# Metis: Training LLMs with FP4 Quantization

arXiv: https://arxiv.org/abs/2509.00404 · HTML: https://mlsanity.com/paper/2509.00404/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 34 references that are in the map.
- First posted on arXiv 30 Aug 2025.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (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)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [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)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [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)
- [Microscaling Data Formats for Deep Learning](https://mlsanity.com/paper/2310.10537/) (2023)
- [Distributed Mean Estimation with Limited Communication](https://mlsanity.com/paper/1611.00429/) (2016)
- [FP8-LM: Training FP8 Large Language Models](https://mlsanity.com/paper/2310.18313/) (2023)
- [LAMBADA: Backward Chaining for Automated Reasoning in Natural Language](https://mlsanity.com/paper/2212.13894/) (2022)
- [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)
- [Rare Tokens Degenerate All Tokens: Improving Neural Text Generation via Adaptive Gradient Gating for Rare Token Embeddings](https://mlsanity.com/paper/2109.03127/) (2021)
- [Training and inference of large language models using 8-bit floating point](https://mlsanity.com/paper/2309.17224/) (2023)
- [HALO: Hadamard-Assisted Lower-Precision Optimization for LLMs](https://mlsanity.com/paper/2501.02625/) (2025)
- [Stable Anisotropic Regularization](https://mlsanity.com/paper/2305.19358/) (2023)

## Built on by (most cited first, 9 of 9)

- [Full-Stack FP4: Stable LLM Pretraining with Quantized Projections, Optimizers, and Attention](https://mlsanity.com/paper/2607.04422/) (2026)
- [HiFloat4 Format for Language Model Pre-training on Ascend NPUs](https://mlsanity.com/paper/2604.08826/) (2026)
- [Spectra: Rethinking Optimizers for LLMs Under Spectral Anisotropy](https://mlsanity.com/paper/2602.11185/) (2026)
- [Dissecting Outlier Dynamics in LLM NVFP4 Pretraining](https://mlsanity.com/paper/2602.02047/) (2026)
- [SD-MoE: Spectral Decomposition for Effective Expert Specialization](https://mlsanity.com/paper/2602.12556/) (2026)
- [UE5M3 FP4 Block Scaling for Stable Language Model Pretraining](https://mlsanity.com/paper/2609.02846/) (2026)
- [The Curse and Blessing of Mean Bias in FP4-Quantized LLM Training](https://mlsanity.com/paper/2603.10444/) (2026)
- [Spectral Allocation: Why Muon Outperforms Adam, and How to Improve Muon](https://mlsanity.com/paper/2608.25990/) (2026)
- [Format-Aware Fusion for Fast FP4 Pretraining](https://mlsanity.com/paper/2610.00053/) (2026)

## Abstract (arXiv)

This work identifies anisotropy in the singular value spectra of parameters, activations, and gradients as the fundamental barrier to low-bit training of large language models (LLMs). These spectra are dominated by a small fraction of large singular values, inducing wide numerical ranges that cause quantization bias and severe spectral distortion, ultimately degrading training performance. This work presents Metis, a spectral-domain quantization framework that partitions anisotropic spectra into narrower sub-distributions for independent quantization, thereby reducing errors and preserving spectral structure. To minimize overhead, Metis leverages two key properties of the dominant spectral subspace: preservation via sparsely random sampling and preservation via random projection, reducing decomposition cost to a negligible level. On LLaMA-3 8B trained with 100B tokens, Metis enables robust W4A4G4 training with FP4 quantization of weights, activations, and gradients, yielding only a 0.4% training loss gap and a 0.1% degradation in downstream accuracy relative to BF16. Beyond matching BF16 fidelity, Metis also surpasses our implementation of Nvidia's recently announced (yet to be publicly released) FP4 recipe, consistently achieving lower loss and higher downstream accuracy while incurring significantly lower computational overhead. The code implementation for Metis is available at: https://anonymous.4open.science/r/Metis-quantization-644B.