# Grass: Compute Efficient Low-Memory LLM Training with Structured Sparse Gradients

arXiv: https://arxiv.org/abs/2406.17660 · HTML: https://mlsanity.com/paper/2406.17660/

## Key facts

- Cited by 18 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 25 Jun 2024.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [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)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [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)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [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)
- [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)
- [signSGD: Compressed Optimisation for Non-Convex Problems](https://mlsanity.com/paper/1802.04434/) (2018)
- [Dolma: an Open Corpus of Three Trillion Tokens for Language Model Pretraining Research](https://mlsanity.com/paper/2402.00159/) (2024)
- [Deep Gradient Compression: Reducing the Communication Bandwidth for Distributed Training](https://mlsanity.com/paper/1712.01887/) (2017)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [How Far Can Camels Go? Exploring the State of Instruction Tuning on Open Resources](https://mlsanity.com/paper/2306.04751/) (2023)
- [8-bit Optimizers via Block-wise Quantization](https://mlsanity.com/paper/2110.02861/) (2021)
- [Sparsified SGD with Memory](https://mlsanity.com/paper/1809.07599/) (2018)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [TernGrad: Ternary Gradients to Reduce Communication in Distributed Deep Learning](https://mlsanity.com/paper/1705.07878/) (2017)
- [PowerSGD: Practical Low-Rank Gradient Compression for Distributed Optimization](https://mlsanity.com/paper/1905.13727/) (2019)

## Built on by (most cited first, 18 of 18)

- [Enhancing Zeroth-order Fine-tuning for Language Models with Low-rank Structures](https://mlsanity.com/paper/2410.07698/) (2024)
- [SubTrack++ : Gradient Subspace Tracking for Scalable LLM Training](https://mlsanity.com/paper/2502.01586/) (2025)
- [CompAct: Compressed Activations for Memory-Efficient LLM Training](https://mlsanity.com/paper/2410.15352/) (2024)
- [Memory-Efficient LLM Pretraining via Minimalist Optimizer Design](https://mlsanity.com/paper/2506.16659/) (2025)
- [Slamming: Training a Speech Language Model on One GPU in a Day](https://mlsanity.com/paper/2502.15814/) (2025)
- [Breaking the Frozen Subspace: Importance Sampling for Low-Rank Optimization in LLM Pretraining](https://mlsanity.com/paper/2502.05790/) (2025)
- [Unbiased Gradient Low-Rank Projection](https://mlsanity.com/paper/2510.17802/) (2025)
- [TensorGRaD: Tensor Gradient Robust Decomposition for Memory-Efficient Neural Operator Training](https://mlsanity.com/paper/2501.02379/) (2025)
- [Scalable Parameter and Memory Efficient Pretraining for LLM: Recent Algorithmic Advances and Benchmarking](https://mlsanity.com/paper/2505.22922/) (2025)
- [Lean and Mean Adaptive Optimization via Subset-Norm and Subspace-Momentum with Convergence Guarantees](https://mlsanity.com/paper/2411.07120/) (2024)
- [QKV Projections Require a Fraction of Their Memory](https://mlsanity.com/paper/2506.02939/) (2025)
- [Memory-Efficient Fine-Tuning via Low-Rank Activation Compression](https://mlsanity.com/paper/2509.23472/) (2025)
- [On the Duality between Gradient Transformations and Adapters](https://mlsanity.com/paper/2502.13811/) (2025)
- [Geometrically Principled Randomized Optimization for Efficient LLM Training](https://mlsanity.com/paper/2510.01878/) (2025)
- [CosmosAlign: Adapting a World Foundation Model for Generative Traffic Video Forecasting](https://mlsanity.com/paper/2608.07693/) (2026)
- [PLUMAGE: Probabilistic Low rank Unbiased Min Variance Gradient Estimator for Efficient Large Model Training](https://mlsanity.com/paper/2505.18313/) (2025)
- [Beyond Perplexity: A Geometric and Spectral Study of Low-Rank Pre-Training](https://mlsanity.com/paper/2605.13652/) (2026)
- [Memory-Efficient Subspace Optimization with Residual Correction: From Momentum SGD to Muon](https://mlsanity.com/paper/2610.19844/) (2026)

## Abstract (arXiv)

Large language model (LLM) training and finetuning are often bottlenecked by limited GPU memory. While existing projection-based optimization methods address this by projecting gradients into a lower-dimensional subspace to reduce optimizer state memory, they typically rely on dense projection matrices, which can introduce computational and memory overheads. In this work, we propose Grass (GRAdient Stuctured Sparsification), a novel approach that leverages sparse projections to transform gradients into structured sparse updates. This design not only significantly reduces memory usage for optimizer states but also minimizes gradient memory footprint, computation, and communication costs, leading to substantial throughput improvements. Extensive experiments on pretraining and finetuning tasks demonstrate that Grass achieves competitive performance to full-rank training and existing projection-based methods. Notably, Grass enables half-precision pretraining of a 13B parameter LLaMA model on a single 40GB A100 GPU--a feat infeasible for previous methods--and yields up to a 2× throughput improvement on an 8-GPU system. Code can be found at https://github.com/aashiqmuhamed/GRASS .