Title: On Predictability of Reinforcement Learning Dynamics for Large Language Models
Primary area: foundation or frontier models, including LLMs
Keywords: Large Language Models, Reinforcement Learning, Interpretability, Low Rank

Abstract: Recent advances in reasoning capabilities of large language models (LLMs) are largely driven by reinforcement learning (RL), yet the underlying parameter dynamics during RL training remain poorly understood. This work identifies two fundamental properties of RL-induced parameter updates in LLMs: (1) Rank-1 Dominance, where the top singular subspace of the parameter update matrix nearly fully determines reasoning improvements, recovering over 99\% of performance gains; and (2) Rank-1 Linear Dynamics, where this dominant subspace evolves linearly throughout training, enabling accurate prediction from early checkpoints. Extensive experiments across 8 LLMs and 7 algorithms validate the generalizability of these properties. More importantly, based on these findings, we propose AlphaRL, a plug-in acceleration framework that extrapolates the final parameter update using a short early training window, achieving up to 2.5× speedup while retaining > 96\% of reasoning performance without extra modules or hyperparameter tuning.  This positions our finding as a versatile and practical tool for large-scale RL, opening a path toward principled, interpretable, and efficient training paradigm for LLMs.

TL;DR: We have discovered the naturally emerging low-rank phenomenon in reinforcement learning and leveraged this phenomenon to design a method that accelerates model training.