GradientStabilizer: Fix the Norm, Not the Gradient

Training instability in modern deep learning systems is frequently triggered by rare but extreme gradient-norm spikes, which can induce oversized parameter updates, corrupt optimizer state, and lead to slow recovery or divergence. Widely used safeguards such as gradient clipping mitigate these failures but require threshold tuning and indiscriminately truncate large updates. We propose GradientStabilizer, a lightweight, drop-in gradient transform that preserves the instantaneous gradient direction while replacing the update magnitude with a statistically stabilized estimate derived from running gradient-norm statistics. We prove that the resulting stabilized magnitude is uniformly bounded on spike steps, independent of the spike size, and show how this boundedness controls optimizer state evolution in adaptive methods. Across LLM pre-training (FP16), quantizationaware pre-training (FP4), ImageNet classification, reinforcement learning, and time-series forecasting, GradientStabilizer consistently improves training stability, widens stable learningrate regions, and reduces divergence relative to clipping-based baselines, even substantially reducing Adam's sensitivity to weight-decay strength. The Code is available at https: