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Advanced Mathematical Methods for Machine Learning, Neural Networks, and Computer...
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Advanced Mathematical Methods for Machine Learning, Neural Networks, and Computer Vision

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 14 June 2026 | Viewed by 2246

Special Issue Editor

Prof. Dr. Guodong Li

E-Mail Website
Guest Editor
School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541002, China
Interests: statistical analysis; data mining; machine learning; chaos theory; information security; image processing

Special Issue Information

Dear Colleagues,

The integration of mathematical methods in machine learning, neural networks, and computer vision has become increasingly vital as AI applications expand across various industries. These methods provide the theoretical foundation for building reliable, interpretable, and efficient AI systems. Recent advances in geometric deep learning, statistical learning theory, and sparse representation have significantly enhanced the performance of AI systems, yet many theoretical challenges remain to be addressed.

We are pleased to invite you to contribute to this Special Issue, which focuses on the application and theoretical underpinnings of mathematical methods in machine learning, neural networks, and computer vision. This Issue will highlight how mathematical theories drive innovative breakthroughs in AI algorithms and promote the practical application of AI technologies.

This Special Issue aims to collect original research articles and reviews exploring the application of mathematical methods in the aforementioned fields. We particularly encourage submissions on geometric deep learning, sparse representation, optimization algorithms, statistical learning theory, and generative models. These studies should provide theoretical support for AI systems and facilitate their application in practical tasks. Other topics of interest include, but are not limited to, sparse models, low-rank structures, stochastic algorithms, and explainability analysis.

In this Special Issue, original research articles and reviews are welcome. Research areas may include geometric deep learning, sparse representation, optimization algorithms, statistical learning theory, generative models, sparse models, low-rank structures, stochastic algorithms, explainability analysis, etc.

We look forward to receiving your contributions.

Prof. Dr. Guodong Li
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-blind 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

  • mathematical optimization
  • optimization algorithms
  • statistics
  • economic mathematics
  • financial mathematics
  • geometric deep learning
  • neural network analysis
  • robust AI design
  • machine learning theory
  • computer vision modeling

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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21 pages, 11650 KB  
Article
PD-CBDM: Training Class-Balancing Diffusion Models with Perceptual Distinguish Loss
by Junyan Hu, Wei Luo, Tong Chen, Xiaobao Yang and Zhiqiang Hou
Mathematics 2026, 14(10), 1576; https://doi.org/10.3390/math14101576 - 7 May 2026
Viewed by 225
Abstract
For image generation, denoising diffusion probabilistic models (DDPMs) have shown strong performance. Nevertheless, under class-imbalanced training data, many existing models tend to overfit head classes, which degrades image quality for tail classes. To mitigate this issue, we propose a new generation method, PD-CBDM [...] Read more.
For image generation, denoising diffusion probabilistic models (DDPMs) have shown strong performance. Nevertheless, under class-imbalanced training data, many existing models tend to overfit head classes, which degrades image quality for tail classes. To mitigate this issue, we propose a new generation method, PD-CBDM (perceptual distinguish loss–class-balancing diffusion models). As a first step, PD-CBDM revises the target-label distribution used for label sampling in the baseline pipeline, so tail classes are sampled more frequently during training; this improves the diversity of generated images while keeping fidelity high. Next, we introduce a perceptual distinguish loss that enlarges the separation (measured by the KL divergence in the reverse process) between the data distributions of head and tail classes, which helps suppress head-class overfitting and improves generation quality across classes. Additionally, we propose a timestep-dependent Self-Attention (TSA) module that injects timestep cues into the self-attention mechanism to model temporal and spatial dependencies together, thereby enhancing noise estimation accuracy and image generation quality. Experiments show that PD-CBDM improves FID from 5.81 to 4.96 on CIFAR100-LT and from 5.46 to 5.03 on CIFAR10-LT, and it is competitive with representative recent methods such as BPA and NoisyTwins. Full article
(This article belongs to the Special Issue Advanced Mathematical Methods for Machine Learning, Neural Networks, and Computer Vision)
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23 pages, 473 KB  
Article
A General Framework for Activation Function Optimization Based on Mollification Theory
by Wentao Zhang, Yutong Zhang, Yuxin Zheng and Wentao Mo
Mathematics 2026, 14(1), 72; https://doi.org/10.3390/math14010072 - 25 Dec 2025
Cited by 1 | Viewed by 957
Abstract
The deep learning paradigm is progressively shifting from non-smooth activation functions, exemplified by ReLU, to smoother alternatives such as GELU and SiLU. This transition is motivated by the fact that non-differentiability introduces challenges for gradient-based optimization, while an expanding body of research demonstrates [...] Read more.
The deep learning paradigm is progressively shifting from non-smooth activation functions, exemplified by ReLU, to smoother alternatives such as GELU and SiLU. This transition is motivated by the fact that non-differentiability introduces challenges for gradient-based optimization, while an expanding body of research demonstrates that smooth activations yield superior convergence, improved generalization, and enhanced training stability. A central challenge, however, is how to systematically transform widely used non-smooth functions into smooth counterparts that preserve their proven representational strengths while improving differentiability and computational efficiency. To address this, we propose a general activation smoothing framework grounded in mollification theory. Leveraging the Epanechnikov kernel, the framework achieves statistical optimality and computational tractability, thereby combining theoretical rigor with practical utility. Within this framework, we introduce Smoothed ReLU (S-ReLU), a novel second-order continuously differentiable (C2) activation derived from ReLU that inherits its favorable properties while mitigating inherent drawbacks. Extensive experiments on CIFAR-10, CIFAR-100, and ImageNet-1K with Vision Transformers and ConvNeXt consistently demonstrate the superior performance of S-ReLU over existing ReLU variants. Beyond computer vision, large-scale fine-tuning experiments on language models further show that S-ReLU surpasses GELU, underscoring its broad applicability across both vision and language domains and its potential to enhance stability and scalability. Full article
(This article belongs to the Special Issue Advanced Mathematical Methods for Machine Learning, Neural Networks, and Computer Vision)
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18 pages, 1759 KB  
Article
VLGA: A Chaos-Enhanced Genetic Algorithm for Optimizing Transformer-Based Prediction of Infectious Diseases
by Guodong Li, Lu Zhang, Fuxin Zhang and Wenxia Xu
Mathematics 2025, 13(24), 3908; https://doi.org/10.3390/math13243908 - 6 Dec 2025
Viewed by 641
Abstract
Accurate and generalizable prediction of infectious disease incidence is essential for proactive public health response. This study proposes a novel hybrid VLGA-Transformer model to address this challenge, validated through tuberculosis (TB) and hepatitis B case studies. Utilizing monthly TB data from Zhejiang Province [...] Read more.
Accurate and generalizable prediction of infectious disease incidence is essential for proactive public health response. This study proposes a novel hybrid VLGA-Transformer model to address this challenge, validated through tuberculosis (TB) and hepatitis B case studies. Utilizing monthly TB data from Zhejiang Province (2013–2023), raw sequences were first decomposed via Variational Mode Decomposition (VMD) to extract intrinsic temporal patterns. To overcome Transformer parameter optimization difficulties, we innovatively integrated the Lorenz attractor into a Genetic Algorithm (GA), creating a Lorenz-attractor-enhanced GA (LGA) that dynamically balances exploration and exploitation. The resulting VLGA-Transformer framework demonstrated superior performance, achieving R2 values of 0.96 for TB and 0.93 for hepatitis B prediction, significantly outperforming benchmark models in both accuracy and stability. When tested on hepatitis B data, the model confirmed its robust cross-disease generalizability. These findings highlight the framework’s dual strengths—high-precision forecasting and robust generalization—providing actionable insights for public health authorities to optimize resource allocation and intervention strategies, thereby advancing data-driven infectious disease control systems. Full article
(This article belongs to the Special Issue Advanced Mathematical Methods for Machine Learning, Neural Networks, and Computer Vision)
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