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Mathematics
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Mathematical Foundations and New Advances in Deep Learning Applications
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Mathematical Foundations and New Advances in Deep Learning Applications

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

Deadline for manuscript submissions: 1 July 2026 | Viewed by 1951

Special Issue Editors

Dr. Chanjun Chun

E-Mail Website
Guest Editor
Department of Computer Engineering, Chosun University, Gwangju, Republic of Korea
Interests: artificial intelligence; deep learning; neural networks; machine learning; speech and audio signal processing
Dr. Geon Woo Lee

E-Mail Website
Guest Editor
School of Information and Communications, Chosun University, Gwangju, Republic of Korea
Interests: artificial intelligence; deep learning; neural networks; machine learning; speech and audio signal processing

Special Issue Information

Dear Colleagues,

The rapid advancement of deep learning has driven innovative applications across diverse domains such as speech processing, computer vision, and IoT technologies but has also brought attention to the underlying mathematical principles and algorithmic strategies that make these breakthroughs possible. Central to the success of deep learning is its foundation in advanced mathematical techniques, such as optimization algorithms, linear algebra, probability theory, and information theory, which allow for the automatic learning of complex representations from large-scale data. This Special Issue seeks to bridge the gap between applied deep learning and the mathematical models that underpin it, highlighting both theoretical contributions and practical applications.

Mathematical methods play a crucial role in speech processing in enhancing speech recognition, synthesis, and emotion detection by driving the design of robust models for noise suppression and feature extraction. Similarly, in computer vision and machine vision, algorithms rooted in mathematical formulations have revolutionized image and video analysis, enabling applications like facial recognition, object detection, and scene understanding. By focusing on the intersection of mathematics and algorithmic innovation, we aim to uncover new ways to optimize neural networks and improve computational efficiency, particularly in resource-constrained environments such as embedded systems and edge computing.

Integrating deep learning with natural language processing and IoT technologies has also opened new avenues for real-time decision making, anomaly detection, and smart automation. However, these advancements are underpinned by key mathematical challenges, including developing more interpretable models, improved optimization techniques, and efficient training algorithms. This Special Issue encourages submissions that focus on the mathematical and algorithmic aspects of deep learning, particularly those that explore novel architectures, transfer learning methods, and the theoretical foundations of model generalization and robustness.

We invite contributions that present innovative research on deep learning algorithms, emphasizing their mathematical underpinnings and real-world applications. By bringing together experts in mathematics, computer science, and engineering, this Special Issue aims to foster interdisciplinary collaboration and showcase how theoretical advances in mathematics can drive practical innovations in deep learning. The goal is to provide a platform for discussing how deep learning can address societal challenges while advancing the theory and application of intelligent systems.

Dr. Chanjun Chun
Dr. Geon Woo Lee
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

  • mathematical methods in deep learning for speech processing
  • algorithms for computer vision applications
  • machine vision and optimization for industrial automation
  • advances in natural language processing: models and algorithms
  • deep learning and mathematical modeling in IoT systems
  • real-time audio and video analysis through neural network algorithms
  • optimization in edge computing and intelligent IoT devices
  • mathematical techniques for sensor data analysis in smart environments
  • cross-disciplinary deep learning applications in healthcare, finance, and security
  • novel neural network architectures for multi-modal data processing
  • adaptive systems and machine learning: theoretical foundations
  • semantic analysis, knowledge representation, and algorithmic approaches
  • deep learning for smart cities and surveillance systems: algorithmic innovations
  • usability and user interaction optimization in AI-driven interfaces
  • evaluation frameworks and methodologies for deep learning-based systems
  • emerging trends in AI-driven automation: mathematical and algorithmic perspectives

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Published Papers (2 papers)

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Research

16 pages, 310 KB  
Article
A Regularized Backbone-Level Cross-Modal Interaction Framework for Stable Temporal Reasoning in Video-Language Models
by Geon-Woo Kim and Ho-Young Jung
Mathematics 2026, 14(6), 996; https://doi.org/10.3390/math14060996 - 15 Mar 2026
Viewed by 409
Abstract
Deep learning approaches for egocentric video understanding often lack a principled theoretical treatment of stability, particularly when dealing with the sparse, noisy, and temporally ambiguous observations characteristic of first-person imaging. In this work, we frame egocentric video question answering not merely as a [...] Read more.
Deep learning approaches for egocentric video understanding often lack a principled theoretical treatment of stability, particularly when dealing with the sparse, noisy, and temporally ambiguous observations characteristic of first-person imaging. In this work, we frame egocentric video question answering not merely as a classification task, but as an ill-posed inverse problem aimed at reconstructing latent semantic intent from stochastically perturbed visual signals. To address the instability inherent in standard dual-encoder architectures, we present a framework with a mathematical interpretation that incorporates gated cross-modal interaction within the transformer backbone. Formally, the video-side update analyzed in this work is defined as a learnable convex combination of unimodal feature representations and cross-modal attention residuals; the full implementation applies analogous gated cross-modal updates bidirectionally. From a regularization perspective, the gating mechanism can be interpreted as an adaptive parameter that balances data fidelity against language-conditioned structural constraints during feature reconstruction. We provide the Bounded Update Property (Lemma 1) and an analytical layer-wise sensitivity bound and empirically demonstrate that the proposed framework achieves measurable improvements in both accuracy and stability on the EgoTaskQA and MSR-VTT benchmarks. On EgoTaskQA, our model improves accuracy from 27.0% to 31.7% (+4.7 pp) and reduces the accuracy drop under 50% frame drop from 3.93 pp to 0.94 pp. On MSR-VTT, our model improves accuracy by 13.0 pp over the dual-encoder baseline. Under severe perturbation (50% frame drop) on MSR-VTT, our model retains 97.7% of its clean performance, whereas the baseline exhibits near-zero drop accompanied by majority-class behavior. These results provide empirical evidence that the proposed interaction induces stable behavior under perturbations in an ill-posed multimodal inference setting, mitigating sensitivity to sampling variability while preserving query-relevant temporal structure. Furthermore, an entropy-based analysis indicates that the gating mechanism prevents excessive diffusion of attention, promoting coherent temporal reasoning. Overall, this work offers a mathematically informed perspective on designing interaction mechanisms for stable multimodal systems, with a focus on robust reasoning under temporal ambiguity. Full article
(This article belongs to the Special Issue Mathematical Foundations and New Advances in Deep Learning Applications)
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23 pages, 3524 KB  
Article
A Diffusion Weighted Ensemble Framework for Robust Short-Horizon Global SST Forecasting from Multivariate GODAS Data
by Gwangun Yu, GilHan Choi, Moonseung Choi, Sun-hong Min and Yonggang Kim
Mathematics 2026, 14(4), 740; https://doi.org/10.3390/math14040740 - 22 Feb 2026
Viewed by 473
Abstract
Accurate time series forecasting of sea surface temperature (SST) is essential for understanding the ocean climate system and large-scale ocean circulation, yet it remains challenging due to regime-dependent variability and correlated errors across heterogeneous prediction models. This study addresses these challenges by formulating [...] Read more.
Accurate time series forecasting of sea surface temperature (SST) is essential for understanding the ocean climate system and large-scale ocean circulation, yet it remains challenging due to regime-dependent variability and correlated errors across heterogeneous prediction models. This study addresses these challenges by formulating SST ensemble time series forecasting aggregation as a stochastic, sample-adaptive weighting problem. We propose a diffusion-conditioned ensemble framework in which heterogeneous base forecasters generate out-of-sample SST predictions that are combined through a noise-conditioned weighting network. The proposed framework produces convex, sample-specific mixture weights without requiring iterative reverse-time sampling. The approach is evaluated on short-horizon global SST forecasting using the Global Ocean Data Assimilation System (GODAS) reanalysis as a representative multivariate dataset. Under a controlled experimental protocol with fixed input windows and one-step-ahead prediction, the proposed method is compared against individual deep learning forecasters and conventional global pooling strategies, including uniform averaging and validation-optimized convex weighting. The results show that adaptive, diffusion-weighted aggregation yields consistent improvements in error metrics over the best single-model baseline and static pooling rules, with more pronounced gains in several mid- to high-latitude regimes. These findings indicate that stochastic, condition-dependent weighting provides an effective and computationally practical framework for enhancing the robustness of multivariate time series forecasting, with direct applicability to global SST prediction from large-scale geophysical reanalysis data. Full article
(This article belongs to the Special Issue Mathematical Foundations and New Advances in Deep Learning Applications)
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