Distributional Clarity: The Hidden Driver of RL-Friendliness in Large Language Models

TL;DR

This paper identifies distributional clarity in probability space as a key factor influencing the reinforcement learning benefits of large language models, and proposes a method to enhance it, leading to improved model performance.

Contribution

It introduces the concept of distributional clarity, quantifies it using the Silhouette Coefficient, and develops a reweighting strategy to improve RL-friendliness in language models.

Findings

High distributional clarity correlates with better RL performance.

Low clarity is linked to logic errors and reasoning instability.

Reweighting low-clarity samples improves model performance on benchmarks.

Abstract

Language model families exhibit striking disparity in their capacity to benefit from reinforcement learning: under identical training, models like Qwen achieve substantial gains, while others like Llama yield limited improvements. Complementing data-centric approaches, we reveal that this disparity reflects a hidden structural property: \textbf{distributional clarity} in probability space. Through a three-stage analysis-from phenomenon to mechanism to interpretation-we uncover that RL-friendly models exhibit intra-class compactness and inter-class separation in their probability assignments to correct vs. incorrect responses. We quantify this clarity using the \textbf{Silhouette Coefficient} ($S$) and demonstrate that (1) high $S$ correlates strongly with RL performance; (2) low $S$ is associated with severe logic errors and reasoning instability. To confirm this property, we introduce a Silhouette-Aware Reweighting strategy that prioritizes low-$S$ samples during training. Experiments across six mathematical benchmarks show consistent improvements across all model families, with gains up to 5.9 points on AIME24. Our work establishes distributional clarity as a fundamental, trainable property underlying RL-Friendliness.