# GWT: Scalable Optimizer State Compression for Large Language Model Training

arXiv: https://arxiv.org/abs/2501.07237 · HTML: https://mlsanity.com/paper/2501.07237/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 61 references that are in the map.
- First posted on arXiv 13 Jan 2025.

## Builds on (most cited first, 30 of 46)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [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)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [Training Deep Nets with Sublinear Memory Cost](https://mlsanity.com/paper/1604.06174/) (2016)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [8-bit Optimizers via Block-wise Quantization](https://mlsanity.com/paper/2110.02861/) (2021)

## Built on by (most cited first, 1 of 1)

- [Evolution of Optimization Methods: Algorithms, Scenarios, and Evaluations](https://mlsanity.com/paper/2604.12968/) (2026)

## Abstract (arXiv)

Training large language models (LLMs) requires substantial memory, a significant fraction of which is consumed by the moment states maintained by adaptive optimizers such as Adam. Existing memory-efficient approaches commonly compress parameters or gradients through low-rank projections, which may discard information outside the selected subspace or incur additional costs from subspace construction and singular value decomposition (SVD). We introduce Gradient Wavelet Transform (GWT), an SVD-free framework that applies a multilevel Haar transform to matrix gradients. GWT maintains first- and second-moment states only for the compact approximation coefficients, while retaining all detail coefficients transiently in each update. We show that the orthogonal transform preserves the complete current gradient and establish gradient alignment and a stationary-point guarantee for smooth objectives under bounded preconditioning and a directly verifiable coarse-momentum coherence condition. Experiments on language-model pre-training and downstream fine-tuning show that GWT reduces estimated model-and-optimizer-state memory by up to 52% while maintaining competitive or improved model quality. On LLaMA-3B pre-training, GWT achieves 1.9× the throughput of 8-bit Adam and is compatible with multiple optimizer families, including Adam, Adam-mini, and Muon.