---
title: "Cross-entropy loss: formula and 42 recent papers"
description: "Cross-entropy loss 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/cross-entropy-loss
markdown_url: https://scholar4ai.com/equations/cross-entropy-loss.md
license: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/)
share_text: "Cross-entropy loss 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: 2026-10-26T14:52:47+09:00
window: 2026-09-27 to 2026-10-26
source: OpenAlex (CC0)
---

# Cross-entropy loss

$$
\mathcal{L} = -\sum_{c=1}^{C} y_c \log \hat y_c
$$

Standard loss for classification: the negative log-probability of the true class.

- area: Machine learning
- 3 papers in the last 7 days
- Names searched for: cross-entropy

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

## Key findings

- Cross-entropy loss 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 (34), Finance (4), Management (2), Operations Research (1) and Economics (1).
- Most of them appeared in Neural Computing and Applications (8), Applied Intelligence (4) and International Journal of Computer Vision (4).
- Often mentioned together with Convolutional neural network (CNN) (26), Scaled dot-product attention (Transformer) (21) and Softmax function (21).
- Datasets named in the same papers: ImageNet (10), OR-Library (8) and CIFAR-10 / CIFAR-100 (6).
- From Oct 2023 to Sep 2026, 116 archived papers mentioned Cross-entropy loss in their title, abstract or keywords, most of them in Jun 2025 (8).

## 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 |
|---|---:|---:|---:|---:|
|  | 45 | 50 | 21 | 116 |

*Papers mentioning Cross-entropy loss, 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 |
| 2026-10-20 | [Weighted UnLearning from Experience for Improved Spurious Correlation Robustness](https://doi.org/10.1007/s10994-026-07164-1) | [Machine Learning](https://scholar4ai.com/journals/machine-learning.md) | Jeff Mitchell, Jesus; id_orcid 0000-0002-9574-4138 Martinez-del-Rincon, Niall McLaughlin | Queen's University Belfast |
| 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 |
| 2026-10-16 | [Generative deep learning for class imbalance in credit risk modeling: comparative evaluation of synthetic oversampling methods and an elastic oversampling extension](https://doi.org/10.1186/s40854-026-00970-5) | [Financial Innovation](https://scholar4ai.com/journals/financial-innovation.md) | Tae Yeon Kwon | Hankuk University of Foreign Studies |
| 2026-10-16 | [An exact solution algorithm for the bi-level optimization problem of electric vehicles charging station placement](https://doi.org/10.1016/j.trb.2026.103620) | [Transportation Research Part B Methodological](https://scholar4ai.com/journals/transportation-research-part-b-methodological.md) | Mobina Nankali, Michael W. Levin | University of Minnesota |
| 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 |
| 2026-10-10 | [TACoS: Weakly supervised learning of two-dimensional materials from scribble annotations to precise segmentation](https://doi.org/10.1016/j.patcog.2026.115084) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Jiabei Chen, Liping Zhang, Jiangbin Wu et al. | Chinese Academy of Sciences; Institute of Semiconductors; University of Chinese Academy of Sciences |
| 2026-10-09 | [Test-time optimization for domain adaptive open vocabulary segmentation](https://doi.org/10.1016/j.neunet.2026.109689) | [Neural Networks](https://scholar4ai.com/journals/neural-networks.md) | Ulindu De Silva, Didula Samaraweera, Sasini Wanigathunga et al. | University of Moratuwa; Stony Brook University; Khalifa University of Science and Technology |
| 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 | [An intelligent cybersecurity framework for banking systems: integrating neural networks, large language models, and federated learning for anti-money laundering and fraud detection](https://doi.org/10.1186/s43093-026-01015-0) | [Future Business Journal](https://scholar4ai.com/journals/future-business-journal.md) | Tanvir Sajid, Sajida Hafeez | National Textile University |
| 2026-10-03 | [Sparse oblique rule boosting for simpler additive rule ensembles](https://doi.org/10.1007/s10618-026-01241-8) | [Data Mining and Knowledge Discovery](https://scholar4ai.com/journals/data-mining-and-knowledge-discovery.md) | Shahrzad Behzadimanesh, Pierre Le Bodic, Geoffrey I. Webb et al. | Monash University; University of Haifa |
| 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 | [Multi-View Contrastive Graph Convolutional Networks with Adaptive Fusion for semi-supervised classification](https://doi.org/10.1016/j.patcog.2026.115211) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Huaichun Xiao, Fadi Dornaika, Jingjun Bi et al. | University of the Basque Country; Ikerbasque; North China University of Water Resources and Electric Power; … |
| 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 | [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 | [RECE Loss: A Reward-Enhanced Cross Entropy Loss Function for Learning with Noisy Labels](https://doi.org/10.1007/s00521-026-12500-6) | [Neural Computing and Applications](https://scholar4ai.com/journals/neural-computing-and-applications.md) | Thi Thu Huong Nguyen, Duy Tung Nguyen, Thanh Tung Nguyen et al. | Thuyloi University; CMC University; Hanoi University of Science and Technology; … |
| 2026-10-01 | [Class-based many-objective neural architecture search for deep classifiers](https://doi.org/10.1007/s00521-026-12510-4) | [Neural Computing and Applications](https://scholar4ai.com/journals/neural-computing-and-applications.md) | Guy Mardiks, Adham Salih, Amiram Moshaiov | Tel Aviv University; Braude College of Engineering Karmiel |
| 2026-10-01 | [Patient-independent EEG seizure detection using channel attention and dual-branch time–frequency features](https://doi.org/10.1007/s00521-026-12518-w) | [Neural Computing and Applications](https://scholar4ai.com/journals/neural-computing-and-applications.md) | Hrishikesh Tiwary, Arnav Bhavsar, H Muralikrishna | Indian Institute of Technology Mandi; Manipal Academy of Higher Education |
| 2026-10-01 | [CL3AN-GNN: curriculum-driven for incremental feature disentanglement with multi-phase attention for class-imbalanced node classification](https://doi.org/10.1007/s00521-026-12579-x) | [Neural Computing and Applications](https://scholar4ai.com/journals/neural-computing-and-applications.md) | Abdul Joseph Fofanah, David Chen, Lian Wen et al. | Griffith University; Chang'an University; Njala 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 | [A comprehensive survey on multimodal sentiment analysis: Approaches, challenges and open issues](https://doi.org/10.1016/j.ijinfomgt.2026.103138) | [International Journal of Information Management](https://scholar4ai.com/journals/international-journal-of-information-management.md) | Fatemeh Hemmatian, Arash Sabbaghi, Mohammad Karim Sohrabi | Islamic Azad University Semnan |
| 2026-10-01 | [Multi-view self-supervised learning for label-flipping robustness in tabular data: a comparative study](https://doi.org/10.1007/s10489-026-07452-2) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | Jinhyeok Jang, Sohee Park, Seung-Soo Nam et al. | Soongsil University |
| 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 | [Decentralized gossip learning and federated averaging for histopathology image classification](https://doi.org/10.1007/s00521-026-12493-2) | [Neural Computing and Applications](https://scholar4ai.com/journals/neural-computing-and-applications.md) | Yusuf Öztürk, Bengisu Atli, Enes Goktekin et al. | Antalya Bilim Üniversitesi; Antalya Bilim University; Ankara 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 | [SLCA++: Unleash the Power of Sequential Fine-Tuning for Continual Learning with Pre-training](https://doi.org/10.1007/s11263-026-03041-5) | [International Journal of Computer Vision](https://scholar4ai.com/journals/international-journal-of-computer-vision.md) | Gengwei Zhang, Liyuan Wang, Guoliang Kang et al. | University of Technology Sydney; Tsinghua University; Beihang University; … |
| 2026-10-01 | [Efficient Test-Time Prompt Tuning for Vision-Language Models](https://doi.org/10.1007/s11263-026-03019-3) | [International Journal of Computer Vision](https://scholar4ai.com/journals/international-journal-of-computer-vision.md) | Yuhan Zhu, Guozhen Zhang, Xu Chen et al. | Nanjing University; Shanghai Artificial Intelligence Laboratory |
| 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 | [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 |
| 2026-09-30 | [Order-flow toxicity in cryptocurrency perpetual futures: Order flow signals, price-impact persistence, and the limits of volatility-based metrics](https://doi.org/10.1016/j.iref.2026.105876) | [International Review of Economics & Finance](https://scholar4ai.com/journals/international-review-of-economics-finance.md) | Suresh Rajendran, Divya Singaravelu |  |
| 2026-09-30 | [P2Mark: Plug-and-play parameter-level watermarking for neural speech generation](https://doi.org/10.1016/j.artint.2026.104627) | [Artificial Intelligence](https://scholar4ai.com/journals/artificial-intelligence.md) | Yong Sheng Ren, Jiangyan Yi, Tao Wang et al. | Chinese Academy of Sciences; Institute of Automation; University of Chinese Academy of Sciences; … |
| 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 | [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 | [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 |
| 2026-09-28 | [Sensory-aware sequential recommendation via review-distilled representations](https://doi.org/10.1016/j.knosys.2026.117071) | [Knowledge-Based Systems](https://scholar4ai.com/journals/knowledge-based-systems.md) | Yeo Chan Yoon, Chanjun Park, KyuHan Koh | Jeju National University; Soongsil University; California State University, Stanislaus |
| 2026-09-28 | [Treatment evaluation at the intensive and extensive margins](https://doi.org/10.1016/j.jeconom.2026.106344) | [Journal of Econometrics](https://scholar4ai.com/journals/journal-of-econometrics.md) | Phillip Heiler, Asbjørn Kaufmann, Bezirgen Veliyev | Aarhus University |

## Cite this page

Scholar4AI. (2026). Cross-entropy loss. Journal Research Rankings. Retrieved October 26, 2026, from https://scholar4ai.com/equations/cross-entropy-loss

```bibtex
@misc{scholar4ai-equations-cross-entropy-loss,
  author = {{Scholar4AI}},
  title = {Cross-entropy loss},
  year = {2026},
  howpublished = {\url{https://scholar4ai.com/equations/cross-entropy-loss}},
  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/).