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The paper identifies a rank-one mean bias as the primary driver of numerical instability in FP4-quantized LLM training, where the anisotropy of LLM representations causes a compression of semantic variation. They demonstrate that this bias systematically emerges across layers and training stages, leading to inflated dynamic ranges. By implementing a simple mean-subtraction operation at the source level, the authors effectively mitigate this instability, achieving performance comparable to BF16 training.
Subtracting the mean from activations unlocks stable FP4 training for LLMs, closing the performance gap with BF16 without complex spectral methods.
Large language models trained on natural language exhibit pronounced anisotropy: a small number of directions concentrate disproportionate energy, while the remaining dimensions form a broad semantic tail. In low-bit training regimes, this geometry becomes numerically unstable. Because blockwise quantization scales are determined by extreme elementwise magnitudes, dominant directions stretch the dynamic range, compressing long-tail semantic variation into narrow numerical bins. We show that this instability is primarily driven by a coherent rank-one mean bias, which constitutes the dominant component of spectral anisotropy in LLM representations. This mean component emerges systematically across layers and training stages and accounts for the majority of extreme activation magnitudes, making it the principal driver of dynamic-range inflation under low precision. Crucially, because the dominant instability is rank-one, it can be eliminated through a simple source-level mean-subtraction operation. This bias-centric conditioning recovers most of the stability benefits of SVD-based spectral methods while requiring only reduction operations and standard quantization kernels. Empirical results on FP4 (W4A4G4) training show that mean removal substantially narrows the loss gap to BF16 and restores downstream performance, providing a hardware-efficient path to stable low-bit LLM training.
