Angles Don't Lie: Unlocking Training-Efficient RL Through the Model's Own Signals

TL;DR

This paper introduces a novel training method for large language models that uses the model's own internal signals, specifically angle concentration, to select impactful training data, significantly improving efficiency and reducing data requirements.

Contribution

It identifies angle concentration as an intrinsic learning signal and develops GAIN-RL, a data selection framework that enhances training efficiency by leveraging this signal.

Findings

GAIN-RL achieves over 2.5x training acceleration

It improves data efficiency, requiring half the data for comparable performance

The approach is effective across diverse tasks and model scales

Abstract

Current Reinforcement Fine-tuning (RFT) paradigms for Large Language Models (LLMs) suffer from sample inefficiency due to the redundant exposure of identical queries under uniform data sampling. While previous work has explored curriculum learning via heuristic difficulty metrics, these strategies exhibit limitations by neglecting the intrinsic learning signals generated by the model itself, thus leading to suboptimal training regimes. In this paper, we identify a model-inherent signal termed angle concentration that effectively reflects an LLM's capacity to learn from specific data. We theoretically and empirically demonstrate a correlation between the angular distribution of token hidden state vectors and the resulting gradient, revealing a learning preference for data exhibiting higher angle concentration. Inspired by this finding, we propose GAIN-RL, a Gradient-driven Angle-Informed Navigated RL framework. By leveraging the model's intrinsic angle concentration signal, GAIN-RL dynamically selects training data in each epoch, ensuring consistently impactful gradient updates and thus significantly enhancing overall training efficiency. Empirical evaluations show that GAIN-RL (GRPO) achieves over a 2.5x acceleration in training efficiency across diverse mathematical and coding tasks and varying model scales. Furthermore, GAIN-RL (GRPO)'s efficient sampling yields data-efficient training, achieving better performance with half the original data compared to vanilla GRPO with full training data. Code is realsed at https://github.com/wangqinsi1/GAINRL/tree/main.