# LoRA-GA: Low-Rank Adaptation with Gradient Approximation

arXiv: https://arxiv.org/abs/2407.05000 · HTML: https://mlsanity.com/paper/2407.05000/

## Key facts

- Cited by 141 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 45 references that are in the map.
- First posted on arXiv 6 Jul 2024.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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 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)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [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)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [Instruction Tuning for Large Language Models: A Survey](https://mlsanity.com/paper/2308.10792/) (2023)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer](https://mlsanity.com/paper/2203.03466/) (2022)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [Gradient Descent Happens in a Tiny Subspace](https://mlsanity.com/paper/1812.04754/) (2018)
- [Feature Learning in Infinite-Width Neural Networks](https://mlsanity.com/paper/2011.14522/) (2020)
- [FedPara: Low-Rank Hadamard Product for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2108.06098/) (2021)
- [AdaMix: Mixture-of-Adaptations for Parameter-efficient Model Tuning](https://mlsanity.com/paper/2210.17451/) (2022)
- [Full Parameter Fine-tuning for Large Language Models with Limited Resources](https://mlsanity.com/paper/2306.09782/) (2023)

## Built on by (most cited first, 30 of 141)

- [CycleResearcher: Improving Automated Research via Automated Review](https://mlsanity.com/paper/2411.00816/) (2024)
- [LoRA-Pro: Are Low-Rank Adapters Properly Optimized?](https://mlsanity.com/paper/2407.18242/) (2024)
- [Make LoRA Great Again: Boosting LoRA with Adaptive Singular Values and Mixture-of-Experts Optimization Alignment](https://mlsanity.com/paper/2502.16894/) (2025)
- [Initialization using Update Approximation is a Silver Bullet for Extremely Efficient Low-Rank Fine-Tuning](https://mlsanity.com/paper/2411.19557/) (2024)
- [Flat-LoRA: Low-Rank Adaptation over a Flat Loss Landscape](https://mlsanity.com/paper/2409.14396/) (2024)
- [Parameter Efficient Fine-tuning via Explained Variance Adaptation](https://mlsanity.com/paper/2410.07170/) (2024)
- [Beyond Zero Initialization: Investigating the Impact of Non-Zero Initialization on LoRA Fine-Tuning Dynamics](https://mlsanity.com/paper/2505.23194/) (2025)
- [On the Crucial Role of Initialization for Matrix Factorization](https://mlsanity.com/paper/2410.18965/) (2024)
- [See Further for Parameter Efficient Fine-tuning by Standing on the Shoulders of Decomposition](https://mlsanity.com/paper/2407.05417/) (2024)
- [LoFT: Low-Rank Adaptation That Behaves Like Full Fine-Tuning](https://mlsanity.com/paper/2505.21289/) (2025)
- [LoRA meets Riemannion: Muon Optimizer for Parametrization-independent Low-Rank Adapters](https://mlsanity.com/paper/2507.12142/) (2025)
- [GoRA: Gradient-driven Adaptive Low Rank Adaptation](https://mlsanity.com/paper/2502.12171/) (2025)
- [DAGPrompT: Pushing the Limits of Graph Prompting with a Distribution-aware Graph Prompt Tuning Approach](https://mlsanity.com/paper/2501.15142/) (2025)
- [LoRA-MGPO: Mitigating Double Descent in Low-Rank Adaptation via Momentum-Guided Perturbation Optimization](https://mlsanity.com/paper/2502.14538/) (2025)
- [GraLoRA: Granular Low-Rank Adaptation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2505.20355/) (2025)
- [On the Convergence Rate of LoRA Gradient Descent](https://mlsanity.com/paper/2512.18248/) (2025)
- [Learning Rate Matters: Vanilla LoRA May Suffice for LLM Fine-tuning](https://mlsanity.com/paper/2602.04998/) (2026)
- [A Stronger Mixture of Low-Rank Experts for Fine-Tuning Foundation Models](https://mlsanity.com/paper/2502.15828/) (2025)
- [PRO-VPT: Distribution-Adaptive Visual Prompt Tuning via Prompt Relocation](https://mlsanity.com/paper/2503.06901/) (2025)
- [AltLoRA: Towards Better Gradient Approximation in Low-Rank Adaptation with Alternating Projections](https://mlsanity.com/paper/2505.12455/) (2025)
- [RefLoRA: Refactored Low-Rank Adaptation for Efficient Fine-Tuning of Large Models](https://mlsanity.com/paper/2505.18877/) (2025)
- [SparseLoRA: Accelerating LLM Fine-Tuning with Contextual Sparsity](https://mlsanity.com/paper/2506.16500/) (2025)
- [Learning Rate Scaling across LoRA Ranks and Transfer to Full Finetuning](https://mlsanity.com/paper/2602.06204/) (2026)
- [COAP: Memory-Efficient Training with Correlation-Aware Gradient Projection](https://mlsanity.com/paper/2412.00071/) (2024)
- [Zero Sum SVD: Balancing Loss Sensitivity for Low Rank LLM Compression](https://mlsanity.com/paper/2602.02848/) (2026)
- [BA-LoRA: Bias-Alleviating Low-Rank Adaptation to Mitigate Catastrophic Inheritance in Large Language Models](https://mlsanity.com/paper/2408.04556/) (2024)
- [MiSS: Revisiting the Trade-off in LoRA with an Efficient Shard-Sharing Structure](https://mlsanity.com/paper/2409.15371/) (2024)
- [The Primacy of Magnitude in Low-Rank Adaptation](https://mlsanity.com/paper/2507.06558/) (2025)
- [PLAN: Proactive Low-Rank Allocation for Continual Learning](https://mlsanity.com/paper/2510.21188/) (2025)
- [Can Muon Fine-tune Adam-Pretrained Models?](https://mlsanity.com/paper/2605.10468/) (2026)

## Abstract (arXiv)

Fine-tuning large-scale pretrained models is prohibitively expensive in terms of computational and memory costs. LoRA, as one of the most popular Parameter-Efficient Fine-Tuning (PEFT) methods, offers a cost-effective alternative by fine-tuning an auxiliary low-rank model that has significantly fewer parameters. Although LoRA reduces the computational and memory requirements significantly at each iteration, extensive empirical evidence indicates that it converges at a considerably slower rate compared to full fine-tuning, ultimately leading to increased overall compute and often worse test performance. In our paper, we perform an in-depth investigation of the initialization method of LoRA and show that careful initialization (without any change of the architecture and the training algorithm) can significantly enhance both efficiency and performance. In particular, we introduce a novel initialization method, LoRA-GA (Low Rank Adaptation with Gradient Approximation), which aligns the gradients of low-rank matrix product with those of full fine-tuning at the first step. Our extensive experiments demonstrate that LoRA-GA achieves a convergence rate comparable to that of full fine-tuning (hence being significantly faster than vanilla LoRA as well as various recent improvements) while simultaneously attaining comparable or even better performance. For example, on the subset of the GLUE dataset with T5-Base, LoRA-GA outperforms LoRA by 5.69% on average. On larger models such as Llama 2-7B, LoRA-GA shows performance improvements of 0.34, 11.52%, and 5.05% on MT-bench, GSM8K, and Human-eval, respectively. Additionally, we observe up to 2-4 times convergence speed improvement compared to vanilla LoRA, validating its effectiveness in accelerating convergence and enhancing model performance. Code is available at https://github.com/Outsider565/LoRA-GA.