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

arXiv: https://arxiv.org/abs/2506.02281 · HTML: https://mlsanity.com/paper/2506.02281/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Builds on (most cited first, 30 of 31)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Symbolic Discovery of Optimization Algorithms](https://mlsanity.com/paper/2302.06675/) (2023)
- [Selection via Proxy: Efficient Data Selection for Deep Learning](https://mlsanity.com/paper/1906.11829/) (2019)
- [ReMax: A Simple, Effective, and Efficient Reinforcement Learning Method for Aligning Large Language Models](https://mlsanity.com/paper/2310.10505/) (2023)
- [DsDm: Model-Aware Dataset Selection with Datamodels](https://mlsanity.com/paper/2401.12926/) (2024)
- [H-CoT: Hijacking the Chain-of-Thought Safety Reasoning Mechanism to Jailbreak Large Reasoning Models, Including OpenAI o1/o3, DeepSeek-R1, and Gemini 2.0 Flash Thinking](https://mlsanity.com/paper/2502.12893/) (2025)
- [Efficient Reinforcement Finetuning via Adaptive Curriculum Learning](https://mlsanity.com/paper/2504.05520/) (2025)
- [Orthogonal Deep Neural Networks](https://mlsanity.com/paper/1905.05929/) (2019)
- [Active Preference Optimization for Sample Efficient RLHF](https://mlsanity.com/paper/2402.10500/) (2024)
- [No Train No Gain: Revisiting Efficient Training Algorithms For Transformer-based Language Models](https://mlsanity.com/paper/2307.06440/) (2023)
- [Neuron-Level Knowledge Attribution in Large Language Models](https://mlsanity.com/paper/2312.12141/) (2023)
- [Configurable Foundation Models: Building LLMs from a Modular Perspective](https://mlsanity.com/paper/2409.02877/) (2024)
- [Towards Data-Centric RLHF: Simple Metrics for Preference Dataset Comparison](https://mlsanity.com/paper/2409.09603/) (2024)
- [HippoMM: Hippocampal-inspired Multimodal Memory for Long Audiovisual Event Understanding](https://mlsanity.com/paper/2504.10739/) (2025)
- [Keyframe-oriented Vision Token Pruning: Enhancing Efficiency of Large Vision Language Models on Long-Form Video Processing](https://mlsanity.com/paper/2503.10742/) (2025)
- [Training-Free Adaptive Diffusion with Bounded Difference Approximation Strategy](https://mlsanity.com/paper/2410.09873/) (2024)
- [CoreInfer: Accelerating Large Language Model Inference with Semantics-Inspired Adaptive Sparse Activation](https://mlsanity.com/paper/2410.18311/) (2024)
- [GIO: Gradient Information Optimization for Training Dataset Selection](https://mlsanity.com/paper/2306.11670/) (2023)
- [Once for Both: Single Stage of Importance and Sparsity Search for Vision Transformer Compression](https://mlsanity.com/paper/2403.15835/) (2024)
- [CoreMatching: A Co-adaptive Sparse Inference Framework with Token and Neuron Pruning for Comprehensive Acceleration of Vision-Language Models](https://mlsanity.com/paper/2505.19235/) (2025)

## Built on by (most cited first, 13 of 13)

- [KVCOMM: Online Cross-context KV-cache Communication for Efficient LLM-based Multi-agent Systems](https://mlsanity.com/paper/2510.12872/) (2025)
- [Vision-Zero: Scalable VLM Self-Improvement via Strategic Gamified Self-Play](https://mlsanity.com/paper/2509.25541/) (2025)
- [AMAS: Adaptively Determining Communication Topology for LLM-based Multi-Agent System](https://mlsanity.com/paper/2510.01617/) (2025)
- [CoBA-RL: Capability-Oriented Budget Allocation for Reinforcement Learning in LLMs](https://mlsanity.com/paper/2602.03048/) (2026)
- [FT-MDT: Extracting Decision Trees from Medical Texts via a Novel Low-rank Adaptation Method](https://mlsanity.com/paper/2510.04655/) (2025)
- [PuzzleCraft: Exploration-Aware Curriculum Learning for Puzzle-Based RLVR in VLMs](https://mlsanity.com/paper/2512.14944/) (2025)
- [When RL Meets Adaptive Speculative Training: A Unified Training-Serving System](https://mlsanity.com/paper/2602.06932/) (2026)
- [EVA: Accelerating LLM Decoding via an Efficient Vector Quantization Architecture](https://mlsanity.com/paper/2605.24144/) (2026)
- [Guiding LLM Post-training Data Engineering with Model Internals from Sparse Autoencoders](https://mlsanity.com/paper/2605.27354/) (2026)
- [Coarse-to-Fine Personalized LLM Impressions for Streamlined Radiology Reports](https://mlsanity.com/paper/2508.15845/) (2025)
- [Curriculum Learning-Guided Progressive Distillation in Large Language Models](https://mlsanity.com/paper/2605.11260/) (2026)
- [A Survey of Reinforcement Learning for Large Language Models under Data Scarcity: Challenges and Solutions](https://mlsanity.com/paper/2604.17312/) (2026)
- [Vortex: Bridging Extreme Compression and Efficient LLM Inference](https://mlsanity.com/paper/2609.12208/) (2026)

## Abstract (arXiv)

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.