for Code Generation](https://mlsanity.com/paper/2502.14382/) (2025)
- [Mathematical exploration and discovery at scale](https://mlsanity.com/paper/2511.02864/) (2025)
- [Inverse-RLignment: Large Language Model Alignment from Demonstrations through Inverse Reinforcement Learning](https://mlsanity.com/paper/2405.15624/) (2024)
- [GRAM: A Generative Foundation Reward Model for Reward Generalization](https://mlsanity.com/paper/2506.14175/) (2025)
- [CodeRL+: Improving Code Generation via Reinforcement with Execution Semantics Alignment](https://mlsanity.com/paper/2510.18471/) (2025)
- [From Novice to Expert: LLM Agent Policy Optimization via Step-wise Reinforcement Learning](https://mlsanity.com/paper/2411.03817/) (2024)
- [ESRL: Efficient Sampling-based Reinforcement Learning for Sequence Generation](https://mlsanity.com/paper/2308.02223/) (2023)
- [RoVRM: A Robust Visual Reward Model Optimized via Auxiliary Textual Preference Data](https://mlsanity.com/paper/2408.12109/) (2024)
- [Beyond Decoder-only: Large Language Models Can be Good Encoders for Machine Translation](https://mlsanity.com/paper/2503.06594/) (2025)
- [MSRL: Scaling Generative Multimodal Reward Modeling via Multi-Stage Reinforcement Learning](https://mlsanity.com/paper/2603.25108/) (2026)
- [HEAL: A Hypothesis-Based Preference-Aware Analysis Framework](https://mlsanity.com/paper/2508.19922/) (2025)
- [Learning Diverse Policies with Soft Self-Generated Guidance](https://mlsanity.com/paper/2402.04539/) (2024)

## Built on by (most cited first, 2 of 2)

- [Learning from Environmental Feedback: Credit Assignment across Multiple Timescales for Agentic Reinforcement Learning](https://mlsanity.com/paper/2608.08255/) (2026)
- [Video-HopChain: Multi-Hop Questions and Confidence-Gated Exploration for Video Reasoning Models](https://mlsanity.com/paper/2609.25773/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) has emerged as a promising paradigm for training reasoning-oriented models by leveraging rule-based reward signals. However, RL training typically tends to improve single-sample success rates (i.e., Pass@1) while offering limited exploration of diverse reasoning trajectories, which is crucial for multi-sample performance (i.e., Pass@k). Our preliminary analysis reveals that this limitation stems from a fundamental squeezing effect, whereby probability mass is excessively concentrated on a narrow subset of high-reward trajectories, restricting genuine exploration and constraining attainable performance under RL training. To address this issue, in this work, we propose Steering Probability Squeezing (SPS), a training paradigm that interleaves conventional RL with inverse reinforcement learning (IRL). SPS treats on-policy rollouts as demonstrations and employs IRL to explicitly reshape the induced trajectory distribution, thereby enhancing exploration without introducing external supervision. Experiments on five commonly used reasoning benchmarks demonstrate that SPS can enable better exploration and improve Pass@k. Beyond algorithmic contributions, we provide an analysis of RL learning dynamics and identify an empirical upper bound on Pass@k, shedding light on intrinsic exploration limits in RL-based reasoning models. Our findings suggest that alternating between RL and IRL offers an effective pathway toward extending the exploration capacity of reasoning-oriented large language models.