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Mathematics
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Artificial Intelligence and Algorithms
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Artificial Intelligence and Algorithms

A Special Issue of Mathematics (ISSN 2227-7390) belonging to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 30 November 2026 | Viewed by 22261

Editor

Prof. Dr. Fuhsing Wang

E-Mail Website
Guest Editor
Department of Information Management, Chinese Culture University Taiwan, Taipei, Taiwan
Interests: artificial intelligence; eLearning; interconnection networks; graph theory; algorithms

Special Issue Information

Dear Colleagues,

The Special Issue, “Artificial Intelligence and Algorithms”, aims to delve into the mathematical foundations and innovative advancements in the rapidly evolving fields of artificial intelligence (AI) and algorithm development. As AI technologies continue to revolutionize various domains, the role of sophisticated mathematical models and algorithms becomes increasingly critical in driving these innovations. This collection seeks to explore the theoretical and foundational aspects of algorithms that underlie AI systems. This includes work in algorithmic complexity, computational models, optimization techniques, and new paradigms in AI.

This Special Issue will highlight key areas where mathematics intersects with AI, including but not limited to optimization techniques, statistical methods, machine learning algorithms, and computational complexity. We seek to explore how mathematical theories and frameworks underpin the development of intelligent systems that can learn, adapt, and make decisions. Topics of interest include the design and analysis of algorithms for deep learning, reinforcement learning, natural language processing, and data mining, as well as the application of advanced mathematical tools such as linear algebra, probability theory, and differential equations in solving complex AI problems.

By bringing together contributions from mathematicians, computer scientists, and AI researchers, this Special Issue aims to provide a comprehensive overview of the state-of-the-art mathematical techniques driving AI. We invite theoretical and applied research papers that present novel mathematical models, innovative algorithms, and their practical applications in AI. This collection will serve as a valuable resource for researchers and practitioners looking to deepen their understanding of the mathematical principles that form the backbone of artificial intelligence and its algorithms.

Prof. Dr. Fuhsing Wang
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • machine learning
  • deep learning
  • neural networks
  • natural language processing
  • computer vision
  • adaptive learning systems
  • big data
  • algorithm optimization
  • cognitive computing

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Published Papers (7 papers)

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Research

20 pages, 1030 KB  
Article
A Leakage-Aware Evaluation of a Multi-Scale Attention Temporal Convolutional Network for Binary Network Intrusion Detection
by Yu Yang, Jinliang Yuan, Minna Gao, Mingmei Chen, Dan Gong and Le Gao
Mathematics 2026, 14(18), 3357; https://doi.org/10.3390/math14183357 - 16 Sep 2026
Viewed by 153
Abstract
Reliable evaluation is as important as model design in benchmark-based network intrusion detection. This study evaluates a Multi-Scale Attention Temporal Convolutional Network (MS-ATCN) for binary intrusion detection under a leakage-aware and reproducibility-oriented protocol on CIC-IDS2017, NSL-KDD, and UNSW-NB15. MS-ATCN combines multi-scale temporal convolution, [...] Read more.
Reliable evaluation is as important as model design in benchmark-based network intrusion detection. This study evaluates a Multi-Scale Attention Temporal Convolutional Network (MS-ATCN) for binary intrusion detection under a leakage-aware and reproducibility-oriented protocol on CIC-IDS2017, NSL-KDD, and UNSW-NB15. MS-ATCN combines multi-scale temporal convolution, channel and temporal attention, and class-weighted focal loss over windows of flow-level records. Because these components are established techniques, the study focuses on their integrated empirical behavior rather than proposing a new learning paradigm. The evaluation includes repeated-seed experiments, seed-aligned Wilcoxon signed-rank tests with Holm correction, component ablations, an exploratory single-run record-order check, a single-seed CIC-IDS2017 day-level holdout, an UNSW-NB15 identifier-restoration stress test, exploratory one-at-a-time hyperparameter perturbations, and computational-efficiency measurements. The repeated-run means show that MS-ATCN is not consistently the best neural model: MLP has higher mean accuracy and Macro-F1 on CIC-IDS2017, XGBoost and LightGBM have the strongest repeated-run results on NSL-KDD and UNSW-NB15, and CNN has higher mean accuracy and Macro-F1 than MS-ATCN on UNSW-NB15. No seed-aligned main-model or ablation comparison reached the Holm-adjusted 0.05 threshold. With five paired seeds, however, the exact two-sided Wilcoxon test cannot attain an unadjusted p-value below 0.0625, so adjusted nonsignificance does not establish equivalence. The exploratory diagnostics indicate sensitivity to split policy and record ordering but do not establish a general benefit from local temporal context. The findings support cautious multi-metric interpretation, strong tabular baselines, repeated-seed reporting, and explicit separation of model-only efficiency from end-to-end deployment performance. Full article
(This article belongs to the Special Issue Artificial Intelligence and Algorithms)
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19 pages, 6004 KB  
Article
Multi-Model Fusion of Lithium Battery SOC Estimation Based on Bayesian Principle
by Funian Hu and Bin Xie
Mathematics 2026, 14(10), 1642; https://doi.org/10.3390/math14101642 - 12 May 2026
Cited by 1 | Viewed by 454
Abstract
The battery management system (BMS) is the core of ensuring the safety and performance of new energy vehicles, and real-time high-precision estimation of battery state of charge (SOC) is its key function, which directly affects battery safety, endurance, and service life. Faced with [...] Read more.
The battery management system (BMS) is the core of ensuring the safety and performance of new energy vehicles, and real-time high-precision estimation of battery state of charge (SOC) is its key function, which directly affects battery safety, endurance, and service life. Faced with the challenges brought by high energy density and ultra-fast charging technology, lithium-ion batteries exhibit strong nonlinear and time-varying characteristics, making it difficult for existing SOC estimation methods to balance computational efficiency and accuracy. This study proposes a Bayesian-based Hammerstein multi-model (MM) fusion algorithm for accurate lithium battery SOC estimation across a wide temperature range, especially under low-temperature conditions. First, two Hammerstein SOC submodels are constructed: a traditional polynomial Hammerstein model and a TPA-Hammerstein model incorporating the temporal pattern attention mechanism. Second, KV-ADAM is employed for parameter training and identification of the submodels. Finally, a Bayesian weighted fusion strategy is used to dynamically integrate the outputs of the two submodels. The experimental results show that this method significantly improves the accuracy and robustness of SOC estimation, overcomes the limitations of a single model under complex dynamic conditions, provides an effective solution for lithium battery SOC estimation, and helps the safe operation of electric vehicles and the sustainable development of the industry. Full article
(This article belongs to the Special Issue Artificial Intelligence and Algorithms)
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37 pages, 29185 KB  
Article
Improved Federated Learning Incentive Mechanism Algorithm Based on Explainable DAG Similarity Evaluation
by Wenhao Lin and Yang Zhou
Mathematics 2025, 13(21), 3507; https://doi.org/10.3390/math13213507 - 2 Nov 2025
Cited by 1 | Viewed by 1669
Abstract
In vehicular networks, inter-vehicle data sharing and collaborative computing improve traffic efficiency and driving experience. However, centralized processing faces challenges with privacy, communication bottlenecks, and real-time performance. This paper proposes a trust assessment mechanism for vehicular federated learning based on graph neural network [...] Read more.
In vehicular networks, inter-vehicle data sharing and collaborative computing improve traffic efficiency and driving experience. However, centralized processing faces challenges with privacy, communication bottlenecks, and real-time performance. This paper proposes a trust assessment mechanism for vehicular federated learning based on graph neural network (GNN) edge weight similarity. An explainable asynchronous federated learning data sharing framework is designed, consisting of permissioned asynchronous federated learning and a locally verifiable directed acyclic graph (DAG). The GNN connection weights perform reputation assessment on edge devices through DAG-based verification, while deep reinforcement learning (DRL) enables explainable node selection to improve asynchronous federated learning efficiency. The proposed explainable incentive mechanism based on GNN edge weight similarity and DAG can not only effectively prevent malicious node attacks but also improve the fairness and explainability of federated learning. Extensive experiments across different participant scales (30–200 nodes), various asynchrony degrees (α = 1–5), and malicious node attack scenarios (up to 50% malicious nodes) demonstrate that our method consistently outperforms state-of-the-art approaches, achieving up to 99.2% accuracy with significant improvements of 1.3–3.1% over existing trust-based federated learning methods and maintaining 95% accuracy even under severe attack conditions. The results show that the proposed scheme performs well in terms of learning accuracy and convergence speed. Full article
(This article belongs to the Special Issue Artificial Intelligence and Algorithms)
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14 pages, 1133 KB  
Article
Empirical Investigation of the Riemann Hypothesis Using Machine Learning: A Falsifiability-Oriented Approach
by Shianghau Wu
Mathematics 2025, 13(17), 2824; https://doi.org/10.3390/math13172824 - 2 Sep 2025
Cited by 1 | Viewed by 5300
Abstract
The Riemann Hypothesis (RH) asserts that all non-trivial zeros of the Riemann zeta function lie on the critical line Re(s) = 0.5, yet no general proof exists despite extensive numerical verification. This study introduces a machine learning–based framework that combines classification, explainability, contradiction [...] Read more.
The Riemann Hypothesis (RH) asserts that all non-trivial zeros of the Riemann zeta function lie on the critical line Re(s) = 0.5, yet no general proof exists despite extensive numerical verification. This study introduces a machine learning–based framework that combines classification, explainability, contradiction testing, and generative modeling to provide empirical evidence consistent with RH. First, discriminative models augmented with SHAP analysis reveal that the real and imaginary parts of ζ(s) contribute stable explanatory signals exclusively along the critical line, while off-line regions exhibit negligible attributions. Second, a contradiction-test framework, constructed from systematically sampled off-line points, shows no indication of spurious zero-like behavior. Finally, a mixture-density variational autoencoder (MDN-VAE) trained on 10,000 zero spacings produces synthetic distributions that closely match the empirical spacing law, with a Kolmogorov–Smirnov test (KS = 0.041, p = 0.075) confirming statistical indistinguishability. Together, these findings demonstrate that machine learning and explainable AI not only reproduce the known statistical properties of zeta zeros but also reinforce the absence of contradictions to RH under extended empirical exploration. While this framework does not constitute a formal proof, it offers a falsifiability-oriented, data-driven methodology for exploring deep mathematical conjectures. This empirical evaluation involved a baseline of 12,005 points, including 5 known zeros, and 15 off-line test points. The Random Forest classifier achieved high accuracy in distinguishing critical-line zeros, and consistently rejected off-line points. The generative models further corroborated these findings. Full article
(This article belongs to the Special Issue Artificial Intelligence and Algorithms)
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40 pages, 3396 KB  
Article
Using KeyGraph and ChatGPT to Detect and Track Topics Related to AI Ethics in Media Outlets
by Wei-Hsuan Li and Hsin-Chun Yu
Mathematics 2025, 13(17), 2698; https://doi.org/10.3390/math13172698 - 22 Aug 2025
Cited by 1 | Viewed by 2385
Abstract
This study examines the semantic dynamics and thematic shifts in artificial intelligence (AI) ethics over time, addressing a notable gap in longitudinal research within the field. In light of the rapid evolution of AI technologies and their associated ethical risks and societal impacts, [...] Read more.
This study examines the semantic dynamics and thematic shifts in artificial intelligence (AI) ethics over time, addressing a notable gap in longitudinal research within the field. In light of the rapid evolution of AI technologies and their associated ethical risks and societal impacts, the research integrates the theory of chance discovery with the KeyGraph algorithm to conduct topic detection through a keyword network built through iterative semantic exploration. ChatGPT is employed for semantic interpretation, enhancing both the accuracy and comprehensiveness of the detected topics. Guided by the double helix model of human–AI interaction, the framework incorporates a dual-layer validation process that combines cross-model semantic similarity analysis with expert-informed quality checks. An analysis of 24 authoritative AI ethics reports published between 2022 and 2024 reveals a consistent trend toward semantic stability, with high cross-model similarity across years (2022: 0.808 ± 0.023; 2023: 0.812 ± 0.013; 2024: 0.828 ± 0.015). Statistical tests confirm significant differences between single-cluster and multi-cluster topic structures (p < 0.05). The thematic findings indicate a shift in AI ethics discourse from a primary emphasis on technical risks to broader concerns involving institutional governance, societal trust, and the regulation of generative AI. Core keywords, such as bias, privacy, and ethics, recur across all years, reflecting the consolidation of an integrated governance framework that encompasses technological robustness, institutional adaptability, and social consensus. This dynamic semantic analysis framework contributes empirically to AI ethics governance and offers actionable insights for researchers and interdisciplinary stakeholders. Full article
(This article belongs to the Special Issue Artificial Intelligence and Algorithms)
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22 pages, 3031 KB  
Article
Research on Emotion-Based Inspiration Mechanism in Art Creation by Generative AI
by Yuan-Chih Yu
Mathematics 2025, 13(16), 2597; https://doi.org/10.3390/math13162597 - 14 Aug 2025
Viewed by 5984
Abstract
This research presents a generative AI mechanism designed to assist artists in finding inspiration and developing ideas during their creative process by leveraging their emotions as a driving force. The proposed iterative inspiration cycle, complete with feedback loops, helps artists digitally capture their [...] Read more.
This research presents a generative AI mechanism designed to assist artists in finding inspiration and developing ideas during their creative process by leveraging their emotions as a driving force. The proposed iterative inspiration cycle, complete with feedback loops, helps artists digitally capture their creative emotions and use them as a guiding “vision” for creating artwork. Within the mechanism, the “Emotion Vision” images, generated from sketch line drawings and creative emotion prompts, are a medium designed to inspire artists. Experimental results demonstrate a positive inspirational effect, particularly in the creation of ‘Abstract Expressionism’ and ‘Impressionism’ artworks. In addition, we introduce the Emotion Vision Score metric, which quantifies the effectiveness of emotional inspiration. This metric evaluates how well “Emotion Vision” images inspire artists by balancing sketch intentions, creative emotions, and inspirational diversity, thus identifying the most effective images for inspiration. This novel mechanism integrates emotional intelligence into AI for art creation, allowing it to understand and replicate human emotion in its outputs. By enhancing emotional depth and ensuring consistency in generative AI, this research aims to advance digital art creation and contribute to the evolution of artistic expression through generative AI. Full article
(This article belongs to the Special Issue Artificial Intelligence and Algorithms)
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16 pages, 3451 KB  
Article
Session-Based Recommendation Method Using Popularity-Stratified Preference Modeling
by Yayelin Mo and Haowen Wang
Mathematics 2025, 13(6), 960; https://doi.org/10.3390/math13060960 - 14 Mar 2025
Cited by 2 | Viewed by 4517
Abstract
Large-scale offline evaluations of user–project interactions in recommendation systems are often biased due to inherent feedback loops. To address this, many studies have employed propensity scoring. In this work, we extend these methods to session-based recommendation tasks by refining propensity scoring calculations to [...] Read more.
Large-scale offline evaluations of user–project interactions in recommendation systems are often biased due to inherent feedback loops. To address this, many studies have employed propensity scoring. In this work, we extend these methods to session-based recommendation tasks by refining propensity scoring calculations to reflect dataset-specific characteristics. We evaluate our approach using neural models, specifically GRU4REC, and K-Nearest Neighbors (KNN)-based models on music and e-commerce datasets. GRU4REC is selected for its proven sequential model and computational efficiency, serving as a robust baseline against which we compare traditional methods. Our analysis of trend distributions reveals significant variations across datasets, and based on these insights, we propose a hierarchical approach that enhances model performance. Experimental results demonstrate substantial improvements over baseline models, providing a clear pathway for mitigating biases in session-based recommendation systems. Full article
(This article belongs to the Special Issue Artificial Intelligence and Algorithms)
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