---
title: "Scaled dot-product attention (Transformer)"
description: "Scaled dot-product attention (Transformer) was mentioned in 203 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #1 of the 104 equations and models mentioned."
url: https://scholar4ai.com/equations/scaled-dot-product-attention-transformer
markdown_url: https://scholar4ai.com/equations/scaled-dot-product-attention-transformer.md
license: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/)
data_url: https://scholar4ai.com/data/rankings.json
updated: 2026-10-26T12:13:05+09:00
window: 2026-09-27 to 2026-10-26
source: OpenAlex (CC0)
---

# Scaled dot-product attention (Transformer)

$$
\mathrm{Attention}(Q, K, V) = \mathrm{softmax}\Big(\frac{Q K^\top}{\sqrt{d_k}}\Big) V
$$

The core operation of Transformer models: each token's output is a weighted average of values, weighted by query-key similarity.

- area: Machine learning
- 16 papers in the last 7 days
- Names searched for: self-attention, attention mechanism, multi-head attention, scaled dot-product attention, Transformer architecture, Transformer-based, vision transformer

Back to the ranking: https://scholar4ai.com/rankings/equations.md

## Key findings

- Scaled dot-product attention (Transformer) was mentioned in 203 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #1 of the 104 equations and models mentioned.
- By journal category: AI (175), Operations Research (11), Management (9), Finance (7) and Economics (1).
- Most of them appeared in Pattern Recognition (33), Neural Computing and Applications (25) and Knowledge-Based Systems (21).
- Often mentioned together with Convolutional neural network (CNN) (58), Graph neural network (graph convolution) (33) and Long short-term memory (LSTM) (30).
- Datasets named in the same papers: OR-Library (16), ImageNet (10) and Twitter / X (8).

*Papers mentioning Scaled dot-product attention (Transformer), newest first. Newest 50 of 203 papers; all of them are in /data/papers.json.*

| Date | Title | Journal | Authors | Affiliations |
|---|---|---|---|---|
| 2026-10-24 | [A priority-aware dual-channel feature fusion method for urban rail service traffic classification](https://doi.org/10.1007/s10489-026-07560-z) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | Xinpeng Liu, Junhui Zhao, Zhengyuan Wu et al. | Beijing Jiaotong University |
| 2026-10-23 | [Neuro-native paradigms of brain foundation models: evolution, taxonomy, and perspectives](https://doi.org/10.1007/s10462-026-11748-7) | [Artificial Intelligence Review](https://scholar4ai.com/journals/artificial-intelligence-review.md) | Zepeng Li, Molei Zhang, Tianyi Li et al. | Lanzhou University |
| 2026-10-23 | [Multimodal continual federated learning for human activity recognition: Trends and challenges](https://doi.org/10.1007/s10489-026-07562-x) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | André L. S. Conde, Rodolfo I. Meneguette, Robson E. De Grande et al. | Universidade Estadual Paulista (Unesp); Institute of Mathematics and Computer Science; Brock University |
| 2026-10-23 | [Collaborative enhancement of global and disentangled representations for sequential recommendation](https://doi.org/10.1007/s10115-026-02921-z) | [Knowledge and Information Systems](https://scholar4ai.com/journals/knowledge-and-information-systems.md) | Li Liu, Yiliang Lai, Chen Lin | Xiamen University; Sanming University; Assumption University; … |
| 2026-10-23 | [Multi-scale wavelet convolutional sampling and cross-stage feature enhancement reconstruction for image compressed sensing](https://doi.org/10.1016/j.patcog.2026.115195) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Le Qin, Zenan Xiong, Jingyao Gong et al. | Nanchang Normal University; Jiangxi Normal University; Jiangsu University; … |
| 2026-10-23 | [AlignVSS: Alignment-enhanced feature propagation and distillation for efficient Video Semantic Segmentation](https://doi.org/10.1016/j.knosys.2026.117222) | [Knowledge-Based Systems](https://scholar4ai.com/journals/knowledge-based-systems.md) | Teng Li, Shumin An, Qingmin Liao et al. | Tsinghua Shenzhen International Graduate School; Tsinghua University; Hong Kong University of Science and Technology; … |
| 2026-10-23 | [MET-FR: Mamba-enhanced Transformer with feature rectification for hyperspectral and LiDAR data fusion and classification](https://doi.org/10.1016/j.patcog.2026.115204) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Yining Feng, Wei Cheng, Zhenhua Mu et al. | Dalian University; Liaoning Normal University |
| 2026-10-22 | [Research on the spatiotemporal prediction of supply chain finance risk contagion based on a dynamic graph attention diffusion mechanism](https://doi.org/10.1186/s40854-026-00980-3) | [Financial Innovation](https://scholar4ai.com/journals/financial-innovation.md) | Yulong Zhang, Yulong Zhang, Yaqing Zhang et al. | Hengshui University; Columbia University |
| 2026-10-22 | [Cut the chit-chat: a new framework for the application of generative language models for portfolio construction](https://doi.org/10.1007/s10479-026-07418-0) | [Annals of Operations Research](https://scholar4ai.com/journals/annals-of-operations-research.md) | Francesco A. Fabozzi, Ionuţ Florescu | Stevens Institute of Technology |
| 2026-10-22 | [Sine function-guided master–slave collaborative network for salient object detection in optical remote sensing images](https://doi.org/10.1007/s10489-026-07528-z) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | Dong Hansong, 罗子江, Zhizhu Ge et al. | Guizhou University; Shunde Polytechnic; Fudan University |
| 2026-10-22 | [Beyond the survey: a systematic empirical study of detection and association in visual MOT](https://doi.org/10.1007/s10462-026-11713-4) | [Artificial Intelligence Review](https://scholar4ai.com/journals/artificial-intelligence-review.md) | Linh Van Ma, Juhua Hu, Wei Cheng et al. | Gwangju Institute of Science and Technology; University of Washington Tacoma |
| 2026-10-21 | [ADGB-ONet: an attention-driven gradient balancing operator network for scattering pressure field prediction](https://doi.org/10.1007/s10489-026-07538-x) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | Anqiang Tan, Jinhong Wu, Yankun Sheng et al. | Huazhong University of Science and Technology |
| 2026-10-21 | [InfoDisent: Explainability of image classification models by information disentanglement](https://doi.org/10.1016/j.knosys.2026.117169) | [Knowledge-Based Systems](https://scholar4ai.com/journals/knowledge-based-systems.md) | Łukasz Struski, Dawid Rymarczyk, Jacek Tabor |  |
| 2026-10-20 | [Boosting the understanding ability of diffusion model with masked image modeling](https://doi.org/10.1016/j.patcog.2026.115123) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Jianning Pei, Yingchao Feng, Hanbo Bi et al. | Chinese Academy of Sciences; Aerospace Information Research Institute; University of Chinese Academy of Sciences |
| 2026-10-20 | [Central description length (CDL) clustering validation index](https://doi.org/10.1016/j.artint.2026.104644) | [Artificial Intelligence](https://scholar4ai.com/journals/artificial-intelligence.md) | Mahdi Shamsi, Soosan Beheshti | McGill University |
| 2026-10-20 | [Test-Time Computing for Referring Multimodal Large Language Models](https://doi.org/10.1007/s11263-026-03100-x) | [International Journal of Computer Vision](https://scholar4ai.com/journals/international-journal-of-computer-vision.md) | Mingrui Wu, Hao Chen, Jiayi Ji et al. | Xiamen University; Tsinghua University; Nankai University |
| 2026-10-19 | [AGformer: Adaptive filtering and gated fusion-attention for multivariate time series forecasting](https://doi.org/10.1016/j.neunet.2026.109759) | [Neural Networks](https://scholar4ai.com/journals/neural-networks.md) | Shu-Xin Xu, Jiang‐Wen Xiao, Peng-Cheng Li et al. | Huazhong University of Science and Technology |
| 2026-10-19 | [TransDiffuser: A transformer-guided diffusion model for few-shot font generation](https://doi.org/10.1016/j.eswa.2026.134801) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Songshui Wu, Tianle Ji, Tao Jiang et al. | Hengyang Normal University; Northwest University |
| 2026-10-19 | [DReX: An explainable deep learning-based multimodal recommendation framework](https://doi.org/10.1016/j.knosys.2026.117184) | [Knowledge-Based Systems](https://scholar4ai.com/journals/knowledge-based-systems.md) | Adamya Shyam, Venkateswara Rao Kagita, Bharti Rana et al. | University of Delhi; National Institute of Technology Warangal |
| 2026-10-18 | [DCDA-Net: A depthwise convolution dilated attention network with temporal weighted loss for seizure prediction](https://doi.org/10.1016/j.neunet.2026.109785) | [Neural Networks](https://scholar4ai.com/journals/neural-networks.md) | Xingchen Dong, Haotian Li, Qiangqiang Chen et al. | Fudan University; Nanjing University of Science and Technology; Nanjing University; … |
| 2026-10-18 | [LLM-Powered Query Expansion for Enhancing Boundary Prediction in Language-Driven Action Localization](https://doi.org/10.1007/s11263-026-03083-9) | [International Journal of Computer Vision](https://scholar4ai.com/journals/international-journal-of-computer-vision.md) | Zirui Shang, Xinxiao Wu, Shuo Yang | Beijing Institute of Technology; Shenzhen MSU-BIT University |
| 2026-10-17 | [TNIA: Target-aware transformer-based node injection attacks on graph neural networks](https://doi.org/10.1016/j.eswa.2026.134772) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Qiongshan Pan, Peng Bao | Beijing Jiaotong University |
| 2026-10-17 | [Semantic similarity score: A new method for mapping intellectual structures in business research](https://doi.org/10.1016/j.jbusres.2026.116582) | [Journal of Business Research](https://scholar4ai.com/journals/journal-of-business-research.md) | Hamid Bekamiri, Christian Richter Østergaard, Bram Timmermans | Aalborg University; Norwegian School of Economics |
| 2026-10-17 | [Order-routed fusion with gate-aware prototype contrast for multimodal sentiment analysis](https://doi.org/10.1016/j.eswa.2026.134799) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Weihai Li, Peng Zhang | Chongqing University of Posts and Telecommunications |
| 2026-10-17 | [CorrCLIPv2: Harnessing Unlabeled Images for Open-Vocabulary Semantic Segmentation](https://doi.org/10.1007/s11263-026-03027-3) | [International Journal of Computer Vision](https://scholar4ai.com/journals/international-journal-of-computer-vision.md) | D H Zhang, Fagui Liu, Quan Tang et al. | South China University of Technology; Peng Cheng Laboratory |
| 2026-10-17 | [FDFNet: A Full-stage Dual-dimensional Fusion Network for Visual Grounding](https://doi.org/10.1016/j.knosys.2026.117189) | [Knowledge-Based Systems](https://scholar4ai.com/journals/knowledge-based-systems.md) | Shishu Hong, Yangchuanlin Cheng, Aoao Zhao et al. | Wuhan University of Technology; Chinese University of Hong Kong |
| 2026-10-17 | [AgriEyeNet: Seeing smarter in agriculture with medium-difficulty aware loss and lightweight adaptive detection](https://doi.org/10.1007/s10489-026-07550-1) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | Jipei Cao, Hanxiang Wang, Mengyao Ma et al. | Qufu Normal University; University of Jinan; Sejong University; … |
| 2026-10-17 | [Tech Mining with LLMs: Unveiling Trends from Corporate Websites](https://doi.org/10.1007/s10614-026-11451-3) | [Computational Economics](https://scholar4ai.com/journals/computational-economics.md) | Xavier Martínez-Barbero, Ana Pastor-Merino, Josep Domènech | Universitat Politècnica de València |
| 2026-10-17 | [Language modeling on tabular data: a survey of foundations, techniques and evolution](https://doi.org/10.1007/s10462-026-11726-z) | [Artificial Intelligence Review](https://scholar4ai.com/journals/artificial-intelligence-review.md) | Yucheng Ruan, Xiang Lan, Jingying Ma et al. | National University of Singapore; Institute of Data Science |
| 2026-10-16 | [DGKT: Dual Graph Kernel Transformer for graph classification](https://doi.org/10.1016/j.patcog.2026.115145) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Lixiang Xu, Weixin Yu, Zezhou Wang et al. | Hefei University; Hefei Institute of Technology; Beijing Normal University; … |
| 2026-10-16 | [Evaluating LLMs for named entity recognition: a cost-benefit analysis in the legal domain](https://doi.org/10.1007/s10115-026-02886-z) | [Knowledge and Information Systems](https://scholar4ai.com/journals/knowledge-and-information-systems.md) | Shefali Singhal, Eoin O’Connell, Niall McCarroll et al. | University of Ulster; Ulster University, Derry-Londonderry Campus; Ulster Hospital |
| 2026-10-16 | [Public technical disclosure of AI implementation in finance: Python-framed evidence from 253 NYSE-listed financial companies](https://doi.org/10.1186/s40854-026-00979-w) | [Financial Innovation](https://scholar4ai.com/journals/financial-innovation.md) | Veliota Drakopoulou | Embry–Riddle Aeronautical University |
| 2026-10-16 | [ITEACH-Net: Inverted teacher-student search network for emotion recognition in conversation](https://doi.org/10.1016/j.artint.2026.104643) | [Artificial Intelligence](https://scholar4ai.com/journals/artificial-intelligence.md) | Haiyang Sun, Zheng Lian, Chenglong Wang et al. | Chinese Academy of Sciences; Institute of Automation; University of Chinese Academy of Sciences; … |
| 2026-10-15 | [Lightweight audiovisual attention cross-perception network for video saliency prediction](https://doi.org/10.1016/j.neunet.2026.109756) | [Neural Networks](https://scholar4ai.com/journals/neural-networks.md) | Liuxin Bao, Zhongyang Hu, Yingjie Jin et al. | Hangzhou Dianzi University; Anqing Normal University |
| 2026-10-15 | [pDOC-STANet: A spatiotemporal attention network for automatic assessment of prolonged disorders of consciousness using fNIRS](https://doi.org/10.1007/s10489-026-07542-1) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | Zehai Li, Yuxin Xing, Shuwei Wang et al. | Zhejiang Normal University; Wenzhou Medical University; Zhejiang Taizhou Hospital; … |
| 2026-10-15 | [VLGRA: Visual-Language Semantic Optimization and Graph Reasoning for cross-modal retrieval](https://doi.org/10.1016/j.ipm.2026.105238) | [Information Processing & Management](https://scholar4ai.com/journals/information-processing-management.md) | Shiyuan Yang, Zhixin Li, 尤忠祥 et al. | Guangxi Normal University |
| 2026-10-15 | [SAR image despeckling via diffusion models with latent-space contrastive alignment](https://doi.org/10.1016/j.eswa.2026.134703) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Fuyu Bo, Jing Fang, Yi Li et al. | Beijing Jiaotong University; Shandong Normal University; Guizhou Province Chemical Industry Research Institute |
| 2026-10-15 | [Enhancing fault prediction in SOA-based systems via hybrid transformer–BiLSTM with COA–SCSO feature selection method](https://doi.org/10.1007/s10115-026-02899-8) | [Knowledge and Information Systems](https://scholar4ai.com/journals/knowledge-and-information-systems.md) | Raghuraj Singh, Kuldeep Kumar | Dr. B. R. Ambedkar National Institute of Technology Jalandhar; National Institute of Technology Kurukshetra |
| 2026-10-15 | [Dynamic attention for container relocation problems: a deep reinforcement learning approach](https://doi.org/10.1007/s10489-026-07525-2) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | Zizhen Zhang, Fengwei Liu, Mengchu Zhou | Sun Yat-sen University; New Jersey Institute of Technology |
| 2026-10-15 | [Dual-view visual-semantic fusion for cursive Urdu HTR: Compact CRNN with confidence-gated zero-shot LLM verification](https://doi.org/10.1016/j.inffus.2026.104865) | [Information Fusion](https://scholar4ai.com/journals/information-fusion.md) | Fakhar Ayub, Muhammad Kashif Khattak, Amin Khan et al. | University of Poonch Rawalakot; Tun Hussein Onn University of Malaysia; Sejong University |
| 2026-10-15 | [Metropolis-scale resilient and trustworthy traffic flow inference using multi-source data](https://doi.org/10.1016/j.trc.2026.106083) | [Transportation Research Part C Emerging Technologies](https://scholar4ai.com/journals/transportation-research-part-c-emerging-technologies.md) | Qishen Zhou, Yifan Zhang, Michail Makridis et al. | Jilin University; City University of Hong Kong; City University of Hong Kong (Dongguan); … |
| 2026-10-14 | [SDDF-BEV: Uncertainty-aware spatio-temporal fusion for pure vision Bird’s-Eye-View 3D object detection](https://doi.org/10.1016/j.knosys.2026.117201) | [Knowledge-Based Systems](https://scholar4ai.com/journals/knowledge-based-systems.md) | Wei Zhang, Xulu Xia, Xingliang Zhu et al. | University of Science and Technology of China; Hefei Institutes of Physical Science; Institute of Intelligent Machines; … |
| 2026-10-14 | [Mitigating spectral decay via wavelet sparse contextual reinforcement for lightweight image super-resolution](https://doi.org/10.1016/j.knosys.2026.117192) | [Knowledge-Based Systems](https://scholar4ai.com/journals/knowledge-based-systems.md) | Qian Wang, Mengyang Wang, Yao Tang et al. | Xi’an University of Posts and Telecommunications; Shanghai Jiao Tong University |
| 2026-10-14 | [FasterAD: Faster and more precise multi-class unsupervised anomaly detection and localization](https://doi.org/10.1016/j.patcog.2026.115101) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Pengjie Tan, Zhen Chen, Wai Keung Wong | Hong Kong Polytechnic University |
| 2026-10-14 | [Echo-DM: Ultrasound marker removal via conditional latent diffusion and region-aware fusion](https://doi.org/10.1016/j.neunet.2026.109757) | [Neural Networks](https://scholar4ai.com/journals/neural-networks.md) | Zhiwei Wang, Tao Huang, Wentao Jiang et al. | Wuhan University; Central Hospital of Wuhan; Hubei University of Technology |
| 2026-10-14 | [Domain-adversarial anatomical graph networks for cross-user human activity recognition](https://doi.org/10.1016/j.inffus.2026.104876) | [Information Fusion](https://scholar4ai.com/journals/information-fusion.md) | Xiaozhou Ye, Kevin I‐Kai Wang | University of Auckland |
| 2026-10-13 | [NoDE: noise-decorrelation embedding for robust long-term multivariate time series forecasting](https://doi.org/10.1007/s10618-026-01281-0) | [Data Mining and Knowledge Discovery](https://scholar4ai.com/journals/data-mining-and-knowledge-discovery.md) | Minhyuk Lee, Hyekyung Yoon, Imseong Park et al. | Seoul National University; Mathematical Sciences Research Institute |
| 2026-10-13 | [3D HyFormer: A hybrid transformer with dense-sparse attention for point cloud semantic segmentation](https://doi.org/10.1016/j.patcog.2026.115126) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | 焦志强 Jiao Zhiqiang, 王康年 Wang Kangnian, Yanhan Zhang et al. | Tianjin University; Tiangong University |
| 2026-10-13 | [Spatial-guided LiDAR spatial-elevation feature enhancement network for fusion classification of hyperspectral and LiDAR data](https://doi.org/10.1016/j.inffus.2026.104871) | [Information Fusion](https://scholar4ai.com/journals/information-fusion.md) | Leiquan Wang, Ang Wei, Zhongwei Li et al. | China University of Petroleum, East China; Ministry of Natural Resources; First Institute of Oceanography |
| 2026-10-13 | [DPCformer: Dual-Prior Calibration Transformer for low-light image enhancement](https://doi.org/10.1016/j.ipm.2026.105217) | [Information Processing & Management](https://scholar4ai.com/journals/information-processing-management.md) | Jiaxiang Wang, Pufen Zhang, Meng Wan et al. | University of Science and Technology Beijing; Chinese Academy of Sciences; Computer Network Information Center; … |