RL for LLM Reasoning Is Sparse Policy Selection, Not Capability Learning

A new arXiv preprint (2605.06241v2) finds that reinforcement learning (RL) for large language model reasoning acts as sparse policy selection rather than capability learning, with only 1–3% of token positions affected and promoted tokens always within the base model's top-5 alternatives. The authors introduce ReasonMaxxer, an RL-free method applying contrastive loss only at entropy-gated decision points, which matches or exceeds full RL performance across three model families, six scales, and six math benchmarks while requiring only tens of problems and minutes of single-GPU training—a roughly three orders of magnitude reduction in training cost.

Computer Science Computation and Language Submitted on 7 May 2026 v1 https://arxiv.org/abs/2605.06241v1 , last revised 8 May 2026 this version, v2 Title:Rethinking RL for LLM Reasoning: It's Sparse Policy Selection, Not Capability Learning View PDF /pdf/2605.06241 HTML experimental https://arxiv.org/html/2605.06241v2 Abstract:Reinforcement learning has become the standard for improving reasoning in large language models, yet evidence increasingly suggests that RL does not teach new strategies; it redistributes probability mass over solutions the base model already contains. In this work, we ask: if RL merely steers the model toward paths it already knows, is the RL optimization loop itself necessary? Through token-level analysis across multiple model families and RL algorithms, we find that RL's beneficial footprint is a sparse, predictable correction concentrated at high-entropy decision points where the model is uncertain which branch to take. Only 1--3\% of token positions are affected, the promoted token always lies within the base model's top-5 alternatives, and targeted corrections at those few positions causally recover a large fraction of RL's accuracy gain, while random corrections fail. The base model's own entropy identifies these positions without any RL-trained model, and the entire correction is low-dimensional, representable in a tiny fraction of model parameters. These findings reframe reasoning improvement as sparse policy selection, not capability acquisition. We translate this insight into ReasonMaxxer, a minimal RL-free method that applies contrastive loss only at entropy-gated decision points, using a few hundred base-model rollouts and no online generation. Across three model families, six scales, and six math reasoning benchmarks, ReasonMaxxer matches or exceeds full RL performance while requiring only tens of problems and minutes of single-GPU training, a reduction in training cost of roughly three orders of magnitude. Submission history From: Ömer Faruk Akgül view email /show-email/2ef80c8d/2605.06241 Thu, 7 May 2026 13:25:05 UTC 438 KB v1 /abs/2605.06241v1 v2 Fri, 8 May 2026 19:48:19 UTC 438 KB References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer What is the Explorer? https://info.arxiv.org/labs/showcase.html arxiv-bibliographic-explorer Connected Papers What is Connected Papers? https://www.connectedpapers.com/about Litmaps What is Litmaps? https://www.litmaps.co/ scite Smart Citations What are Smart Citations? https://www.scite.ai/ Code, Data and Media Associated with this Article alphaXiv What is alphaXiv? https://alphaxiv.org/ CatalyzeX Code Finder for Papers What is CatalyzeX? https://www.catalyzex.com DagsHub What is DagsHub? https://dagshub.com/ Gotit.pub What is GotitPub? http://gotit.pub/faq Hugging Face What is Huggingface? https://huggingface.co/huggingface ScienceCast What is ScienceCast? https://sciencecast.org/welcome Demos Recommenders and Search Tools Influence Flower What are Influence Flowers? https://influencemap.cmlab.dev/ CORE Recommender What is CORE? https://core.ac.uk/services/recommender arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs https://info.arxiv.org/labs/index.html .