# FOCUS: FP4 Optimization via Coupled-Relaxation and Dual-Granularity Scaling

arXiv: https://arxiv.org/abs/2608.01847 · HTML: https://mlsanity.com/paper/2608.01847/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 39 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Builds on (most cited first, 30 of 32)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [Microscaling Data Formats for Deep Learning](https://mlsanity.com/paper/2310.10537/) (2023)
- [FlatQuant: Flatness Matters for LLM Quantization](https://mlsanity.com/paper/2410.09426/) (2024)
- [OstQuant: Refining Large Language Model Quantization with Orthogonal and Scaling Transformations for Better Distribution Fitting](https://mlsanity.com/paper/2501.13987/) (2025)
- [LLM-FP4: 4-Bit Floating-Point Quantized Transformers](https://mlsanity.com/paper/2310.16836/) (2023)
- [Four Over Six: More Accurate NVFP4 Quantization with Adaptive Block Scaling](https://mlsanity.com/paper/2512.02010/) (2025)
- [Bridging the Gap Between Promise and Performance for Microscaling FP4 Quantization](https://mlsanity.com/paper/2509.23202/) (2025)
- [Block Rotation is All You Need for MXFP4 Quantization](https://mlsanity.com/paper/2511.04214/) (2025)
- [INT v.s. FP: A Comprehensive Study of Fine-Grained Low-bit Quantization Formats](https://mlsanity.com/paper/2510.25602/) (2025)
- [ARCQuant: Boosting NVFP4 Quantization with Augmented Residual Channels for LLMs](https://mlsanity.com/paper/2601.07475/) (2026)
- [Benchmarking Post-Training Quantization of Large Language Models under Microscaling Floating Point Formats](https://mlsanity.com/paper/2601.09555/) (2026)
- [DuQuant++: Fine-grained Rotation Enhances Microscaling FP4 Quantization](https://mlsanity.com/paper/2604.17789/) (2026)
- [RaZeR: Pushing the Limits of NVFP4 Quantization with Redundant Zero Remapping](https://mlsanity.com/paper/2501.04052/) (2025)
- [Unveiling the Potential of Quantization with MXFP4: Strategies for Quantization Error Reduction](https://mlsanity.com/paper/2603.08713/) (2026)
- [BATQuant: Outlier-resilient MXFP4 Quantization via Learnable Block-wise Optimization](https://mlsanity.com/paper/2603.16590/) (2026)

## Built on by (most cited first, 2 of 2)

- [QuantForge: Discovering Residual Decompositions for MXFP4 Post-Training Quantization](https://mlsanity.com/paper/2609.34680/) (2026)
- [RATIO: Reasoning Analysis and Token-level Inference Optimization for Quantized Reasoning Models](https://mlsanity.com/paper/2609.39801/) (2026)

## Abstract (arXiv)

Large language models (LLMs) achieve remarkable performance but are expensive to deploy due to their enormous size. FP4 quantization, with formats such as MXFP4 and NVFP4, offers an appealing solution with native hardware support on modern accelerators. However, maintaining accuracy under FP4 precision remains difficult. A key bottleneck lies in scale optimization: existing methods tightly couple the quantization and dequantization scales, forcing both to conform to the discrete low-precision format required by hardware, such as E8M0 in MXFP4. Yet the quantization scale is never stored and need not obey this constraint, suggesting a significant untapped optimization space. In this work, we propose FOCUS, a post-training quantization framework with end-to-end scale learning for FP4 Optimization via Coupled-Relaxation and Dual-Granularity Scaling. Coupled-Relaxation Scaling (CRS) relaxes the tight coupling between quantization and dequantization scales with a learnable full-precision coefficient, enabling more effective optimization without breaking hardware compliance. Dual-Granularity Scaling (DGS) further refines the quantization scale at a finer sub-block granularity, allowing more precise adaptation to local weight distributions. Experiments across multiple LLM families and benchmarks show that FOCUS achieves state-of-the-art FP4 accuracy under both MXFP4 and NVFP4 formats, while introducing no additional inference overhead. Code and quantized models will be released at https://github.com/tencent/AngelSlim.