# Parameter Efficient Quasi-Orthogonal Fine-Tuning via Givens Rotation

arXiv: https://arxiv.org/abs/2404.04316 · HTML: https://mlsanity.com/paper/2404.04316/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 56 references that are in the map.
- First posted on arXiv 5 Apr 2024.

## Builds on (most cited first, 30 of 40)

- [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)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [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)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [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)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [P-Tuning v2: Prompt Tuning Can Be Comparable to Fine-tuning Universally Across Scales and Tasks](https://mlsanity.com/paper/2110.07602/) (2021)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [A Large-scale Study of Representation Learning with the Visual Task Adaptation Benchmark](https://mlsanity.com/paper/1910.04867/) (2019)
- [Controlling Text-to-Image Diffusion by Orthogonal Finetuning](https://mlsanity.com/paper/2306.07280/) (2023)
- [Scaling Down to Scale Up: A Guide to Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.15647/) (2023)
- [UniPELT: A Unified Framework for Parameter-Efficient Language Model Tuning](https://mlsanity.com/paper/2110.07577/) (2021)
- [FacT: Factor-Tuning for Lightweight Adaptation on Vision Transformer](https://mlsanity.com/paper/2212.03145/) (2022)

## Built on by (most cited first, 21 of 21)

- [DeCo: Decoupling Token Compression from Semantic Abstraction in Multimodal Large Language Models](https://mlsanity.com/paper/2405.20985/) (2024)
- [VLFeedback: A Large-Scale AI Feedback Dataset for Large Vision-Language Models Alignment](https://mlsanity.com/paper/2410.09421/) (2024)
- [LoRA Dropout as a Sparsity Regularizer for Overfitting Control](https://mlsanity.com/paper/2404.09610/) (2024)
- [TC-RAG:Turing-Complete RAG's Case study on Medical LLM Systems](https://mlsanity.com/paper/2408.09199/) (2024)
- [Exploring Sparsity for Parameter Efficient Fine Tuning Using Wavelets for Vision](https://mlsanity.com/paper/2505.12532/) (2025)
- [Orthogonal Finetuning Made Scalable](https://mlsanity.com/paper/2506.19847/) (2025)
- [Orthogonal Finetuning for Direct Preference Optimization](https://mlsanity.com/paper/2409.14836/) (2024)
- [MoORE: SVD-based Model MoE-ization for Conflict- and Oblivion-Resistant Multi-Task Adaptation](https://mlsanity.com/paper/2506.14436/) (2025)
- [Magical: Medical Lay Language Generation via Semantic Invariance and Layperson-tailored Adaptation](https://mlsanity.com/paper/2508.08730/) (2025)
- [Efficient Orthogonal Fine-Tuning with Principal Subspace Adaptation](https://mlsanity.com/paper/2505.11235/) (2025)
- [Transformed Low-rank Adaptation via Tensor Decomposition and Its Applications to Text-to-image Models](https://mlsanity.com/paper/2501.08727/) (2025)
- [Efficient Adaptation of Pre-trained Vision Transformer underpinned by Approximately Orthogonal Fine-Tuning Strategy](https://mlsanity.com/paper/2507.13260/) (2025)
- [Weights-Rotated Preference Optimization for Large Language Models](https://mlsanity.com/paper/2508.17637/) (2025)
- [Exploring Representation Invariance in Finetuning](https://mlsanity.com/paper/2503.07399/) (2025)
- [TabularQGAN: A quantum generative model for tabular data synthesis](https://mlsanity.com/paper/2505.22533/) (2025)
- [Orthogonal Concept Erasure for Diffusion Models](https://mlsanity.com/paper/2605.28902/) (2026)
- [Outlier Smoothing with Closed-Form Rotations for W4A4 Large Language Model Quantization](https://mlsanity.com/paper/2511.22316/) (2025)
- [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)
- [Structured Hyperedge Adaptation for Parameter-Efficient Fine-Tuning of Vision Transformers](https://mlsanity.com/paper/2606.22383/) (2026)
- [Orthogonal Yet Coupled: Decoupling Geometric Components for Model Merging](https://mlsanity.com/paper/2609.37564/) (2026)

## Abstract (arXiv)

With the increasingly powerful performances and enormous scales of pretrained models, promoting parameter efficiency in fine-tuning has become a crucial need for effective and efficient adaptation to various downstream tasks. One representative line of fine-tuning methods is Orthogonal Fine-tuning (OFT), which rigorously preserves the angular distances within the parameter space to preserve the pretrained knowledge. Despite the empirical effectiveness, OFT still suffers low parameter efficiency at O(d2) and limited capability of downstream adaptation. Inspired by Givens rotation, in this paper, we proposed quasi-Givens Orthogonal Fine-Tuning (qGOFT) to address the problems. We first use O(d) Givens rotations to accomplish arbitrary orthogonal transformation in SO(d) with provable equivalence, reducing parameter complexity from O(d2) to O(d). Then we introduce flexible norm and relative angular adjustments under soft orthogonality regularization to enhance the adaptation capability of downstream semantic deviations. Extensive experiments on various tasks and pretrained models validate the effectiveness of our methods.