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[2602.14872] On the Learning Dynamics of RLVR at the Edge of Competence
Summary
This paper explores the learning dynamics of Reinforcement Learning with Verifiable Rewards (RLVR), focusing on its effectiveness in overcoming long-horizon reasoning challenges through a theoretical framework and empirical validation.
Why It Matters
Understanding the learning dynamics of RLVR is crucial as it addresses the limitations of traditional reinforcement learning in complex reasoning tasks. The insights can inform the design of more effective training datasets and algorithms, potentially leading to significant advancements in AI capabilities.
Key Takeaways
- RLVR can enhance performance in complex reasoning tasks by addressing long-horizon challenges.
- The smoothness of the difficulty spectrum in training data significantly impacts learning dynamics.
- Grokking-type phase transitions can occur with abrupt difficulty changes, leading to learning plateaus.
- A well-designed mixture of training data can facilitate continuous improvement in model capabilities.
- The paper employs Fourier analysis tools to analyze training dynamics effectively.
Computer Science > Machine Learning arXiv:2602.14872 (cs) [Submitted on 16 Feb 2026] Title:On the Learning Dynamics of RLVR at the Edge of Competence Authors:Yu Huang, Zixin Wen, Yuejie Chi, Yuting Wei, Aarti Singh, Yingbin Liang, Yuxin Chen View a PDF of the paper titled On the Learning Dynamics of RLVR at the Edge of Competence, by Yu Huang and 6 other authors View PDF Abstract:Reinforcement learning with verifiable rewards (RLVR) has been a main driver of recent breakthroughs in large reasoning models. Yet it remains a mystery how rewards based solely on final outcomes can help overcome the long-horizon barrier to extended reasoning. To understand this, we develop a theory of the training dynamics of RL for transformers on compositional reasoning tasks. Our theory characterizes how the effectiveness of RLVR is governed by the smoothness of the difficulty spectrum. When data contains abrupt discontinuities in difficulty, learning undergoes grokking-type phase transitions, producing prolonged plateaus before progress recurs. In contrast, a smooth difficulty spectrum leads to a relay effect: persistent gradient signals on easier problems elevate the model's capabilities to the point where harder ones become tractable, resulting in steady and continuous improvement. Our theory explains how RLVR can improve performance at the edge of competence, and suggests that appropriately designed data mixtures can yield scalable gains. As a technical contribution, our analysis develops...