# VectorFit : Adaptive Singular & Bias Vector Fine-Tuning of Pre-trained Foundation Models

arXiv: https://arxiv.org/abs/2503.19530 · HTML: https://mlsanity.com/paper/2503.19530/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 59 references that are in the map.
- First posted on arXiv 25 Mar 2025.

## Builds on (most cited first, 30 of 38)

- [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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [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)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Robust Speech Recognition via Large-Scale Weak Supervision](https://mlsanity.com/paper/2212.04356/) (2022)
- [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)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [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)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [Abstractive Text Summarization Using Sequence-to-Sequence RNNs and Beyond](https://mlsanity.com/paper/1602.06023/) (2016)
- [StarCoder: may the source be with you!](https://mlsanity.com/paper/2305.06161/) (2023)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Scaling Vision Transformers to 22 Billion Parameters](https://mlsanity.com/paper/2302.05442/) (2023)
- [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)
- [Controlling Text-to-Image Diffusion by Orthogonal Finetuning](https://mlsanity.com/paper/2306.07280/) (2023)
- [Parameter-Efficient Orthogonal Finetuning via Butterfly Factorization](https://mlsanity.com/paper/2311.06243/) (2023)

## Built on by (most cited first, 1 of 1)

- [Exploring Sparsity for Parameter Efficient Fine Tuning Using Wavelets for Vision](https://mlsanity.com/paper/2505.12532/) (2025)

## Abstract (arXiv)

Popular PEFT methods reduce trainable parameter count for fine-tuning by parameterizing new low-rank or sparse trainable weights in parallel to the frozen pre-trained weights W. However, these weights are trained from scratch, and there exists a performance gap between these methods and full fine-tuning, especially in low-budget settings. We introduce VectorFit, a new way of parameterization that efficiently utilizes the existing knowledge embedded in W by adaptively training their singular vectors and biases. We show that utilizing the structural and transformational properties of W in this way can lead to high-rank incremental weight matrices Delta W, comparable to that of full fine-tuning. VectorFit delivers superior results with 9boldsymbol× fewer trainable parameters than the leading PEFT methods. Through comprehensive experiments across 19 datasets covering a wide range of language and vision tasks such as natural language understanding and generation, question answering, image classification, and image generation, we demonstrate that VectorFit surpasses baselines in terms of performance as a function of parameter-efficiency.