# GaLore+: Boosting Low-Rank Adaptation for LLMs with Cross-Head Projection

arXiv: https://arxiv.org/abs/2412.19820 · HTML: https://mlsanity.com/paper/2412.19820/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 42 references that are in the map.
- First posted on arXiv 15 Dec 2024.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (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)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [Learning multiple visual domains with residual adapters](https://mlsanity.com/paper/1705.08045/) (2017)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [Compacter: Efficient Low-Rank Hypercomplex Adapter Layers](https://mlsanity.com/paper/2106.04647/) (2021)
- [ChatDoctor: A Medical Chat Model Fine-Tuned on a Large Language Model Meta-AI (LLaMA) Using Medical Domain Knowledge](https://mlsanity.com/paper/2303.14070/) (2023)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [Parameter-efficient Multi-task Fine-tuning for Transformers via Shared Hypernetworks](https://mlsanity.com/paper/2106.04489/) (2021)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)
- [The E2E Dataset: New Challenges For End-to-End Generation](https://mlsanity.com/paper/1706.09254/) (2017)
- [WARP: Word-level Adversarial ReProgramming](https://mlsanity.com/paper/2101.00121/) (2021)
- [Scaling Down to Scale Up: A Guide to Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.15647/) (2023)
- [QA-LoRA: Quantization-Aware Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2309.14717/) (2023)
- [Exploring Versatile Generative Language Model Via Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2004.03829/) (2020)
- [Adam-mini: Use Fewer Learning Rates To Gain More](https://mlsanity.com/paper/2406.16793/) (2024)
- [Flora: Low-Rank Adapters Are Secretly Gradient Compressors](https://mlsanity.com/paper/2402.03293/) (2024)
- [Multi-Head Attention: Collaborate Instead of Concatenate](https://mlsanity.com/paper/2006.16362/) (2020)
- [RoSA: Accurate Parameter-Efficient Fine-Tuning via Robust Adaptation](https://mlsanity.com/paper/2401.04679/) (2024)
- [Fast Algorithms for Robust PCA via Gradient Descent](https://mlsanity.com/paper/1605.07784/) (2016)

## Built on by (most cited first, 8 of 8)

- [CoLA: Compute-Efficient Pre-Training of LLMs via Low-Rank Activation](https://mlsanity.com/paper/2502.10940/) (2025)
- [Memory-Efficient LLM Pretraining via Minimalist Optimizer Design](https://mlsanity.com/paper/2506.16659/) (2025)
- [AltLoRA: Towards Better Gradient Approximation in Low-Rank Adaptation with Alternating Projections](https://mlsanity.com/paper/2505.12455/) (2025)
- [Reparameterized LLM Training via Orthogonal Equivalence Transformation](https://mlsanity.com/paper/2506.08001/) (2025)
- [LORENZA: Enhancing Generalization in Low-Rank Gradient LLM Training via Efficient Zeroth-Order Adaptive SAM](https://mlsanity.com/paper/2502.19571/) (2025)
- [Scalable Parameter and Memory Efficient Pretraining for LLM: Recent Algorithmic Advances and Benchmarking](https://mlsanity.com/paper/2505.22922/) (2025)
- [POET-X: Memory-efficient LLM Training by Scaling Orthogonal Transformation](https://mlsanity.com/paper/2603.05500/) (2026)
- [Train Large, Deploy Compact: Structured Compression for Compact Low-Rank Adaptation](https://mlsanity.com/paper/2510.00192/) (2025)

## Abstract (arXiv)

Recent low-rank training methods, such as GaLore, have significantly reduced the memory required to optimize large language models (LLMs). However, these methods often suffer from time-consuming low-rank projection estimations. In particular, the singular value decomposition (SVD) in GaLore can consume more than 80% of the total training time. To address this issue, we propose GaLore+, which uses cross-head low-rank projection to reduce the substantial time consumption in estimating low-rank projections for multi-head attention. In addition, we employ randomized subspace iteration to achieve fast SVD. To further enhance performance, we propose sparsely coded residuals to reduce the errors caused by low-rank approximation on the first- and second-order moments of the optimizers and weight updates. We evaluate GaLore+ on arithmetic reasoning and natural language generation datasets. Our experiments demonstrate that GaLore+ delivers superior performance while achieving approximately 4× fine-tuning speed compared to vanilla GaLore.