# Delta-LoRA: Fine-Tuning High-Rank Parameters with the Delta of Low-Rank Matrices

arXiv: https://arxiv.org/abs/2309.02411 · HTML: https://mlsanity.com/paper/2309.02411/

## Key facts

- Cited by 74 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 37 references that are in the map.
- First posted on arXiv 5 Sep 2023.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [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)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Align before Fuse: Vision and Language Representation Learning with Momentum Distillation](https://mlsanity.com/paper/2107.07651/) (2021)
- [Rethinking Semantic Segmentation from a Sequence-to-Sequence Perspective with Transformers](https://mlsanity.com/paper/2012.15840/) (2020)
- [Don't Give Me the Details, Just the Summary! Topic-Aware Convolutional Neural Networks for Extreme Summarization](https://mlsanity.com/paper/1808.08745/) (2018)
- [DeBERTaV3: Improving DeBERTa using ELECTRA-Style Pre-Training with Gradient-Disentangled Embedding Sharing](https://mlsanity.com/paper/2111.09543/) (2021)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [A Survey on Deep Transfer Learning](https://mlsanity.com/paper/1808.01974/) (2018)
- [Parameter-Efficient Transfer Learning with Diff Pruning](https://mlsanity.com/paper/2012.07463/) (2020)
- [DyLoRA: Parameter Efficient Tuning of Pre-trained Models using Dynamic Search-Free Low-Rank Adaptation](https://mlsanity.com/paper/2210.07558/) (2022)
- [Full Parameter Fine-tuning for Large Language Models with Limited Resources](https://mlsanity.com/paper/2306.09782/) (2023)
- [One-for-All: Generalized LoRA for Parameter-Efficient Fine-tuning](https://mlsanity.com/paper/2306.07967/) (2023)
- [Sparse Progressive Distillation: Resolving Overfitting under Pretrain-and-Finetune Paradigm](https://mlsanity.com/paper/2110.08190/) (2021)

## Built on by (most cited first, 30 of 74)

- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [MM-LLMs: Recent Advances in MultiModal Large Language Models](https://mlsanity.com/paper/2401.13601/) (2024)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)
- [Parameter-Efficient Fine-Tuning Methods for Pretrained Language Models: A Critical Review and Assessment](https://mlsanity.com/paper/2312.12148/) (2023)
- [Parameter-Efficient Orthogonal Finetuning via Butterfly Factorization](https://mlsanity.com/paper/2311.06243/) (2023)
- [Low-Rank Few-Shot Adaptation of Vision-Language Models](https://mlsanity.com/paper/2405.18541/) (2024)
- [A Survey on LoRA of Large Language Models](https://mlsanity.com/paper/2407.11046/) (2024)
- [Riemannian Preconditioned LoRA for Fine-Tuning Foundation Models](https://mlsanity.com/paper/2402.02347/) (2024)
- [K-LoRA: Unlocking Training-Free Fusion of Any Subject and Style LoRAs](https://mlsanity.com/paper/2502.18461/) (2025)
- [Parameter-Efficient Fine-Tuning for Foundation Models](https://mlsanity.com/paper/2501.13787/) (2025)
- [LoRA Dropout as a Sparsity Regularizer for Overfitting Control](https://mlsanity.com/paper/2404.09610/) (2024)
- [Spectral Adapter: Fine-Tuning in Spectral Space](https://mlsanity.com/paper/2405.13952/) (2024)
- [Parameter Efficient Fine-tuning via Explained Variance Adaptation](https://mlsanity.com/paper/2410.07170/) (2024)
- [MELoRA: Mini-Ensemble Low-Rank Adapters for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2402.17263/) (2024)
- [LoRA-Mixer: Coordinate Modular LoRA Experts Through Serial Attention Routing](https://mlsanity.com/paper/2507.00029/) (2025)
- [Random Masking Finds Winning Tickets for Parameter Efficient Fine-tuning](https://mlsanity.com/paper/2405.02596/) (2024)
- [SVFit: Parameter-Efficient Fine-Tuning of Large Pre-Trained Models Using Singular Values](https://mlsanity.com/paper/2409.05926/) (2024)
- [Quantum-PEFT: Ultra parameter-efficient fine-tuning](https://mlsanity.com/paper/2503.05431/) (2025)
- [FedSVD: Adaptive Orthogonalization for Private Federated Learning with LoRA](https://mlsanity.com/paper/2505.12805/) (2025)
- [DeLoRA: Decoupling Angles and Strength in Low-rank Adaptation](https://mlsanity.com/paper/2503.18225/) (2025)
- [Learning Rate Matters: Vanilla LoRA May Suffice for LLM Fine-tuning](https://mlsanity.com/paper/2602.04998/) (2026)
- [A Fine-tuning Enhanced RAG System with Quantized Influence Measure as AI Judge](https://mlsanity.com/paper/2402.17081/) (2024)
- [AltLoRA: Towards Better Gradient Approximation in Low-Rank Adaptation with Alternating Projections](https://mlsanity.com/paper/2505.12455/) (2025)
- [Why Steering Works: Toward a Unified View of Language Model Parameter Dynamics](https://mlsanity.com/paper/2602.02343/) (2026)
- [BA-LoRA: Bias-Alleviating Low-Rank Adaptation to Mitigate Catastrophic Inheritance in Large Language Models](https://mlsanity.com/paper/2408.04556/) (2024)
- [AutoLoRA: AutoGuidance Meets Low-Rank Adaptation for Diffusion Models](https://mlsanity.com/paper/2410.03941/) (2024)
- [Breaking the Frozen Subspace: Importance Sampling for Low-Rank Optimization in LLM Pretraining](https://mlsanity.com/paper/2502.05790/) (2025)
- [Orthogonal Finetuning Made Scalable](https://mlsanity.com/paper/2506.19847/) (2025)
- [The Primacy of Magnitude in Low-Rank Adaptation](https://mlsanity.com/paper/2507.06558/) (2025)
- [KD-LoRA: A Hybrid Approach to Efficient Fine-Tuning with LoRA and Knowledge Distillation](https://mlsanity.com/paper/2410.20777/) (2024)

## Abstract (arXiv)

In this paper, we present Delta-LoRA, which is a novel parameter-efficient approach to fine-tune large language models (LLMs). In contrast to LoRA and other low-rank adaptation methods such as AdaLoRA, Delta-LoRA not only updates the low-rank matrices bA and bB, but also propagate the learning to the pre-trained weights bW via updates utilizing the delta of the product of two low-rank matrices (bA(t+1)bB(t+1) - bA(t)bB(t)). Such a strategy effectively addresses the limitation that the incremental update of low-rank matrices is inadequate for learning representations capable for downstream tasks. Moreover, as the update of bW does not need to compute the gradients of bW and store their momentums, Delta-LoRA shares comparable memory requirements and computational costs with LoRA. Extensive experiments show that Delta-LoRA significantly outperforms existing low-rank adaptation methods. We further support these results with comprehensive analyses that underscore the effectiveness of Delta-LoRA.