All Work And No Play Makes Jack a Dull Boy: Understanding and Preventing Catastrophic Strategy Collapse in RLVR

Qiyuan Huang, Tianshi Xu, Meng Li

During post-training of large language models (LLMs) with Reinforcement Learning with Verifiable Rewards (RLVR), GRPO-style algorithms can exhibit severe late-stage collapse. Prompt-based probing reveals that this is not benign strategic pruning, but a harmful contraction of effective strategy capacity that makes distinct reasoning strategies increasingly inaccessible. To characterize this phenomenon, we define strategies through trajectory-level policy-update interactions and develop a unified theoretical framework combining optimization dynamics and information theory. We prove that major RLVR objectives progressively concentrate probability mass onto a single strategy, while sustaining nontrivial task accuracy requires a minimum strategy capacity. The conflict between these two results provides a mechanistic explanation for catastrophic collapse. We further derive the {Mirrored Entanglement Index (MEI)} as a lightweight online warning signal. To prevent collapse, we propose \textbf{Mesh Learning}, which exposes multiple reasoning strategies and prevents any single strategy from dominating optimization. Across AIME26, AIME25, MATH-500, GPQA, and LiveCodeBench, Mesh Learning…