# UFO-ViT: High Performance Linear Vision Transformer without Softmax

arXiv: https://arxiv.org/abs/2109.14382 · HTML: https://mlsanity.com/paper/2109.14382/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 54 references that are in the map.
- First posted on arXiv 29 Sep 2021.

## Builds on (most cited first, 30 of 48)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Pyramid Vision Transformer: A Versatile Backbone for Dense Prediction without Convolutions](https://mlsanity.com/paper/2102.12122/) (2021)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [MMDetection: Open MMLab Detection Toolbox and Benchmark](https://mlsanity.com/paper/1906.07155/) (2019)
- [Rethinking Semantic Segmentation from a Sequence-to-Sequence Perspective with Transformers](https://mlsanity.com/paper/2012.15840/) (2020)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Tokens-to-Token ViT: Training Vision Transformers from Scratch on ImageNet](https://mlsanity.com/paper/2101.11986/) (2021)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)

## Built on by (most cited first, 11 of 11)

- [Spikformer: When Spiking Neural Network Meets Transformer](https://mlsanity.com/paper/2209.15425/) (2022)
- [DaViT: Dual Attention Vision Transformers](https://mlsanity.com/paper/2204.03645/) (2022)
- [MB-TaylorFormer: Multi-branch Efficient Transformer Expanded by Taylor Formula for Image Dehazing](https://mlsanity.com/paper/2308.14036/) (2023)
- [Hydra Attention: Efficient Attention with Many Heads](https://mlsanity.com/paper/2209.07484/) (2022)
- [Spikformer V2: Join the High Accuracy Club on ImageNet with an SNN Ticket](https://mlsanity.com/paper/2401.02020/) (2024)
- [HiViT: Hierarchical Vision Transformer Meets Masked Image Modeling](https://mlsanity.com/paper/2205.14949/) (2022)
- [MPCViT: Searching for Accurate and Efficient MPC-Friendly Vision Transformer with Heterogeneous Attention](https://mlsanity.com/paper/2211.13955/) (2022)
- [FsaNet: Frequency Self-attention for Semantic Segmentation](https://mlsanity.com/paper/2211.15595/) (2022)
- [PriViT: Vision Transformers for Fast Private Inference](https://mlsanity.com/paper/2310.04604/) (2023)
- [Transformer-Based Approaches for Sensor-Based Human Activity Recognition: Opportunities and Challenges](https://mlsanity.com/paper/2410.13605/) (2024)
- [vGamba: Attentive State Space Bottleneck for efficient Long-range Dependencies in Visual Recognition](https://mlsanity.com/paper/2503.21262/) (2025)

## Abstract (arXiv)

Vision transformers have become one of the most important models for computer vision tasks. Although they outperform prior works, they require heavy computational resources on a scale that is quadratic to N. This is a major drawback of the traditional self-attention (SA) algorithm. Here, we propose the Unit Force Operated Vision Transformer (UFO-ViT), a novel SA mechanism that has linear complexity. The main approach of this work is to eliminate nonlinearity from the original SA. We factorize the matrix multiplication of the SA mechanism without complicated linear approximation. By modifying only a few lines of code from the original SA, the proposed models outperform most transformer-based models on image classification and dense prediction tasks on most capacity regimes.