Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.6
2.2
Journals
Mathematics
Special Issues
Mathematical Foundations and Optimization Techniques for Large Language Models
share announcement

Mathematical Foundations and Optimization Techniques for Large Language Models

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

Deadline for manuscript submissions: 31 May 2026 | Viewed by 2257

Special Issue Editors

Dr. Hao Chen

E-Mail Website
Guest Editor
Faculty of Data Science, City University of Macau, Macau, China
Interests: large language model; embodied AI; recommendation
Dr. Yinlong Liu

E-Mail Website
Guest Editor
Faculty of Data Science, City University of Macau, Macau, China
Interests: global optimization algorithm; robotics and artificial intelligence; geometric vision
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, large language models (LLMs) have become a cornerstone of artificial intelligence, driving advancements in natural language processing, knowledge reasoning, multimodal intelligence, and embodied/agentic AI. However, the rapid development of LLMs also presents significant challenges in mathematical foundations, computational optimization, and efficient deployment. This Special Issue aims to present innovative research on the mathematical theories and optimization methodologies underlying the design, training, and application of LLMs.

We invite researchers to submit original research articles, reviews, and perspectives on topics including, but not limited to, the following:

  • Mathematical analysis of transformer architectures and attention mechanisms
  • Modeling and optimization of multimodal LLMs
  • Design and applications of LLMs for recommendation systems
  • Development of LLMs for embodied AI applications
  • Security and adversarial robustness in LLMs
  • Optimization algorithms for training billion-parameter models
  • Theoretical frameworks for model interpretability and explainability
  • Distributed and federated learning strategies for LLMs
  • Efficient inference techniques with provable computational bounds
  • Information-theoretic approaches to knowledge representation
  • Causal reasoning and logical formalization in LLMs

We encourage submissions that encompass mathematical analyses, innovative optimization methodologies, and practical implementations that address the scalability, efficiency, and theoretical limitations of LLMs. Both theoretical advancements and applied studies, including experimental validations, are welcome.

We look forward to your contributions!

Dr. Hao Chen
Dr. Yinlong Liu
Guest Editors

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

  • large language models (LLMs)
  • mathematical foundations of LLMs
  • optimization techniques for LLMs
  • multimodal LLMs
  • LLMs for recommendation systems
  • embodied AI and LLMs
  • LLM security and robustness

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

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

Published Papers (2 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

34 pages, 1144 KB  
Article
BAF–FedLLM: Behavior-Aware Federated Modeling of Student Actions via Privacy-Preserving Large Language Model
by Wei Ji, Zuobin Ying and Hanying Gan
Mathematics 2026, 14(4), 604; https://doi.org/10.3390/math14040604 - 9 Feb 2026
Viewed by 507
Abstract
Analyzing fine-grained student actions across institutions can drive timely feedback, early warning, and personalized support, yet it is constrained by privacy regulations, heterogeneous curricula, and non-IID behavior logs. This paper introduces BAF–FedLLM, a behavior-aware federated modeling framework that adapts large language models to [...] Read more.
Analyzing fine-grained student actions across institutions can drive timely feedback, early warning, and personalized support, yet it is constrained by privacy regulations, heterogeneous curricula, and non-IID behavior logs. This paper introduces BAF–FedLLM, a behavior-aware federated modeling framework that adapts large language models to next-action and outcome prediction without centralizing student data. The key idea is to treat multichannel interaction streams as semantically typed action tokens linked by a learned ActionGraph, and to align their temporal structure with an LLM through behavior prompts that inject domain context (task, resource, pedagogy, and affordance cues). We propose three novel components: (i) BP–FIT, a behavior-prompted federated instruction tuning scheme that trains low-rank adapters locally and aggregates them with secure masking and Rényi–DP accounting to ensure client-level privacy; (ii) ProtoAlign, a cross-client prototype contrastive objective that shares only noisy class-conditional anchors via secure aggregation to mitigate drift under non-IID partitions; and (iii) CBR, a causal behavior regularizer that penalizes intervention-sensitive shortcuts by enforcing invariance of predicted risks across detected instructional regimes. We further derive convergence guarantees for federated instruction tuning with noisy, partial participation and provide end-to-end privacy bounds. On three public education datasets (EdNet, ASSISTments, and OULAD) with institution-level partitions, BAF–FedLLM improves next-action AUC by 4.2–7.1% over strong federated baselines while reducing expected calibration error by up to 28% and communication by 5× through adapter sparsity, under a typical privacy budget of ε≈1.7 at δ=10−5. These results indicate that behavior-aware prompting and prototype alignment make LLMs practical for privacy-preserving student action analysis at scale, offering a principled path to deployable, regulation-compliant analytics across diverse learning ecosystems. Full article
(This article belongs to the Special Issue Mathematical Foundations and Optimization Techniques for Large Language Models)
►▼ Show Figures

Figure 1

34 pages, 7105 KB  
Article
A Safety and Security-Centered Evaluation Framework for Large Language Models via Multi-Model Judgment
by Jinxin Zhang, Yunhao Xia, Hong Zhong, Weichen Lu, Qingwei Deng and Changsheng Wan
Mathematics 2026, 14(1), 90; https://doi.org/10.3390/math14010090 - 26 Dec 2025
Viewed by 1308
Abstract
The pervasive deployment of large language models (LLMs) has given rise to mounting concerns regarding the safety and security of the content generated by these models. Nevertheless, the absence of comprehensive evaluation methods constitutes a substantial obstacle to the effective assessment and enhancement [...] Read more.
The pervasive deployment of large language models (LLMs) has given rise to mounting concerns regarding the safety and security of the content generated by these models. Nevertheless, the absence of comprehensive evaluation methods constitutes a substantial obstacle to the effective assessment and enhancement of the safety and security of LLMs. In this paper, we develop the Safety and Security (S&S) Benchmark, integrating multi-source data to ensure comprehensive evaluation. The benchmark comprises 44,872 questions covering ten major risk categories and 76 fine-grained risk points, including high-risk dimensions such as malicious content generation and jailbreak attacks. In addition, this paper introduces an automated evaluation framework based on multi-model judgment. Experimental results demonstrate that this mechanism significantly improves both accuracy and reliability: compared with single-model judgment (GPT-4o, 0.973 accuracy), the proposed multi-model framework achieves 0.986 accuracy while maintaining a similar evaluation time (~1 h) and exhibits strong consistency with expert annotations. Furthermore, adversarial robustness experiments show that our synthesized attack data effectively increases the attack success rate across multiple LLMs, such as from 14.76% to 27.60% on GPT-4o and from 18.24% to 30.35% on Qwen-2.5-7B-Instruct, indicating improved sensitivity to security risks. The proposed unified scoring metric system enables comprehensive model comparison; summarized ranking results show that GPT-4o achieves consistently high scores across ten safety and security dimensions (e.g., 96.26 in ELR, 97.63 in PSI), while competitive open-source models such as Qwen2.5-72B-Instruct and DeepSeek-V3 also achieve strong performance (e.g., 96.70 and 97.63 in PSI, respectively). Although all models demonstrate strong alignment in the safety dimension, they exhibit pronounced weaknesses in security—particularly against jailbreak and adversarial attacks—highlighting critical vulnerabilities and providing actionable direction for future model hardening. This work provides a comprehensive, scalable solution and high-quality data support for automated evaluation of LLMs. Full article
(This article belongs to the Special Issue Mathematical Foundations and Optimization Techniques for Large Language Models)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-2
Back to TopTop