# Effective Quantization of Muon Optimizer States

arXiv: https://arxiv.org/abs/2509.23106 · HTML: https://mlsanity.com/paper/2509.23106/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 55 references that are in the map.
- First posted on arXiv 27 Sep 2025.

## Builds on (most cited first, 30 of 44)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [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)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [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)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [PyTorch FSDP: Experiences on Scaling Fully Sharded Data Parallel](https://mlsanity.com/paper/2304.11277/) (2023)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models](https://mlsanity.com/paper/2508.06471/) (2025)

## Built on by (most cited first, 11 of 11)

- [MuonEq: Balancing Before Orthogonalization with Lightweight Equilibration](https://mlsanity.com/paper/2603.28254/) (2026)
- [Full-Stack FP4: Stable LLM Pretraining with Quantized Projections, Optimizers, and Attention](https://mlsanity.com/paper/2607.04422/) (2026)
- [Understanding Quantization of Optimizer States in LLM Pre-training: Dynamics of State Staleness and Effectiveness of State Resets](https://mlsanity.com/paper/2603.16731/) (2026)
- [OLion: Approaching the Hadamard Ideal by Intersecting Spectral and ℓ∞ Implicit Biases](https://mlsanity.com/paper/2602.01105/) (2026)
- [MuonQ: Enhancing Low-Bit Muon Quantization via Directional Fidelity Optimization](https://mlsanity.com/paper/2605.11396/) (2026)
- [Muse: Representation Geometry of Muon Beyond Normalized Momentum](https://mlsanity.com/paper/2607.14536/) (2026)
- [Stochastic Rounding Increases Small Singular Values](https://mlsanity.com/paper/2606.00312/) (2026)
- [Zero-order Parameter-free Optimization for LMO-based Methods: Novel Approach for Efficient Fine-tuning](https://mlsanity.com/paper/2606.14970/) (2026)
- [Blog: Survey of Optimizers](https://mlsanity.com/paper/2608.28557/) (2026)
- [Rounding in Preconditioner Space: Redesigning 4-bit AdamW Optimizer-State Quantization](https://mlsanity.com/paper/2610.12444/) (2026)
- [Memory-Efficient Subspace Optimization with Residual Correction: From Momentum SGD to Muon](https://mlsanity.com/paper/2610.19844/) (2026)

## Abstract (arXiv)

The Muon optimizer, based on matrix orthogonalization, has recently shown faster convergence and better computational efficiency over AdamW in LLM pre-training. However, the memory overhead of maintaining high-precision optimizer states remains a challenge for large-scale deployment. In this paper, we introduce the 8-bit Muon optimizer using blockwise quantization. In extensive Chinchilla-optimal experiments on pre-training models of up to 2.7B in size and fine-tuning them for instruction following, we demonstrate that 8-bit Muon achieves parity with Muon in terms of validation loss and downstream benchmarks, while achieving up to a 62% reduction in optimizer state footprint. Crucially, we show that Muon's update mechanism is uniquely compatible with a simple linear quantization scheme, bypassing the complex dynamic scaling required for quantized AdamW. We supplement our empirical findings with a theoretical analysis of Muon's robustness to quantization noise.