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Recent Advances of Neural Network Optimization and Algorithms in Deep Learning

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: closed (30 April 2026) | Viewed by 25701

Editor

Dr. Yang Liu

E-Mail Website
Guest Editor
The School of Telecommunications Engineering, Xidian University, Xi’an 710071, China
Interests: machine learning; computer vision; data mining; optimization; deep learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, neural networks, as one of the hottest artificial intelligence technologies, have made breakthroughs and driven the rapid development of science and technology. However, due to the complexity of neural network structures and algorithm optimization, their future development still faces many challenges. The optimization of neural networks is a key factor in improving their performance. This Special Issue aims to demonstrate (1) weight initialization, optimization and regularization of neural network algorithms; and (2) adaptive learning, distributed learning and reinforcement learning in neural networks. The editors hope to collect a number of research studies reporting the recent developments in the related research topics. In addition, researchers can promote their innovative ideas on the topic of recent advances in neural network optimization in the field of deep learning by submitting manuscripts to this Special Issue.

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but are not limited to) the following:

  1. Weight initialization, optimization and regularization in neural network algorithms;
  2. Adaptive learning, distributed learning and reinforcement learning in neural networks;
  3. A review of recent advances of neural network optimization and algorithms.

I look forward to receiving your contributions.

Dr. Yang Liu
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

  • neural networks
  • optimizer
  • regularization
  • distributed learning
  • reinforcement learning

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Published Papers (4 papers)

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Research

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20 pages, 1418 KB  
Article
A Multimodal Fake News Detection Method Based on Contrastive Learning and Variational Autoencoder
by Baowen Wu, Ruijiao Hu, Jilin Wang, Xin Sui, Jiaxing Sun, Jie Liu and Youli Qu
Mathematics 2026, 14(10), 1773; https://doi.org/10.3390/math14101773 - 21 May 2026
Viewed by 509
Abstract
Fake news often exhibits pronounced bias and misleading content. To foster a harmonious information environment, there is an urgent need for rapid fake news identification. Fake news detection can assess news authenticity by analyzing multidimensional information such as text, images, and comments. This [...] Read more.
Fake news often exhibits pronounced bias and misleading content. To foster a harmonious information environment, there is an urgent need for rapid fake news identification. Fake news detection can assess news authenticity by analyzing multidimensional information such as text, images, and comments. This automated approach significantly reduces human and material resource costs. However, existing detection methods often focus on extracting textual features, employing coarse-grained fusion techniques when integrating multi-modal information, and neglecting the inherent correlations between different modalities. Meanwhile, these methods rely on static network structures and fixed feature weighting strategies, lacking targeted neural network optimization and adaptive learning mechanisms, which results in insufficient interpretability and limited generalization performance across most detection approaches. To address these challenges, from the perspective of neural network optimization and regularization enhancement, this paper proposes a multi-modal fake news detection method based on contrastive learning and variational autoencoders. Firstly, we design a dual-contrastive learning loss function as a specialized regularization strategy for multimodal neural networks. By learning features through comparing similar and dissimilar samples, it more effectively captures correlations across multimodal data, optimizing the feature distribution and enhancing the model’s generalization capability via contrastive regularization. Second, it introduces a variational autoencoder to realize adaptive learning and dynamic weight optimization assigned to unimodal and multimodal features during decision-making. This adaptive mechanism enables the model to distinguish the relative importance of different modal information, optimizing the decision-making process of the multimodal neural network and thereby improving detection accuracy. Experiments conducted on the public Chinese dataset Weibo and English dataset Twitter demonstrate that the proposed optimized network architecture outperforms other multimodal methods by 3% to 8% in terms of detection accuracy, validating the superiority of this neural network optimization-based approach for multimodal fake news detection tasks. Full article
(This article belongs to the Special Issue Recent Advances of Neural Network Optimization and Algorithms in Deep Learning)
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28 pages, 1687 KB  
Article
MaGNet-BN: Markov-Guided Bayesian Neural Networks for Calibrated Long-Horizon Sequence Forecasting and Community Tracking
by Daozheng Qu and Yanfei Ma
Mathematics 2025, 13(17), 2740; https://doi.org/10.3390/math13172740 - 26 Aug 2025
Cited by 12 | Viewed by 2115
Abstract
Forecasting over dynamic graph environments necessitates modeling both long-term temporal dependencies and evolving structural patterns. We propose MaGNet-BN, a modular framework that simultaneously performs probabilistic forecasting and dynamic community detection on temporal graphs. MaGNet-BN integrates Bayesian node embeddings for uncertainty modeling, prototype-guided [...] Read more.
Forecasting over dynamic graph environments necessitates modeling both long-term temporal dependencies and evolving structural patterns. We propose MaGNet-BN, a modular framework that simultaneously performs probabilistic forecasting and dynamic community detection on temporal graphs. MaGNet-BN integrates Bayesian node embeddings for uncertainty modeling, prototype-guided Louvain clustering for community discovery, Markov-based transition modeling to preserve temporal continuity, and reinforcement-based refinement to improve structural boundary accuracy. Evaluated on real-world datasets in pedestrian mobility, energy consumption, and retail demand, our model achieves on average 11.48% lower MSE, 6.62% lower NLL, and 10.82% higher Modularity (Q) compared with the best-performing baselines, with peak improvements reaching 12.0% in MSE, 7.9% in NLL, and 16.0% in Q on individual datasets. It also improves uncertainty calibration (PICP) and temporal community coherence (tARI). Ablation studies highlight the complementary strengths of each component. Overall, MaGNet-BN delivers a structure-aware and uncertainty-calibrated forecasting system that models both temporal evolution and dynamic community formation, with a modular design enabling interpretable predictions and scalable applications across smart cities, energy systems, and personalized services. Full article
(This article belongs to the Special Issue Recent Advances of Neural Network Optimization and Algorithms in Deep Learning)
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24 pages, 739 KB  
Article
CPEL: A Causality-Aware, Parameter-Efficient Learning Framework for Adaptation of Large Language Models with Case Studies in Geriatric Care and Beyond
by Jinzhong Xu, Junyi Gao, Xiaoming Liu, Guan Yang, Jie Liu, Yang Long, Ziyue Huang and Kai Yang
Mathematics 2025, 13(15), 2460; https://doi.org/10.3390/math13152460 - 30 Jul 2025
Cited by 2 | Viewed by 1676
Abstract
Adapting Large Language Models (LLMs) to specialized domains like geriatric care remains a significant challenge due to the limited availability of domain-specific data and the difficulty of achieving efficient yet effective fine-tuning. Current methods often fail to effectively harness domain-specific causal insights, which [...] Read more.
Adapting Large Language Models (LLMs) to specialized domains like geriatric care remains a significant challenge due to the limited availability of domain-specific data and the difficulty of achieving efficient yet effective fine-tuning. Current methods often fail to effectively harness domain-specific causal insights, which are crucial for understanding and solving complex problems in low-resource domains.To address these challenges, we propose Causality-Aware, Parameter-Efficient Learning (CPEL), a novel framework that leverages domain-specific causal relationships to guide a multi-layer, parameter-efficient fine-tuning process for more effective domain adaptation. By embedding causal reasoning into the model’s adaptation pipeline, CPEL enables efficient specialization in the target domain while maintaining strong task-specific performance. Specifically, the Causal Prompt Generator of CPEL extracts and applies domain-specific causal structures, generating adaptive prompts that effectively guide the model’s learning process. Complementing this, the MPEFT module employs a dual-adapter mechanism to balance domain-level adaptation with downstream task optimization. This cohesive design ensures that CPEL achieves resource efficiency while capturing domain knowledge in a structured and interpretable manner. Based on this framework, we delved into its application in the field of geriatric care and trained a specialized large language model (Geriatric Care LLaMA) tailored for the aged-care domain, leveraging its capacity to efficiently integrate domain expertise. Experimental results from question-answering tasks demonstrate that CPEL improves ROUGE scores by 9–14% compared to mainstream LLMs and outperforms frontier models by 1–2 points in auto-scoring tasks. In summary, CPEL demonstrates robust generalization and cross-domain adaptability, highlighting its scalability and effectiveness as a transformative solution for domain adaptation in specialized, resource-constrained fields. Full article
(This article belongs to the Special Issue Recent Advances of Neural Network Optimization and Algorithms in Deep Learning)
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Review

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29 pages, 647 KB  
Review
Recent Advances in Optimization Methods for Machine Learning: A Systematic Review
by Xiaodong Liu, Huaizhou Qi, Suisui Jia, Yongjing Guo and Yang Liu
Mathematics 2025, 13(13), 2210; https://doi.org/10.3390/math13132210 - 7 Jul 2025
Cited by 31 | Viewed by 19619
Abstract
This systematic review explores modern optimization methods for machine learning, distinguishing between gradient-based techniques using derivative information and population-based approaches employing stochastic search. Key innovations focus on enhanced regularization, adaptive control mechanisms, and biologically inspired strategies to address challenges like scaling to large [...] Read more.
This systematic review explores modern optimization methods for machine learning, distinguishing between gradient-based techniques using derivative information and population-based approaches employing stochastic search. Key innovations focus on enhanced regularization, adaptive control mechanisms, and biologically inspired strategies to address challenges like scaling to large models, navigating complex non-convex landscapes, and adapting to dynamic constraints. These methods underpin core ML tasks including model training, hyperparameter tuning, and feature selection. While significant progress is evident, limitations in scalability and theoretical guarantees persist, directing future work toward more robust and adaptive frameworks to advance AI applications in areas like autonomous systems and scientific discovery. Full article
(This article belongs to the Special Issue Recent Advances of Neural Network Optimization and Algorithms in Deep Learning)
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