# LoLDU: Low-Rank Adaptation via Lower-Diag-Upper Decomposition for Parameter-Efficient Fine-Tuning

arXiv: https://arxiv.org/abs/2410.13618 · HTML: https://mlsanity.com/paper/2410.13618/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 76 references that are in the map.
- First posted on arXiv 17 Oct 2024.

## Builds on (most cited first, 30 of 53)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (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)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [An Image is Worth One Word: Personalizing Text-to-Image Generation using Textual Inversion](https://mlsanity.com/paper/2208.01618/) (2022)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [Visual Prompt Tuning](https://mlsanity.com/paper/2203.12119/) (2022)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [Multi-Concept Customization of Text-to-Image Diffusion](https://mlsanity.com/paper/2212.04488/) (2022)
- [LLaMA-Adapter: Efficient Fine-tuning of Language Models with Zero-init Attention](https://mlsanity.com/paper/2303.16199/) (2023)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://mlsanity.com/paper/2301.13688/) (2023)
- [OpenAssistant Conversations -- Democratizing Large Language Model Alignment](https://mlsanity.com/paper/2304.07327/) (2023)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [ImageNet-21K Pretraining for the Masses](https://mlsanity.com/paper/2104.10972/) (2021)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)

## Built on by (most cited first, 6 of 6)

- [Tensor Product Attention Is All You Need](https://mlsanity.com/paper/2501.06425/) (2025)
- [Don't Forget the Nonlinearity: Unlocking Activation Functions in Efficient Fine-Tuning](https://mlsanity.com/paper/2509.13240/) (2025)
- [Localized LoRA-MoE: Block-wise Low-Rank Experts With Adaptive Routing](https://mlsanity.com/paper/2607.05114/) (2026)
- [Localized LoRA: A Structured Low-Rank Approximation for Efficient Fine-Tuning](https://mlsanity.com/paper/2506.00236/) (2025)
- [Early Intervention for VFM-based Multimodal Medical Image Classification](https://mlsanity.com/paper/2603.17514/) (2026)
- [What Does the Rank Buy? A Spectral and Distributional Analysis of Low-Rank Adaptation](https://mlsanity.com/paper/2609.32002/) (2026)

## Abstract (arXiv)

The rapid growth of model scale has necessitated substantial computational resources for fine-tuning. Existing approach such as Low-Rank Adaptation (LoRA) has sought to address the problem of handling the large updated parameters in full fine-tuning. However, LoRA utilize random initialization and optimization of low-rank matrices to approximate updated weights, which can result in suboptimal convergence and an accuracy gap compared to full fine-tuning. To address these issues, we propose LoLDU, a Parameter-Efficient Fine-Tuning (PEFT) approach that significantly reduces trainable parameters by 2600 times compared to regular PEFT methods while maintaining comparable performance. LoLDU leverages Lower-Diag-Upper Decomposition (LDU) to initialize low-rank matrices for faster convergence and orthogonality. We focus on optimizing the diagonal matrix for scaling transformations. To the best of our knowledge, LoLDU has the fewest parameters among all PEFT approaches. We conducted extensive experiments across 4 instruction-following datasets, 6 natural language understanding (NLU) datasets, 8 image classification datasets, and image generation datasets with multiple model types (LLaMA2, RoBERTa, ViT, and Stable Diffusion), providing a comprehensive and detailed analysis. Our open-source code can be accessed at hrefhttps://github.com/SKDDJ/LoLDUhttps://github.com/SKDDJ/LoLDU.