# VeRA: Vector-based Random Matrix Adaptation

arXiv: https://arxiv.org/abs/2310.11454 · HTML: https://mlsanity.com/paper/2310.11454/

## Key facts

- Cited by 300 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 40 references that are in the map.
- First posted on arXiv 17 Oct 2023.

## Builds on (most cited first, 27 of 27)

- [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)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [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)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [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)
- [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)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [Random Feature Attention](https://mlsanity.com/paper/2103.02143/) (2021)
- [The E2E Dataset: New Challenges For End-to-End Generation](https://mlsanity.com/paper/1706.09254/) (2017)
- [What's Hidden in a Randomly Weighted Neural Network?](https://mlsanity.com/paper/1911.13299/) (2019)
- [DyLoRA: Parameter Efficient Tuning of Pre-trained Models using Dynamic Search-Free Low-Rank Adaptation](https://mlsanity.com/paper/2210.07558/) (2022)
- [AdapterDrop: On the Efficiency of Adapters in Transformers](https://mlsanity.com/paper/2010.11918/) (2020)
- [Exploring Versatile Generative Language Model Via Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2004.03829/) (2020)
- [LoRA-FA: Efficient and Effective Low Rank Representation Fine-tuning](https://mlsanity.com/paper/2308.03303/) (2023)
- [Training BatchNorm and Only BatchNorm: On the Expressive Power of Random Features in CNNs](https://mlsanity.com/paper/2003.00152/) (2020)
- [Delta-LoRA: Fine-Tuning High-Rank Parameters with the Delta of Low-Rank Matrices](https://mlsanity.com/paper/2309.02411/) (2023)

## Built on by (most cited first, 30 of 300)

- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [ReFT: Representation Finetuning for Language Models](https://mlsanity.com/paper/2404.03592/) (2024)
- [LoRA vs Full Fine-tuning: An Illusion of Equivalence](https://mlsanity.com/paper/2410.21228/) (2024)
- [MiLoRA: Harnessing Minor Singular Components for Parameter-Efficient LLM Finetuning](https://mlsanity.com/paper/2406.09044/) (2024)
- [LoRA-XS: Low-Rank Adaptation with Extremely Small Number of Parameters](https://mlsanity.com/paper/2405.17604/) (2024)
- [Tied-Lora: Enhancing parameter efficiency of LoRA with weight tying](https://mlsanity.com/paper/2311.09578/) (2023)
- [LoFiT: Localized Fine-tuning on LLM Representations](https://mlsanity.com/paper/2406.01563/) (2024)
- [The Impact of Initialization on LoRA Finetuning Dynamics](https://mlsanity.com/paper/2406.08447/) (2024)
- [K-LoRA: Unlocking Training-Free Fusion of Any Subject and Style LoRAs](https://mlsanity.com/paper/2502.18461/) (2025)
- [Mixture-of-Subspaces in Low-Rank Adaptation](https://mlsanity.com/paper/2406.11909/) (2024)
- [SaLoRA: Safety-Alignment Preserved Low-Rank Adaptation](https://mlsanity.com/paper/2501.01765/) (2025)
- [LoRA-drop: Efficient LoRA Parameter Pruning based on Output Evaluation](https://mlsanity.com/paper/2402.07721/) (2024)
- [Advancing Parameter Efficiency in Fine-tuning via Representation Editing](https://mlsanity.com/paper/2402.15179/) (2024)
- [Low-Rank Adaptation for Foundation Models: A Comprehensive Review](https://mlsanity.com/paper/2501.00365/) (2024)
- [ALoRA: Allocating Low-Rank Adaptation for Fine-tuning Large Language Models](https://mlsanity.com/paper/2403.16187/) (2024)
- [Towards Robust and Parameter-Efficient Knowledge Unlearning for LLMs](https://mlsanity.com/paper/2408.06621/) (2024)
- [MoRA: High-Rank Updating for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2405.12130/) (2024)
- [Lottery Ticket Adaptation: Mitigating Destructive Interference in LLMs](https://mlsanity.com/paper/2406.16797/) (2024)
- [HSplitLoRA: A Heterogeneous Split Parameter-Efficient Fine-Tuning Framework for Large Language Models](https://mlsanity.com/paper/2505.02795/) (2025)
- [BAdam: A Memory Efficient Full Parameter Optimization Method for Large Language Models](https://mlsanity.com/paper/2404.02827/) (2024)
- [Unlearning Backdoor Attacks for LLMs with Weak-to-Strong Knowledge Distillation](https://mlsanity.com/paper/2410.14425/) (2024)
- [Compressible Dynamics in Deep Overparameterized Low-Rank Learning & Adaptation](https://mlsanity.com/paper/2406.04112/) (2024)
- [Affective Computing in the Era of Large Language Models: A Survey from the NLP Perspective](https://mlsanity.com/paper/2408.04638/) (2024)
- [Compress then Serve: Serving Thousands of LoRA Adapters with Little Overhead](https://mlsanity.com/paper/2407.00066/) (2024)
- [The Universal Weight Subspace Hypothesis](https://mlsanity.com/paper/2512.05117/) (2025)
- [A Practitioner's Guide to Continual Multimodal Pretraining](https://mlsanity.com/paper/2408.14471/) (2024)
- [Generated Data with Fake Privacy: Hidden Dangers of Fine-tuning Large Language Models on Generated Data](https://mlsanity.com/paper/2409.11423/) (2024)
- [Initialization using Update Approximation is a Silver Bullet for Extremely Efficient Low-Rank Fine-Tuning](https://mlsanity.com/paper/2411.19557/) (2024)

## Abstract (arXiv)

Low-rank adapation (LoRA) is a popular method that reduces the number of trainable parameters when finetuning large language models, but still faces acute storage challenges when scaling to even larger models or deploying numerous per-user or per-task adapted models. In this work, we present Vector-based Random Matrix Adaptation (VeRA), which significantly reduces the number of trainable parameters compared to LoRA, yet maintains the same performance. It achieves this by using a single pair of low-rank matrices shared across all layers and learning small scaling vectors instead. We demonstrate its effectiveness on the GLUE and E2E benchmarks, image classification tasks, and show its application in instruction-tuning of 7B and 13B language models.