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

arXiv: https://arxiv.org/abs/2603.10444 · HTML: https://mlsanity.com/paper/2603.10444/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 42 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 29 of 29)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [DataComp-LM: In search of the next generation of training sets for language models](https://mlsanity.com/paper/2406.11794/) (2024)
- [All-but-the-Top: Simple and Effective Postprocessing for Word Representations](https://mlsanity.com/paper/1702.01417/) (2017)
- [FP8 Formats for Deep Learning](https://mlsanity.com/paper/2209.05433/) (2022)
- [SVDQuant: Absorbing Outliers by Low-Rank Components for 4-Bit Diffusion Models](https://mlsanity.com/paper/2411.05007/) (2024)
- [All Bark and No Bite: Rogue Dimensions in Transformer Language Models Obscure Representational Quality](https://mlsanity.com/paper/2109.04404/) (2021)
- [BERT Busters: Outlier Dimensions that Disrupt Transformers](https://mlsanity.com/paper/2105.06990/) (2021)
- [FP8 Quantization: The Power of the Exponent](https://mlsanity.com/paper/2208.09225/) (2022)
- [WhiteningBERT: An Easy Unsupervised Sentence Embedding Approach](https://mlsanity.com/paper/2104.01767/) (2021)
- [Optimizing Large Language Model Training Using FP4 Quantization](https://mlsanity.com/paper/2501.17116/) (2025)
- [Outliers Dimensions that Disrupt Transformers Are Driven by Frequency](https://mlsanity.com/paper/2205.11380/) (2022)
- [FP4 All the Way: Fully Quantized Training of LLMs](https://mlsanity.com/paper/2505.19115/) (2025)
- [Training LLMs with MXFP4](https://mlsanity.com/paper/2502.20586/) (2025)
- [HALO: Hadamard-Assisted Lower-Precision Optimization for LLMs](https://mlsanity.com/paper/2501.02625/) (2025)
- [Metis: Training LLMs with FP4 Quantization](https://mlsanity.com/paper/2509.00404/) (2025)

## Built on by (most cited first, 1 of 1)

- [Transformer MLP Gate Thresholds Are Couplings to a Carried Reference Direction](https://mlsanity.com/paper/2609.31956/) (2026)

## Abstract (arXiv)

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: https://anonymous.4open.science/r/averis-504D.