The Curse and Blessing of Mean Bias in FP4-Quantized LLM Training

[Submitted on 11 Mar 2026 (v1), last revised 12 Jun 2026 (this version, v2)]

Authors:Hengjie Cao, Zhendong Huang, Mengyi Chen, Yifeng Yang, Fang Dong, Anrui Chen, Ruijun Huang, Xin Zhang, Mingzhi Dong, Yujiang Wang, Jinlong Hou, Qin Lv, Robert P.Dick, Yuan Cheng, Tun Lu, Fan Yang, Yixuan Chen, Li Shang

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Abstract:FP4 training promises substantial memory and compute savings for large language models, but remains fragile because blockwise quantization is dictated by extreme activation magnitudes, which inflate dynamic range and compress long-tail signals. We identify a counterintuitive source of this failure: dominant activation outliers are not merely arbitrary sparse events, but are largely induced by a coherent rank-one mean bias, whose direction aligns with the leading anisotropic spectral component. This mean component strengthens during training, is amplified and reshaped by attention and FFN operators, and increasingly dominates top activation magnitudes. Crucially, this discovery reveals that a seemingly complex outlier-suppression problem admits a truly simple solution: isolate the coherent mean before quantization. We therefore propose Averis, a mean-residual splitting quantization method that separates the mean component using only reductions and elementwise subtractions before FP4 quantization. Across Qwen3 0.6B Dense trained on 100B tokens and Qwen3 7B A1.5B MoE trained on 50B tokens, Averis enables robust W4A4G4 FP4 training, reducing BF16 loss gaps to 1.19%/0.81% versus 2.05%/1.10% for NVIDIA’s recently released Hadamard-based outlier-smoothing method, while limiting downstream gaps to 0.89/0.71 points. With only 2.20% end-to-end overhead over vanilla NVFP4, about 30% of NVIDIA’s Hadamard-based design, Averis provides a hardware-efficient path to stable low-bit LLM training. Complementary to Hadamard, Averis further reduces the Qwen3-0.6B loss and downstream gaps to 0.94% and 0.73 points when combined. Code is available at: this https URL.

Submission history

From: Hengjie Cao [view email]
[v1] Wed, 11 Mar 2026 05:59:12 UTC (1,453 KB)
[v2] Fri, 12 Jun 2026 08:52:38 UTC (1,504 KB)