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The softmax function is a widely used activation function in the output layers of neural networks, responsible for converting raw scores into class probabilities while introducing essential non-linearity. Implementing Softmax efficiently…

The quadratic complexity of softmax attention presents a major obstacle for scaling Transformers to high-resolution vision tasks. Existing linear attention variants often replace the softmax with Gaussian kernels to reduce complexity, but…

Computer Vision and Pattern Recognition · Computer Science 2026-04-23 Zhe Feng , Sen Lian , Changwei Wang , Muyang Zhang , Tianlong Tan , Rongtao Xu , Weiliang Meng , Xiaopeng Zhang

Vision transformers (ViTs) have been successfully applied in image classification tasks recently. In this paper, we show that, unlike convolution neural networks (CNNs)that can be improved by stacking more convolutional layers, the…

Computer Vision and Pattern Recognition · Computer Science 2021-04-20 Daquan Zhou , Bingyi Kang , Xiaojie Jin , Linjie Yang , Xiaochen Lian , Zihang Jiang , Qibin Hou , Jiashi Feng

Recently, vision transformers have become very popular. However, deploying them in many applications is computationally expensive partly due to the Softmax layer in the attention block. We introduce a simple but effective, Softmax-free…

Computer Vision and Pattern Recognition · Computer Science 2024-03-26 Soroush Abbasi Koohpayegani , Hamed Pirsiavash

Vision Transformer (ViT) architectures are becoming increasingly popular and widely employed to tackle computer vision applications. Their main feature is the capacity to extract global information through the self-attention mechanism,…

Computer Vision and Pattern Recognition · Computer Science 2024-05-06 Lorenzo Papa , Paolo Russo , Irene Amerini , Luping Zhou

Transformers have demonstrated a competitive performance across a wide range of vision tasks, while it is very expensive to compute the global self-attention. Many methods limit the range of attention within a local window to reduce…

Computer Vision and Pattern Recognition · Computer Science 2022-11-01 Zhenzhe Hechen , Wei Huang , Yixin Zhao

Vision Transformers (ViTs) based vision foundation models (VFMs) have achieved remarkable performance across diverse vision tasks, but suffer from quadratic complexity that limits scalability to long sequences. Existing linear attention…

Computer Vision and Pattern Recognition · Computer Science 2026-03-18 Yifan Li , Seunghyun Yoon , Viet Dac Lai , Franck Dernoncourt , Jason Kuen , Yu Kong , Trung Bui

Softmax attention is a central component of transformer architectures, yet its nonlinear structure poses significant challenges for theoretical analysis. We develop a unified, measure-based framework for studying single-layer softmax…

Machine Learning · Computer Science 2025-12-15 Etienne Boursier , Claire Boyer

Large transformer models have achieved state-of-the-art results in numerous natural language processing tasks. Among the pivotal components of the transformer architecture, the attention mechanism plays a crucial role in capturing token…

Computation and Language · Computer Science 2026-03-16 Yichuan Deng , Zhao Song , Kaijun Yuan , Tianyi Zhou

Recently, Vision Transformer (ViT) has continuously established new milestones in the computer vision field, while the high computation and memory cost makes its propagation in industrial production difficult. Pruning, a traditional model…

Computer Vision and Pattern Recognition · Computer Science 2022-09-22 Zhenglun Kong , Peiyan Dong , Xiaolong Ma , Xin Meng , Mengshu Sun , Wei Niu , Xuan Shen , Geng Yuan , Bin Ren , Minghai Qin , Hao Tang , Yanzhi Wang

Transformers, composed of multiple self-attention layers, hold strong promises toward a generic learning primitive applicable to different data modalities, including the recent breakthroughs in computer vision achieving state-of-the-art…

Computer Vision and Pattern Recognition · Computer Science 2021-12-07 Sayak Paul , Pin-Yu Chen

The deployment of Vision Transformers (ViTs) on hardware platforms, specially Field-Programmable Gate Arrays (FPGAs), presents many challenges, which are mainly due to the substantial computational and power requirements of their non-linear…

Computer Vision and Pattern Recognition · Computer Science 2024-08-19 Mohammad Erfan Sadeghi , Arash Fayyazi , Seyedarmin Azizi , Massoud Pedram

Recent state-of-the-art performances of Vision Transformers (ViT) in computer vision tasks demonstrate that a general-purpose architecture, which implements long-range self-attention, could replace the local feature learning operations of…

Vision Transformers (ViTs) with self-attention modules have recently achieved great empirical success in many vision tasks. Due to non-convex interactions across layers, however, theoretical learning and generalization analysis is mostly…

Machine Learning · Computer Science 2023-11-15 Hongkang Li , Meng Wang , Sijia Liu , Pin-yu Chen

At the core of the popular Transformer architecture is the self-attention mechanism, which dynamically assigns softmax weights to each input token so that the model can focus on the most salient information. However, the softmax structure…

Machine Learning · Computer Science 2025-05-27 Fanqi Yan , Huy Nguyen , Pedram Akbarian , Nhat Ho , Alessandro Rinaldo

Recently, Vision Transformers (ViTs) have attracted a lot of attention in the field of computer vision. Generally, the powerful representative capacity of ViTs mainly benefits from the self-attention mechanism, which has a high computation…

Computer Vision and Pattern Recognition · Computer Science 2023-10-12 Deli Yu , Teng Xi , Jianwei Li , Baopu Li , Gang Zhang , Haocheng Feng , Junyu Han , Jingtuo Liu , Errui Ding , Jingdong Wang

The quadratic complexity of the attention mechanism represents one of the biggest hurdles for processing long sequences using Transformers. Current methods, relying on sparse representations or stateful recurrence, sacrifice token-to-token…

Machine Learning · Computer Science 2025-06-06 Tobias Christian Nauen , Sebastian Palacio , Andreas Dengel

We present a novel method that extends the self-attention mechanism of a vision transformer (ViT) for more accurate object detection across diverse datasets. ViTs show strong capability for image understanding tasks such as object…

Computer Vision and Pattern Recognition · Computer Science 2024-12-30 Tan Nguyen , Coy D. Heldermon , Corey Toler-Franklin

Vision Transformer (ViT) has achieved excellent performance and demonstrated its promising potential in various computer vision tasks. The wide deployment of ViT in real-world tasks requires a thorough understanding of the societal impact…

Computer Vision and Pattern Recognition · Computer Science 2024-07-23 Bowei Tian , Ruijie Du , Yanning Shen

The softmax function is widely used in artificial neural networks for the multiclass classification problems, where the softmax transformation enforces the output to be positive and sum to one, and the corresponding loss function allows to…

Machine Learning · Computer Science 2021-12-24 Shaoshi Sun , Zhenyuan Zhang , BoCheng Huang , Pengbin Lei , Jianlin Su , Shengfeng Pan , Jiarun Cao