# GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection

arXiv: https://arxiv.org/abs/2403.03507 · HTML: https://mlsanity.com/paper/2403.03507/

## Key facts

- Cited by 463 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 57 references that are in the map.
- First posted on arXiv 6 Mar 2024.

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

- [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)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [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)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [Scaling Vision Transformers](https://mlsanity.com/paper/2106.04560/) (2021)
- [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)
- [OpenAssistant Conversations -- Democratizing Large Language Model Alignment](https://mlsanity.com/paper/2304.07327/) (2023)
- [8-bit Optimizers via Block-wise Quantization](https://mlsanity.com/paper/2110.02861/) (2021)
- [Gradient Descent Happens in a Tiny Subspace](https://mlsanity.com/paper/1812.04754/) (2018)
- [ReLoRA: High-Rank Training Through Low-Rank Updates](https://mlsanity.com/paper/2307.05695/) (2023)
- [Delta Tuning: A Comprehensive Study of Parameter Efficient Methods for Pre-trained Language Models](https://mlsanity.com/paper/2203.06904/) (2022)
- [S-LoRA: Serving Thousands of Concurrent LoRA Adapters](https://mlsanity.com/paper/2311.03285/) (2023)
- [LoRA-FA: Efficient and Effective Low Rank Representation Fine-tuning](https://mlsanity.com/paper/2308.03303/) (2023)
- [ATOMO: Communication-efficient Learning via Atomic Sparsification](https://mlsanity.com/paper/1806.04090/) (2018)
- [Full Parameter Fine-tuning for Large Language Models with Limited Resources](https://mlsanity.com/paper/2306.09782/) (2023)
- [A Spectral Condition for Feature Learning](https://mlsanity.com/paper/2310.17813/) (2023)
- [Flora: Low-Rank Adapters Are Secretly Gradient Compressors](https://mlsanity.com/paper/2402.03293/) (2024)
- [Continual Learning in Low-rank Orthogonal Subspaces](https://mlsanity.com/paper/2010.11635/) (2020)
- [Chain of LoRA: Efficient Fine-tuning of Language Models via Residual Learning](https://mlsanity.com/paper/2401.04151/) (2024)
- [Stable and low-precision training for large-scale vision-language models](https://mlsanity.com/paper/2304.13013/) (2023)
- [Fast low-rank estimation by projected gradient descent: General statistical and algorithmic guarantees](https://mlsanity.com/paper/1509.03025/) (2015)

## Built on by (most cited first, 30 of 463)

- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [NVILA: Efficient Frontier Visual Language Models](https://mlsanity.com/paper/2412.04468/) (2024)
- [SOAP: Improving and Stabilizing Shampoo using Adam](https://mlsanity.com/paper/2409.11321/) (2024)
- [SVDQuant: Absorbing Outliers by Low-Rank Components for 4-Bit Diffusion Models](https://mlsanity.com/paper/2411.05007/) (2024)
- [LoRA-GA: Low-Rank Adaptation with Gradient Approximation](https://mlsanity.com/paper/2407.05000/) (2024)
- [Adam-mini: Use Fewer Learning Rates To Gain More](https://mlsanity.com/paper/2406.16793/) (2024)
- [On-Device Language Models: A Comprehensive Review](https://mlsanity.com/paper/2409.00088/) (2024)
- [LISA: Layerwise Importance Sampling for Memory-Efficient Large Language Model Fine-Tuning](https://mlsanity.com/paper/2403.17919/) (2024)
- [NorMuon: Making Muon more efficient and scalable](https://mlsanity.com/paper/2510.05491/) (2025)
- [LoRA-Pro: Are Low-Rank Adapters Properly Optimized?](https://mlsanity.com/paper/2407.18242/) (2024)
- [Dion: Distributed Orthonormalized Updates](https://mlsanity.com/paper/2504.05295/) (2025)
- [A Survey on LoRA of Large Language Models](https://mlsanity.com/paper/2407.11046/) (2024)
- [Palu: Compressing KV-Cache with Low-Rank Projection](https://mlsanity.com/paper/2407.21118/) (2024)
- [The Curse of Depth in Large Language Models](https://mlsanity.com/paper/2502.05795/) (2025)
- [Lean Copilot: Large Language Models as Copilots for Theorem Proving in Lean](https://mlsanity.com/paper/2404.12534/) (2024)
- [ASGO: Adaptive Structured Gradient Optimization](https://mlsanity.com/paper/2503.20762/) (2025)
- [The Path Not Taken: RLVR Provably Learns Off the Principals](https://mlsanity.com/paper/2511.08567/) (2025)
- [APOLLO: SGD-like Memory, AdamW-level Performance](https://mlsanity.com/paper/2412.05270/) (2024)
- [Enhancing Zeroth-order Fine-tuning for Language Models with Low-rank Structures](https://mlsanity.com/paper/2410.07698/) (2024)
- [Understanding the Performance and Estimating the Cost of LLM Fine-Tuning](https://mlsanity.com/paper/2408.04693/) (2024)
- [Cautious Optimizers: Improving Training with One Line of Code](https://mlsanity.com/paper/2411.16085/) (2024)
- [Med-MoE: Mixture of Domain-Specific Experts for Lightweight Medical Vision-Language Models](https://mlsanity.com/paper/2404.10237/) (2024)
- [SLTrain: a sparse plus low-rank approach for parameter and memory efficient pretraining](https://mlsanity.com/paper/2406.02214/) (2024)
- [CorDA: Context-Oriented Decomposition Adaptation of Large Language Models for Task-Aware Parameter-Efficient Fine-tuning](https://mlsanity.com/paper/2406.05223/) (2024)
- [Fira: Can We Achieve Full-rank Training of LLMs Under Low-rank Constraint?](https://mlsanity.com/paper/2410.01623/) (2024)
- [Memory-Efficient LLM Training with Online Subspace Descent](https://mlsanity.com/paper/2408.12857/) (2024)
- [Q-GaLore: Quantized GaLore with INT4 Projection and Layer-Adaptive Low-Rank Gradients](https://mlsanity.com/paper/2407.08296/) (2024)
- [LDAdam: Adaptive Optimization from Low-Dimensional Gradient Statistics](https://mlsanity.com/paper/2410.16103/) (2024)

## Abstract (arXiv)

Training Large Language Models (LLMs) presents significant memory challenges, predominantly due to the growing size of weights and optimizer states. Common memory-reduction approaches, such as low-rank adaptation (LoRA), add a trainable low-rank matrix to the frozen pre-trained weight in each layer, reducing trainable parameters and optimizer states. However, such approaches typically underperform training with full-rank weights in both pre-training and fine-tuning stages since they limit the parameter search to a low-rank subspace and alter the training dynamics, and further, may require full-rank warm start. In this work, we propose Gradient Low-Rank Projection (GaLore), a training strategy that allows full-parameter learning but is more memory-efficient than common low-rank adaptation methods such as LoRA. Our approach reduces memory usage by up to 65.5% in optimizer states while maintaining both efficiency and performance for pre-training on LLaMA 1B and 7B architectures with C4 dataset with up to 19.7B tokens, and on fine-tuning RoBERTa on GLUE tasks. Our 8-bit GaLore further reduces optimizer memory by up to 82.5% and total training memory by 63.3%, compared to a BF16 baseline. Notably, we demonstrate, for the first time, the feasibility of pre-training a 7B model on consumer GPUs with 24GB memory (e.g., NVIDIA RTX 4090) without model parallel, checkpointing, or offloading strategies.