# Pushing the Limits of Low-Bit Optimizers: A Focus on EMA Dynamics

arXiv: https://arxiv.org/abs/2505.00347 · HTML: https://mlsanity.com/paper/2505.00347/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 73 references that are in the map.
- First posted on arXiv 1 May 2025.

## Builds on (most cited first, 30 of 55)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Visual Genome: Connecting Language and Vision Using Crowdsourced Dense Image Annotations](https://mlsanity.com/paper/1602.07332/) (2016)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Evaluating Object Hallucination in Large Vision-Language Models](https://mlsanity.com/paper/2305.10355/) (2023)
- [Towards VQA Models That Can Read](https://mlsanity.com/paper/1904.08920/) (2019)
- [MME: A Comprehensive Evaluation Benchmark for Multimodal Large Language Models](https://mlsanity.com/paper/2306.13394/) (2023)
- [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)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [COCO-Stuff: Thing and Stuff Classes in Context](https://mlsanity.com/paper/1612.03716/) (2016)

## Built on by (most cited first, 5 of 5)

- [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)
- [MuonQ: Enhancing Low-Bit Muon Quantization via Directional Fidelity Optimization](https://mlsanity.com/paper/2605.11396/) (2026)
- [Beyond Dense Adam States: Adaptive Log-Space Quantization for Memory-Efficient Optimizers](https://mlsanity.com/paper/2608.22322/) (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)

## Abstract (arXiv)

The rapid scaling of models has led to prohibitively high training and fine-tuning costs. A major factor accounting for memory consumption is the widespread use of stateful optimizers (e.g., Adam), which maintain auxiliary information of even 2x the model size in order to achieve optimal convergence. We therefore present SOLO in this work to spawn a novel type of optimizer that requires an extremely light memory footprint. While previous efforts have achieved certain success in 8-bit or 4-bit cases, SOLO enables Adam-style optimizers to maintain quantized states with precision as low as 3 bits, or even 2 bits. This immense progress is due to the identification and resolution of two key challenges: the signal swamping problem in unsigned quantization that results in unchanged state dynamics, and the increased gradient variance in signed quantization that leads to incorrect descent directions. The theoretical analysis suggests a tailored logarithmic quantization for the former and a precision-specific momentum hyperparameter for the latter. SOLO can thus be seamlessly applied to Adam-style optimizers, leading to substantial memory savings with minimal accuracy loss.