# Parameter-Efficient Fine-Tuning with Circulant and Diagonal Vectors

arXiv: https://arxiv.org/abs/2505.00580 · HTML: https://mlsanity.com/paper/2505.00580/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 1 May 2025.

## Builds on (most cited first, 28 of 28)

- [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)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [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)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [End-to-end Autonomous Driving: Challenges and Frontiers](https://mlsanity.com/paper/2306.16927/) (2023)
- [Parameter-efficient Multi-task Fine-tuning for Transformers via Shared Hypernetworks](https://mlsanity.com/paper/2106.04489/) (2021)
- [LST: Ladder Side-Tuning for Parameter and Memory Efficient Transfer Learning](https://mlsanity.com/paper/2206.06522/) (2022)
- [Parameter-Efficient Fine-Tuning with Discrete Fourier Transform](https://mlsanity.com/paper/2405.03003/) (2024)
- [Conditional Adapters: Parameter-efficient Transfer Learning with Fast Inference](https://mlsanity.com/paper/2304.04947/) (2023)
- [CirCNN: Accelerating and Compressing Deep Neural Networks Using Block-CirculantWeight Matrices](https://mlsanity.com/paper/1708.08917/) (2017)
- [CosmicMan: A Text-to-Image Foundation Model for Humans](https://mlsanity.com/paper/2404.01294/) (2024)
- [C-LSTM: Enabling Efficient LSTM using Structured Compression Techniques on FPGAs](https://mlsanity.com/paper/1803.06305/) (2018)
- [LaMDA: Large Model Fine-Tuning via Spectrally Decomposed Low-Dimensional Adaptation](https://mlsanity.com/paper/2406.12832/) (2024)
- [Open Challenges and Opportunities in Federated Foundation Models Towards Biomedical Healthcare](https://mlsanity.com/paper/2405.06784/) (2024)

## Built on by (most cited first, 2 of 2)

- [CDFlow: Building Invertible Layers with Circulant and Diagonal Matrices](https://mlsanity.com/paper/2510.25323/) (2025)
- [Compact Circulant Layers with Spectral Priors](https://mlsanity.com/paper/2602.21965/) (2026)

## Abstract (arXiv)

Foundation models have achieved tremendous success in different domains. However, their huge computation and storage complexity make these models difficult to fine-tune and also less applicable in practice. Recent study shows training in Fourier domain can be an effective fine-tuning method in terms of both model performance and number of training parameters. In this work, we propose to further reduce the complexity by the factorization through the product of interleaved circulant and diagonal matrices. In addition, we address the case of non-square fine-tuning weights by partitioning the circulant matrix into blocks. Our method avoids the construction of weight change matrix and utilizes 1D fast Fourier transform (FFT) instead of 2D FFT. Experimental results show that our method achieves similar or better performance across various tasks with much less floating-point operations (FLOPs) and the number of trainable parameters.