Decomposing MXFP4 quantization error for LLM reinforcement learning: reducible bias, recoverable deadzone, and an irreducible floor

MXFP4 arithmetic can dramatically accelerate reinforcement learning (RL) post-training of large language models (LLMs), yet the quantization error introduces severe accuracy degradation. Existing work treats the quantization error as a monolithic noise term, missing the distinct mechanisms upon interpreting how quantization error damages training. We prove an exact three-way decomposition of quantization error and show how each component dominates a distinct RL training pathway. Our theoretical and empirical analysis decomposes the MXFP4 quantization error into three additive components: "scale bias" from power-of-two rounding, "deadzone truncation" from zeroing small values, and "grid noise" from rounding to the nearest 4-bit grid. Each component dominates a distinct RL failure mode: scale bias accumulates multiplicatively through the backward pass, affecting gradient accuracy; deadzone truncation degrades rollout quality; and grid noise raises the policy's entropy. We combine corrections that are RL failure mode-targeted but not component-exclusive: Macro-block scaling to reduce scale bias, Outlier Fallback recovers deadzone entries, but also partially reduces scale bias induced error, and Adaptive Quantization Noise (AQN) for controlling the policy entropy. On Qwen2.5-3B dense and Qwen3-30B-A3B-Base mixture-of-experts model, the targeted corrections recover BF16 accuracy to within 0.7% and 3.0% respectively.