# Bridging The Gap between Low-rank and Orthogonal Adaptation via Householder Reflection Adaptation

arXiv: https://arxiv.org/abs/2405.17484 · HTML: https://mlsanity.com/paper/2405.17484/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 67 references that are in the map.
- First posted on arXiv 24 May 2024.

## Builds on (most cited first, 30 of 49)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (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)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [T2I-Adapter: Learning Adapters to Dig out More Controllable Ability for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.08453/) (2023)
- [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)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [DeepSpeed-MoE: Advancing Mixture-of-Experts Inference and Training to Power Next-Generation AI Scale](https://mlsanity.com/paper/2201.05596/) (2022)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)
- [SPoT: Better Frozen Model Adaptation through Soft Prompt Transfer](https://mlsanity.com/paper/2110.07904/) (2021)
- [DyLoRA: Parameter Efficient Tuning of Pre-trained Models using Dynamic Search-Free Low-Rank Adaptation](https://mlsanity.com/paper/2210.07558/) (2022)
- [Parameter-Efficient Fine-Tuning Methods for Pretrained Language Models: A Critical Review and Assessment](https://mlsanity.com/paper/2312.12148/) (2023)

## Built on by (most cited first, 15 of 15)

- [Learning Rate Matters: Vanilla LoRA May Suffice for LLM Fine-tuning](https://mlsanity.com/paper/2602.04998/) (2026)
- [Orthogonal Finetuning Made Scalable](https://mlsanity.com/paper/2506.19847/) (2025)
- [MoORE: SVD-based Model MoE-ization for Conflict- and Oblivion-Resistant Multi-Task Adaptation](https://mlsanity.com/paper/2506.14436/) (2025)
- [Parameter-Efficient Fine-Tuning via Circular Convolution](https://mlsanity.com/paper/2407.19342/) (2024)
- [Calibrating and Rotating: A Unified Framework for Weight Conditioning in PEFT](https://mlsanity.com/paper/2511.00051/) (2025)
- [CLOVER: Cross-Layer Orthogonal Vectors Pruning and Fine-Tuning](https://mlsanity.com/paper/2411.17426/) (2024)
- [Transformed Low-rank Adaptation via Tensor Decomposition and Its Applications to Text-to-image Models](https://mlsanity.com/paper/2501.08727/) (2025)
- [HOFT: Householder Orthogonal Fine-tuning](https://mlsanity.com/paper/2505.16531/) (2025)
- [Low-Rank Adaptation Redux for Large Models](https://mlsanity.com/paper/2604.21905/) (2026)
- [PAID: Pairwise Angular-Invariant Decomposition for Continual Test-Time Adaptation](https://mlsanity.com/paper/2506.02453/) (2025)
- [SliceFine: The Universal Winning-Slice Hypothesis for Pretrained Networks](https://mlsanity.com/paper/2510.08513/) (2025)
- [A Comparative Study of Adaptation Strategies for Time Series Foundation Models in Anomaly Detection](https://mlsanity.com/paper/2601.00446/) (2026)
- [LOFT: Low-Rank Orthogonal Fine-Tuning via Task-Aware Support Selection](https://mlsanity.com/paper/2605.11872/) (2026)
- [LoCO: Low-rank Compositional Rotation Fine-tuning](https://mlsanity.com/paper/2605.15916/) (2026)
- [YOLO-PEFT: Parameter-Efficient Fine-Tuning on YOLO Family](https://mlsanity.com/paper/2608.07051/) (2026)

## Abstract (arXiv)

While following different technical routes, both low-rank and orthogonal adaptation techniques can efficiently adapt large-scale pre-training models in specific tasks or domains based on a small piece of trainable parameters. In this study, we bridge the gap between these two techniques, proposing a simple but effective adaptation method based on Householder reflections. Given a pre-trained model, our method fine-tunes its layers by multiplying each frozen weight matrix with an orthogonal matrix constructed by a chain of learnable Householder reflections (HRs). This HR-based orthogonal fine-tuning is equivalent to an adaptive low-rank adaptation. Moreover, we show that the orthogonality of the reflection planes corresponding to the HRs impacts the model capacity and regularity. The analysis motivates us to regularize the orthogonality of the HRs, leading to different implementations of the proposed Householder reflection adaptation (HRA) method. Compared with state-of-the-art methods, HRA achieves superior performance with fewer learnable parameters when adapting large language models and conditional image generators. The code of the experiments is available at urlhttps://github.com/DaShenZi721/HRA, and the method has been merged into the hrefhttps://github.com/huggingface/peftPEFT package.