# Four Over Six: More Accurate NVFP4 Quantization with Adaptive Block Scaling

arXiv: https://arxiv.org/abs/2512.02010 · HTML: https://mlsanity.com/paper/2512.02010/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 40 references that are in the map.
- First posted on arXiv 1 Dec 2025.

## Builds on (most cited first, 30 of 30)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [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)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [Gated Attention for Large Language Models: Non-linearity, Sparsity, and Attention-Sink-Free](https://mlsanity.com/paper/2505.06708/) (2025)
- [The case for 4-bit precision: k-bit Inference Scaling Laws](https://mlsanity.com/paper/2212.09720/) (2022)
- [A Study of BFLOAT16 for Deep Learning Training](https://mlsanity.com/paper/1905.12322/) (2019)
- [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)
- [Quantizable Transformers: Removing Outliers by Helping Attention Heads Do Nothing](https://mlsanity.com/paper/2306.12929/) (2023)
- [Pretraining Large Language Models with NVFP4](https://mlsanity.com/paper/2509.25149/) (2025)
- [LLM-FP4: 4-Bit Floating-Point Quantized Transformers](https://mlsanity.com/paper/2310.16836/) (2023)
- [Optimizing Large Language Model Training Using FP4 Quantization](https://mlsanity.com/paper/2501.17116/) (2025)
- [FP4 All the Way: Fully Quantized Training of LLMs](https://mlsanity.com/paper/2505.19115/) (2025)
- [Quartet: Native FP4 Training Can Be Optimal for Large Language Models](https://mlsanity.com/paper/2505.14669/) (2025)
- [Systematic Outliers in Large Language Models](https://mlsanity.com/paper/2502.06415/) (2025)
- [Mitigating the Impact of Outlier Channels for Language Model Quantization with Activation Regularization](https://mlsanity.com/paper/2404.03605/) (2024)
- [Recipes for Pre-training LLMs with MXFP8](https://mlsanity.com/paper/2506.08027/) (2025)
- [SWAN-GPT: An Efficient and Scalable Approach for Long-Context Language Modeling](https://mlsanity.com/paper/2504.08719/) (2025)
- [INT v.s. FP: A Comprehensive Study of Fine-Grained Low-bit Quantization Formats](https://mlsanity.com/paper/2510.25602/) (2025)

## Built on by (most cited first, 30 of 35)

- [LongLive-2.0: An NVFP4 Parallel Infrastructure for Long Video Generation](https://mlsanity.com/paper/2605.18739/) (2026)
- [Quartet II: Accurate LLM Pre-Training in NVFP4 by Improved Unbiased Gradient Estimation](https://mlsanity.com/paper/2601.22813/) (2026)
- [M2XFP: A Metadata-Augmented Microscaling Data Format for Efficient Low-bit Quantization](https://mlsanity.com/paper/2601.19213/) (2026)
- [DuQuant++: Fine-grained Rotation Enhances Microscaling FP4 Quantization](https://mlsanity.com/paper/2604.17789/) (2026)
- [Full-Stack FP4: Stable LLM Pretraining with Quantized Projections, Optimizers, and Attention](https://mlsanity.com/paper/2607.04422/) (2026)
- [High-Rate Quantized Matrix Multiplication I](https://mlsanity.com/paper/2601.17187/) (2026)
- [WaterSIC: Information-Theoretically (Near) Optimal Linear Layer Quantization](https://mlsanity.com/paper/2603.04956/) (2026)
- [BATQuant: Outlier-resilient MXFP4 Quantization via Learnable Block-wise Optimization](https://mlsanity.com/paper/2603.16590/) (2026)
- [HiFloat4 Format for Language Model Pre-training on Ascend NPUs](https://mlsanity.com/paper/2604.08826/) (2026)
- [FAAR: Format-Aware Adaptive Rounding for NVFP4](https://mlsanity.com/paper/2603.22370/) (2026)
- [Adaptive Block-Scaled Data Types](https://mlsanity.com/paper/2603.28765/) (2026)
- [SOAR: Scale Optimization for Accurate Reconstruction in NVFP4 Quantization](https://mlsanity.com/paper/2605.12245/) (2026)
- [Normalized Architectures are Natively 4-Bit](https://mlsanity.com/paper/2605.06067/) (2026)
- [Grid Games: The Power of Multiple Grids for Quantizing Large Language Models](https://mlsanity.com/paper/2605.12327/) (2026)
- [Rethinking Shrinkage Bias in LLM FP4 Pretraining: Geometric Origin, Systemic Impact, and UFP4 Recipe](https://mlsanity.com/paper/2606.20381/) (2026)
- [FOCUS: FP4 Optimization via Coupled-Relaxation and Dual-Granularity Scaling](https://mlsanity.com/paper/2608.01847/) (2026)
- [H-Scale: Hessian-Guided Scale Refinement for NVFP4 Sub-Byte LLM Inference](https://mlsanity.com/paper/2608.28113/) (2026)
- [UE5M3 FP4 Block Scaling for Stable Language Model Pretraining](https://mlsanity.com/paper/2609.02846/) (2026)
- [QuantClaw: Precision Where It Matters for OpenClaw](https://mlsanity.com/paper/2604.22577/) (2026)
- [Decomposing MXFP4 quantization error for LLM reinforcement learning: reducible bias, recoverable deadzone, and an irreducible floor](https://mlsanity.com/paper/2605.20402/) (2026)
- [GPTQ-intrinsic LoRA: A Near-optimal Algorithm for Low-precision Quantization with Low-rank Adaptation](https://mlsanity.com/paper/2606.01412/) (2026)
- [Miles v0.1: Production-Level Post-Training](https://mlsanity.com/paper/2609.08368/) (2026)
- [SemanticDialect: Semantic-Aware Mixed-Format Quantization for Video Diffusion Transformers](https://mlsanity.com/paper/2603.02883/) (2026)
- [Finer is Better (with the Right Scaling)](https://mlsanity.com/paper/2605.08565/) (2026)
- [A Hardware-Aware, Per-Layer Methodology for Post-Training Quantization of Large Language Models](https://mlsanity.com/paper/2605.14929/) (2026)
- [ReSET: Accurate Latency-Critical NVFP4 Reasoning via Step-Aware Temperature Scaling](https://mlsanity.com/paper/2606.13233/) (2026)
- [SharQ: Bridging Activation Sparsity and FP4 Quantization for LLM Inference](https://mlsanity.com/paper/2606.26587/) (2026)
- [Heterogeneity-Aware Microscaling for Efficient Low-Bit LLM Inference](https://mlsanity.com/paper/2608.03867/) (2026)
- [Transforms for LLM Quantization: The Great Inversion and Format Co-Design](https://mlsanity.com/paper/2608.25188/) (2026)
- [OCGQuant: Outlier-Companion Grouping for NVFP4 Quantization](https://mlsanity.com/paper/2609.00066/) (2026)

## Abstract (arXiv)

As large language models have grown larger, interest has grown in low-precision numerical formats such as NVFP4 as a way to improve speed and reduce memory usage. However, quantizing models to NVFP4 remains challenging as the lack of precision generally degrades model performance. In this work, we address this issue with Four Over Six (4/6), a modification to the block-scaled NVFP4 quantization algorithm that yields reduced quantization error. Unlike integer formats, floating point formats have non-uniform step sizes which create larger quantization error on larger values. 4/6 takes advantage of this by adaptively scaling some blocks to smaller FP4 values, making the distribution of representable values more uniform and reducing quantization error for near-maximal values. We show that 4/6 can be implemented efficiently on modern hardware accelerators, resulting in performance gains during both pre-training and inference with minimal computational overhead. In pre-training experiments with the Nemotron 3 Nano 30B-A3B model architecture, we find that 4/6 brings training loss closer to BF16 compared to models trained with current state-of-the-art NVFP4 training recipes. Our code is available at https://github.com/mit-han-lab/fouroversix.