M-GRPO: Stabilizing Self-Supervised Reinforcement Learning for Large Language Models with Momentum-Anchored Policy Optimization

Self-supervised reinforcement learning (RL) presents a promising approach for enhancing the reasoning capabilities of Large Language Models (LLMs) without reliance on expensive human-annotated data. However, we find that existing methods suffer from a critical failure mode under long-horizon training: a "policy collapse" where performance precipitously degrades. We diagnose this instability and demonstrate that simply scaling the number of rollouts -- a common strategy to improve performance -- only delays, but does not prevent, this collapse. To counteract this instability, we first introduce M-GRPO (Momentum-Anchored Group Relative Policy Optimization), a framework that leverages a slowly evolving momentum model to provide a stable training target. In addition, we identify that this process is often accompanied by a rapid collapse in policy entropy, resulting in a prematurely confident and suboptimal policy. To specifically address this issue, we propose a second contribution: an adaptive filtering method based on the interquartile range (IQR) that dynamically prunes low-entropy trajectories, preserving essential policy diversity. Our extensive experiments on multiple reasoning benchmarks demonstrate that M-GRPO stabilizes the training process while the IQR filter prevents premature convergence. The combination of these two innovations leads to superior training stability and state-of-the-art performance.