Angles Don’t Lie: Unlocking Training‑Efficient RL Through the Model’s Own Signals

Hancheng Ye (Duke University, Duke University) · Qinsi Wang (Duke University) · Yuzhe Fu (Duke University) · Yueqian Lin (Duke Kunshan University) · Jianyi Zhang (Duke University) · Yiran Chen (Duke University) · Kurt Keutzer (EECS, UC Berkeley) · Jinghan Ke (University of Science and Technology of China) · Chenfeng Xu (Together AI/UT Austin)

angle concentrationangular distributioncurriculum learningdata-efficient traininggain-rlgradient correlationgradient-driven angle-informed navigated rlheuristic difficulty metricsimpactful gradient updateslearning preferencereinforcement fine-tuning sample inefficiencytoken hidden state vectorstraining data selection

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 2.5$\times$ 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.