Training stability is a key bottleneck in low-precision language model training: efficient low-cost paths can still produce short-lived numerical risks at a small set of operators. We formulate this as runtime stability control and present **G**radient **N**orm-to-**M**ean **R**atio (**GNMR**), a lightweight controller that compares each recoverable unit’s current gradient norm with its historical mean. Together with 𝛥-GNMR for abrupt short-window increases, GNMR maps local risk signals to bounded recovery actions under a hard maxO budget and a short lock interval, without changing the numerical format, kernel, or backend recipe. Across activation-quantization stress, DeepSeek-style recipe-level training, and LLaMA-2 13B fine-tuning, GNMR preserves high-fidelity quality with sparse, budgeted recovery. These results support GNMR as a backend-agnostic controller to improve low-precision training stability while preserving low-cost execution.

Training large language models (LLMs) at 4-bit precision offers substantial efficiency gains but remains challenging due to the limited dynamic range and coarse numerical resolution. Existing 4-bit training pipelines typically rely on max-scaling, which is ill-suited for heavy-tailed LLM tensor distributions and leads to severe under-utilization of the FP4 quantization grid in the low-magnitude region. This effect causes pronounced representation collapse and large rounding errors for the values that dominate LLM computation. In this work, we derive the theoretically optimal scaling for FP4 under heavy-tailed inputs, revealing why max-scaling is intrinsically suboptimal. Guided by this analysis, we propose Half-S, a simple and efficient scaling strategy that uses half-scaling as a hardware-friendly default and falls back to an MSE-based clipping threshold when needed, yielding a close approximation to the theoretical optimum under real LLM statistics. Extensive experiments on large-scale pretraining and downstream fine-tuning show that Half-S consistently narrows the gap to BF16 in both convergence and final model quality, while preserving the efficiency benefits of 4-bit computation. Under native FP4 support, Half-S is estimated to provide up to 1.8× end-to-end training speedup. These results indicate that Half-S provides a simple and effective correction to max-scaling, substantially improving the stability and accuracy of 4-bit LLM training.