---
title: "Softmax function: formula and 42 recent papers"
description: "Softmax function was mentioned in 42 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #24 of the 104 equations and models mentioned."
url: https://scholar4ai.com/equations/softmax-function
markdown_url: https://scholar4ai.com/equations/softmax-function.md
license: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/)
share_text: "Softmax function was mentioned in 42 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #24 of the 104 equations and models mentioned."
data_url: https://scholar4ai.com/data/rankings.json
updated: 2026-10-26T14:32:25+09:00
window: 2026-09-27 to 2026-10-26
source: OpenAlex (CC0)
---

# Softmax function

$$
\mathrm{softmax}(z)_i = \frac{e^{z_i}}{\sum_{j=1}^{K} e^{z_j}}
$$

Turns a vector of scores into probabilities.

- area: Machine learning
- 5 papers in the last 7 days
- Names searched for: softmax

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

## Key findings

- Softmax function was mentioned in 42 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #24 of the 104 equations and models mentioned.
- By journal category: AI (37), Finance (3) and Operations Research (2).
- Most of them appeared in International Journal of Computer Vision (6), Neural Networks (5) and Expert Systems with Applications (5).
- Often mentioned together with Scaled dot-product attention (Transformer) (26), Convolutional neural network (CNN) (21) and Cross-entropy loss (21).
- Datasets named in the same papers: OR-Library (8), ImageNet (7) and CIFAR-10 / CIFAR-100 (4).
- From Oct 2023 to Sep 2026, 91 archived papers mentioned Softmax function in their title, abstract or keywords, most of them in Sep 2026 (10).

## Mentions over 36 months

*Papers mentioning it by publication month, Oct 2023 to Sep 2026 (titles, abstracts and keywords)*

| Trend | Oct 23–Sep 24 | Oct 24–Sep 25 | Oct 25–Sep 26 | 36 months |
|---|---:|---:|---:|---:|
|  | 38 | 31 | 22 | 91 |

*Papers mentioning Softmax function, newest first.*

| 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 | [From pixels to profits: trading arbitrage portfolios based on image representations](https://doi.org/10.1007/s11408-026-00507-x) | [Financial markets and portfolio management](https://scholar4ai.com/journals/financial-markets-and-portfolio-management.md) | Niklas Paluszkiewicz | Universität Ulm |
| 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 |
| 2026-10-20 | [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 | [Reusability report: multi-sample omics network inference operates in distinct robustness regimes defined by prior knowledge and data availability](https://doi.org/10.1038/s42256-026-01311-y) | [Nature Machine Intelligence](https://scholar4ai.com/journals/nature-machine-intelligence.md) | Xabier Martinez‐de‐Morentin, Sameer Ahmad Khan, Itziar Cenzano et al. | King Abdullah University of Science and Technology; Ilia State University; Karolinska University Hospital; … |
| 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 |
| 2026-10-17 | [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 | [MonoPRIO: Adaptive prior conditioning for unified monocular 3D object detection](https://doi.org/10.1016/j.patcog.2026.115138) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Leon Davies, Qinggang Meng, Mohamad Saada et al. | Loughborough University; University of Southern Denmark |
| 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 | [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; … |
| 2026-10-14 | [Dynamic gain neuromodulation attenuates stability gaps during continual joint training](https://doi.org/10.1016/j.neunet.2026.109767) | [Neural Networks](https://scholar4ai.com/journals/neural-networks.md) | Alejandro Rodriguez-Garcia, Anindya Ghosh, Srikanth Ramaswamy | Newcastle University |
| 2026-10-12 | [Gaussian Splatting for real-time scene reconstruction: Methods, systems, and trade-offs](https://doi.org/10.1016/j.patcog.2026.115120) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Ashim Dahal, Rabab Abdelfattah, Nick Rahimi | University of Southern Mississippi |
| 2026-10-11 | [LiteSent: a lightweight adaptive multi-scale framework for social media and review-based sentiment classification](https://doi.org/10.1016/j.knosys.2026.117207) | [Knowledge-Based Systems](https://scholar4ai.com/journals/knowledge-based-systems.md) | Dharmendra Dangi, Dheeraj Kumar Dixit, Amit Bhagat | Indian Institute of Information Technology Bhopal; Madhav Institute of Technology & Science; Maulana Azad National Institute of Technology |
| 2026-10-10 | [Adjusting modal contributions via differential-driven SoftMax fusion for RGB-IR object detection](https://doi.org/10.1016/j.neunet.2026.109707) | [Neural Networks](https://scholar4ai.com/journals/neural-networks.md) | Hang Yu, Jun Zhang, Rui Ding et al. | Chongqing University; Civil Aviation Administration of China |
| 2026-10-08 | [JTCSE: Joint tensor-modulus constraints and cross-attention for unsupervised contrastive learning of sentence embeddings](https://doi.org/10.1016/j.neunet.2026.109724) | [Neural Networks](https://scholar4ai.com/journals/neural-networks.md) | Tianyu Zong, Bingkang Shi, Hongzhu Yi et al. | University of Chinese Academy of Sciences |
| 2026-10-06 | [Chronologically consistent large language models](https://doi.org/10.1016/j.jfineco.2026.104374) | [Journal of Financial Economics](https://scholar4ai.com/journals/journal-of-financial-economics.md) | Songrun He, Linying Lv, Asaf Manela et al. | Chinese University of Hong Kong; Washington University in St. Louis; University of Iowa |
| 2026-10-03 | [Uncertainty quantification for trustworthy deep learning: Methods and measures](https://doi.org/10.1016/j.neunet.2026.109699) | [Neural Networks](https://scholar4ai.com/journals/neural-networks.md) | H. Martin Gillis, Thomas P. Trappenberg | Dalhousie University |
| 2026-10-02 | [RL-Axial: Learning When to Compute Global Context for Multimodal Segmentation](https://doi.org/10.1007/s12559-026-10661-z) | [Cognitive Computation](https://scholar4ai.com/journals/cognitive-computation.md) | Dong Xing, Hang Yang, Jinhe Zhang et al. | Chinese Academy of Sciences; Changchun Institute of Optics, Fine Mechanics and Physics; University of Chinese Academy of Sciences |
| 2026-10-01 | [TFMNet: A Decomposition-Driven Hierarchical Framework for Multi-Step Forecasting of Nonstationary Industrial Time Series](https://doi.org/10.1016/j.eswa.2026.134826) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Wenkui Bian, Dakuo He, Runda Jia et al. | Northeastern University; Beijing General Research Institute of Mining and Metallurgy |
| 2026-10-01 | [Alzheimer’s multimodal diagnosis: enhancing cross-attention between speech and text](https://doi.org/10.1007/s00521-026-12482-5) | [Neural Computing and Applications](https://scholar4ai.com/journals/neural-computing-and-applications.md) | Kewen Ding, Azadeh Noori Hoshyar, Tanusri Bhattacharya et al. | Federation University; Western Sydney University; Myer Foundation; … |
| 2026-10-01 | [ARION: Attention-Optimized Transformer Inference on Encrypted Data](https://doi.org/10.1016/j.eswa.2026.134756) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Linhan Yang, Jingwei Chen, Wangchen Dai et al. | Sun Yat-sen University; Chongqing Institute of Green and Intelligent Technology; University of Chinese Academy of Sciences; … |
| 2026-10-01 | [Rebuilding to remember: Reconstruction-driven regularization for information-preserving in clustering graph pooling](https://doi.org/10.1016/j.patcog.2026.115135) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Wenju Hou, Jie Hong, Jialin Liu et al. | Jilin University; Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University; Sun Yat-sen University |
| 2026-10-01 | [SYNAPSE-X: a calibration-aware vision transformer framework for selective referral in multi-class brain tumor MRI classification](https://doi.org/10.1007/s00521-026-12608-9) | [Neural Computing and Applications](https://scholar4ai.com/journals/neural-computing-and-applications.md) | Sadaf Tabatabaee, Mohammad T. Khasawneh | Binghamton University |
| 2026-10-01 | [Incentive deadlocks and collaborative breakthroughs in digital transformation: an agent‑based evolutionary game of platform strategies for traditional logistics enterprises](https://doi.org/10.1016/j.tre.2026.105299) | [Transportation Research Part E Logistics and Transportation Review](https://scholar4ai.com/journals/transportation-research-part-e-logistics-and-transportation-review.md) | Yutong Wu, Weimin Ma | Tongji University |
| 2026-10-01 | [DIRU: dendrite-inspired recurrent units for learning chaotic dynamics and neonatal epilepsy time series](https://doi.org/10.1007/s00521-026-12526-w) | [Neural Computing and Applications](https://scholar4ai.com/journals/neural-computing-and-applications.md) | Alessandro Crimi, Cristiano Micheli, Tiziana Currieri et al. | University of Agriculture in Krakow; AGH University of Krakow; Technische Universität Ilmenau; … |
| 2026-10-01 | [RDD: Improving Structure from Motion with a Robust Feature Detector and Descriptor](https://doi.org/10.1007/s11263-026-03061-1) | [International Journal of Computer Vision](https://scholar4ai.com/journals/international-journal-of-computer-vision.md) | G Chen, Tianwen Fu, Haiwei Chen et al. | University of Southern California; Creative Technologies (United States) |
| 2026-10-01 | [ANNE: adaptive neuron network expansion for 2D medical image segmentation](https://doi.org/10.1007/s10489-026-07503-8) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | Abel A. Reyes, Sidike Paheding | Michigan Technological University; Fairfield University |
| 2026-10-01 | [From 3D perception to safety reasoning: an intelligent hybrid framework for real-time underground mine monitoring](https://doi.org/10.1016/j.eswa.2026.134601) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Pasindu Ranasinghe, Simit Raval, Dibyayan Patra et al. | UNSW Sydney; University of Southern Queensland |
| 2026-10-01 | [CLIDD: Cross-Layer Independent Deformable Description for Efficient and Discriminative Local Feature Representation](https://doi.org/10.1007/s11263-026-03063-z) | [International Journal of Computer Vision](https://scholar4ai.com/journals/international-journal-of-computer-vision.md) | Haodi Yao, Fenghua He, Ning Hao et al. | Harbin Institute of Technology; Beijing Institute for General Artificial Intelligence |
| 2026-10-01 | [HR-INR: Continuous Space-Time Video Super-Resolution via Event Camera](https://doi.org/10.1007/s11263-026-03034-4) | [International Journal of Computer Vision](https://scholar4ai.com/journals/international-journal-of-computer-vision.md) | Yunfan Lu, Yusheng Wang, Zipeng Wang et al. | The Hong Kong University of Science and Technology (Guangzhou); The University of Tokyo; Hong Kong University of Science and Technology; … |
| 2026-10-01 | [Privacy Leakage on DNNs: A Survey of Model Inversion Attacks and Defenses](https://doi.org/10.1007/s11263-026-03049-x) | [International Journal of Computer Vision](https://scholar4ai.com/journals/international-journal-of-computer-vision.md) | Hao Fang, Yixiang Qiu, Hongyao Yu et al. | Tsinghua Shenzhen International Graduate School; Tsinghua University; Harbin Institute of Technology; … |
| 2026-09-30 | [ASSMamba: Prototype-conditioned spectral routing and direction-aware state-space learning for hyperspectral image classification](https://doi.org/10.1016/j.eswa.2026.134589) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Lei Zhu, Yikai Su, Liang Dong et al. |  |
| 2026-09-30 | [TIC: Co-optimization of training and inference for efficient image-text retrieval](https://doi.org/10.1016/j.neunet.2026.109696) | [Neural Networks](https://scholar4ai.com/journals/neural-networks.md) | 尤忠祥, Shiyuan Yang, Zhixin Li | Guangxi Normal University |
| 2026-09-30 | [Towards optimized forward–forward training for neural networks](https://doi.org/10.1007/s10462-026-11668-6) | [Artificial Intelligence Review](https://scholar4ai.com/journals/artificial-intelligence-review.md) | Yomna Abdulgawad Elnady, Amany Mahmoud Sarhan, Mohammad Ali Eita | Tanta University; ElSewedy University of Technology |
| 2026-09-29 | [Rethinking linear attention as fast weight programmers with routing and nonlinearity](https://doi.org/10.1016/j.eswa.2026.134596) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Yuan Cao, Dong Wang | Beijing Jiaotong University |
| 2026-09-28 | [Self-Organized Context Dependent Processing in Neural Networks](https://doi.org/10.1007/s12559-026-10624-4) | [Cognitive Computation](https://scholar4ai.com/journals/cognitive-computation.md) | Hao GuangFu, Yang Chen, Sainan Qin et al. | Chinese Academy of Sciences; Institute of Automation; University of Chinese Academy of Sciences; … |
| 2026-09-28 | [Exponential decay-augmented transformers for interpretable temporal reasoning](https://doi.org/10.1016/j.knosys.2026.117108) | [Knowledge-Based Systems](https://scholar4ai.com/journals/knowledge-based-systems.md) | Jothi Prakash V, S. Arul Antran Vijay | Karpagam Academy of Higher Education |
| 2026-09-28 | [CausalCACTUS: A Causally Consistent and Context-Aware Framework for Counterfactual Explanations](https://doi.org/10.1007/s10994-026-07155-2) | [Machine Learning](https://scholar4ai.com/journals/machine-learning.md) | Zhendong Wang, Diego García, José María Enguita et al. | KTH Royal Institute of Technology; Universidad de Oviedo |
| 2026-09-28 | [Mapping the RAG landscape: a four-axis taxonomy of efficiency, defense, interactivity, and reasoning](https://doi.org/10.1007/s10462-026-11715-2) | [Artificial Intelligence Review](https://scholar4ai.com/journals/artificial-intelligence-review.md) | Meghana Sunil, Vaddepalli Shravya, Shravan Venkatraman et al. | Vellore Institute of Technology University; Mohamed bin Zayed University of Artificial Intelligence |
| 2026-09-28 | [scDEAN: a lightweight adaptive fusion model for clustering scRNA-seq data](https://doi.org/10.1007/s10489-026-07502-9) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | Subhashis Chatterjee, Rohit Bose | Indian Institute of Technology Dhanbad |
| 2026-09-28 | [DAMEL: Dual-axis multi-expert learning for class-imbalanced learning](https://doi.org/10.1016/j.knosys.2026.117115) | [Knowledge-Based Systems](https://scholar4ai.com/journals/knowledge-based-systems.md) | Hyuck Lee, Taemin Park, Heeyoung Kim | Korea Advanced Institute of Science and Technology |

## Cite this page

Scholar4AI. (2026). Softmax function. Journal Research Rankings. Retrieved October 26, 2026, from https://scholar4ai.com/equations/softmax-function

```bibtex
@misc{scholar4ai-equations-softmax-function,
  author = {{Scholar4AI}},
  title = {Softmax function},
  year = {2026},
  howpublished = {\url{https://scholar4ai.com/equations/softmax-function}},
  urldate = {2026-10-26},
  note = {Journal Research Rankings; data from OpenAlex (CC0); licensed CC BY-NC 4.0}
}
```

License: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/).