# Memory Efficient Optimizers with 4-bit States

arXiv: https://arxiv.org/abs/2309.01507 · HTML: https://mlsanity.com/paper/2309.01507/

## Key facts

- Cited by 54 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 58 references that are in the map.
- First posted on arXiv 4 Sep 2023.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [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)
- [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)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [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)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [fairseq: A Fast, Extensible Toolkit for Sequence Modeling](https://mlsanity.com/paper/1904.01038/) (2019)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [Training Deep Nets with Sublinear Memory Cost](https://mlsanity.com/paper/1604.06174/) (2016)
- [GLM-130B: An Open Bilingual Pre-trained Model](https://mlsanity.com/paper/2210.02414/) (2022)

## Built on by (most cited first, 30 of 54)

- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [SageAttention: Accurate 8-Bit Attention for Plug-and-play Inference Acceleration](https://mlsanity.com/paper/2410.02367/) (2024)
- [Adam-mini: Use Fewer Learning Rates To Gain More](https://mlsanity.com/paper/2406.16793/) (2024)
- [In Search of Adam's Secret Sauce](https://mlsanity.com/paper/2505.21829/) (2025)
- [COAT: Compressing Optimizer states and Activation for Memory-Efficient FP8 Training](https://mlsanity.com/paper/2410.19313/) (2024)
- [A Survey of Low-bit Large Language Models: Basics, Systems, and Algorithms](https://mlsanity.com/paper/2409.16694/) (2024)
- [Zeroth-Order Fine-Tuning of LLMs in Random Subspaces](https://mlsanity.com/paper/2410.08989/) (2024)
- [VeLoRA: Memory Efficient Training using Rank-1 Sub-Token Projections](https://mlsanity.com/paper/2405.17991/) (2024)
- [4-bit Shampoo for Memory-Efficient Network Training](https://mlsanity.com/paper/2405.18144/) (2024)
- [Grass: Compute Efficient Low-Memory LLM Training with Structured Sparse Gradients](https://mlsanity.com/paper/2406.17660/) (2024)
- [AdaRankGrad: Adaptive Gradient-Rank and Moments for Memory-Efficient LLMs Training and Fine-Tuning](https://mlsanity.com/paper/2410.17881/) (2024)
- [SubTrack++ : Gradient Subspace Tracking for Scalable LLM Training](https://mlsanity.com/paper/2502.01586/) (2025)
- [Propulsion: Steering LLM with Tiny Fine-Tuning](https://mlsanity.com/paper/2409.10927/) (2024)
- [Memory-Efficient Optimization with Factorized Hamiltonian Descent](https://mlsanity.com/paper/2406.09958/) (2024)
- [Identifying Sensitive Weights via Post-quantization Integral](https://mlsanity.com/paper/2503.01901/) (2025)
- [Low-Precision Training of Large Language Models: Methods, Challenges, and Opportunities](https://mlsanity.com/paper/2505.01043/) (2025)
- [QFT: Quantized Full-parameter Tuning of LLMs with Affordable Resources](https://mlsanity.com/paper/2310.07147/) (2023)
- [Exploring Quantization for Efficient Pre-Training of Transformer Language Models](https://mlsanity.com/paper/2407.11722/) (2024)
- [Parameter-Efficient Fine-Tuning of Large Language Models using Semantic Knowledge Tuning](https://mlsanity.com/paper/2410.08598/) (2024)
- [FRUGAL: Memory-Efficient Optimization by Reducing State Overhead for Scalable Training](https://mlsanity.com/paper/2411.07837/) (2024)
- [Leveraging Coordinate Momentum in SignSGD and Muon: Memory-Optimized Zero-Order](https://mlsanity.com/paper/2506.04430/) (2025)
- [Adapprox: Adaptive Approximation in Adam Optimization via Randomized Low-Rank Matrices](https://mlsanity.com/paper/2403.14958/) (2024)
- [No More Adam: Learning Rate Scaling at Initialization is All You Need](https://mlsanity.com/paper/2412.11768/) (2024)
- [SAGE: A Framework of Precise Retrieval for RAG](https://mlsanity.com/paper/2503.01713/) (2025)
- [GradPower: Powering Gradients for Faster Language Model Pre-Training](https://mlsanity.com/paper/2505.24275/) (2025)
- [Full-Stack FP4: Stable LLM Pretraining with Quantized Projections, Optimizers, and Attention](https://mlsanity.com/paper/2607.04422/) (2026)
- [Breaking the Frozen Subspace: Importance Sampling for Low-Rank Optimization in LLM Pretraining](https://mlsanity.com/paper/2502.05790/) (2025)
- [100K or 100 Days: Trade-offs when Pre-Training with Academic Resources](https://mlsanity.com/paper/2410.23261/) (2024)
- [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)
- [LORENZA: Enhancing Generalization in Low-Rank Gradient LLM Training via Efficient Zeroth-Order Adaptive SAM](https://mlsanity.com/paper/2502.19571/) (2025)

## Abstract (arXiv)

Optimizer states are a major source of memory consumption for training neural networks, limiting the maximum trainable model within given memory budget. Compressing the optimizer states from 32-bit floating points to lower bitwidth is promising to reduce the training memory footprint, while the current lowest achievable bitwidth is 8-bit. In this work, we push optimizer states bitwidth down to 4-bit through a detailed empirical analysis of first and second moments. Specifically, we find that moments have complicated outlier patterns, that current block-wise quantization cannot accurately approximate. We use a smaller block size and propose to utilize both row-wise and column-wise information for better quantization. We further identify a zero point problem of quantizing the second moment, and solve this problem with a linear quantizer that excludes the zero point. Our 4-bit optimizers are evaluated on a wide variety of benchmarks including natural language understanding, machine translation, image classification, and instruction tuning. On all the tasks our optimizers can achieve comparable accuracy with their full-precision counterparts, while enjoying better memory efficiency.