Rethinking RL for LLM Reasoning: It's Sparse Policy Selection, Not Capability Learning

TL;DR

This paper shows that reinforcement learning improves large language model reasoning mainly through sparse, targeted corrections at uncertain decision points, rather than teaching new capabilities.

Contribution

It introduces ReasonMaxxer, a minimal RL-free method that applies contrastive loss at high-entropy points, matching RL performance with significantly less training.

Findings

RL affects only 1-3% of token positions, within top-5 alternatives.

Base model entropy can identify correction points without RL.

ReasonMaxxer achieves comparable performance with minimal data and training time.

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.