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  1. Article ; Online: Theory of deep convolutional neural networks: Downsampling.

    Zhou, Ding-Xuan

    Neural networks : the official journal of the International Neural Network Society

    2020  Volume 124, Page(s) 319–327

    Abstract: Establishing a solid theoretical foundation for structured deep neural networks is greatly desired due to the successful applications of deep learning in various practical domains. This paper aims at an approximation theory of deep convolutional neural ... ...

    Abstract Establishing a solid theoretical foundation for structured deep neural networks is greatly desired due to the successful applications of deep learning in various practical domains. This paper aims at an approximation theory of deep convolutional neural networks whose structures are induced by convolutions. To overcome the difficulty in theoretical analysis of the networks with linearly increasing widths arising from convolutions, we introduce a downsampling operator to reduce the widths. We prove that the downsampled deep convolutional neural networks can be used to approximate ridge functions nicely, which hints some advantages of these structured networks in terms of approximation or modeling. We also prove that the output of any multi-layer fully-connected neural network can be realized by that of a downsampled deep convolutional neural network with free parameters of the same order, which shows that in general, the approximation ability of deep convolutional neural networks is at least as good as that of fully-connected networks. Finally, a theorem for approximating functions on Riemannian manifolds is presented, which demonstrates that deep convolutional neural networks can be used to learn manifold features of data.
    MeSH term(s) Deep Learning
    Language English
    Publishing date 2020-01-25
    Publishing country United States
    Document type Journal Article
    ZDB-ID 740542-x
    ISSN 1879-2782 ; 0893-6080
    ISSN (online) 1879-2782
    ISSN 0893-6080
    DOI 10.1016/j.neunet.2020.01.018
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    In stock of ZB MED Cologne/Königswinter

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  2. Book ; Online: Nonparametric regression using over-parameterized shallow ReLU neural networks

    Yang, Yunfei / Zhou, Ding-Xuan

    2023  

    Abstract: It is shown that over-parameterized neural networks can achieve minimax optimal rates of convergence (up to logarithmic factors) for learning functions from certain smooth function classes, if the weights are suitably constrained or regularized. ... ...

    Abstract It is shown that over-parameterized neural networks can achieve minimax optimal rates of convergence (up to logarithmic factors) for learning functions from certain smooth function classes, if the weights are suitably constrained or regularized. Specifically, we consider the nonparametric regression of estimating an unknown $d$-variate function by using shallow ReLU neural networks. It is assumed that the regression function is from the H\"older space with smoothness $\alpha<(d+3)/2$ or a variation space corresponding to shallow neural networks, which can be viewed as an infinitely wide neural network. In this setting, we prove that least squares estimators based on shallow neural networks with certain norm constraints on the weights are minimax optimal, if the network width is sufficiently large. As a byproduct, we derive a new size-independent bound for the local Rademacher complexity of shallow ReLU neural networks, which may be of independent interest.
    Keywords Statistics - Machine Learning ; Computer Science - Machine Learning ; Mathematics - Statistics Theory
    Subject code 519
    Publishing date 2023-06-14
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  3. Book ; Online: Optimal rates of approximation by shallow ReLU$^k$ neural networks and applications to nonparametric regression

    Yang, Yunfei / Zhou, Ding-Xuan

    2023  

    Abstract: We study the approximation capacity of some variation spaces corresponding to shallow ReLU$^k$ neural networks. It is shown that sufficiently smooth functions are contained in these spaces with finite variation norms. For functions with less smoothness, ... ...

    Abstract We study the approximation capacity of some variation spaces corresponding to shallow ReLU$^k$ neural networks. It is shown that sufficiently smooth functions are contained in these spaces with finite variation norms. For functions with less smoothness, the approximation rates in terms of the variation norm are established. Using these results, we are able to prove the optimal approximation rates in terms of the number of neurons for shallow ReLU$^k$ neural networks. It is also shown how these results can be used to derive approximation bounds for deep neural networks and convolutional neural networks (CNNs). As applications, we study convergence rates for nonparametric regression using three ReLU neural network models: shallow neural network, over-parameterized neural network, and CNN. In particular, we show that shallow neural networks can achieve the minimax optimal rates for learning H\"older functions, which complements recent results for deep neural networks. It is also proven that over-parameterized (deep or shallow) neural networks can achieve nearly optimal rates for nonparametric regression.

    Comment: Version 3 improves some approximation bounds by using recent results from arXiv:2307.15285
    Keywords Statistics - Machine Learning ; Computer Science - Machine Learning
    Subject code 006
    Publishing date 2023-04-04
    Publishing country us
    Document type Book ; Online
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  4. Article ; Online: Generalization Analysis of CNNs for Classification on Spheres.

    Feng, Han / Huang, Shuo / Zhou, Ding-Xuan

    IEEE transactions on neural networks and learning systems

    2023  Volume 34, Issue 9, Page(s) 6200–6213

    Abstract: Deep learning based on deep convolutional neural networks (CNNs) is extremely efficient in solving classification problems in speech recognition, computer vision, and many other fields. But there is no enough theoretical understanding about this topic, ... ...

    Abstract Deep learning based on deep convolutional neural networks (CNNs) is extremely efficient in solving classification problems in speech recognition, computer vision, and many other fields. But there is no enough theoretical understanding about this topic, especially the generalization ability of the induced CNN algorithms. In this article, we develop some generalization analysis of a deep CNN algorithm for binary classification with data on spheres. An essential property of the classification problem is the lack of continuity or high smoothness of the target function associated with a convex loss function such as the hinge loss. This motivates us to consider the approximation of functions in the L
    Language English
    Publishing date 2023-09-01
    Publishing country United States
    Document type Journal Article
    ISSN 2162-2388
    ISSN (online) 2162-2388
    DOI 10.1109/TNNLS.2021.3134675
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  5. Article ; Online: Probing nanomechanical interactions of SARS-CoV-2 variants Omicron and XBB with common surfaces.

    Xiao, Yuelong / Zheng, Bin / Ding, Xuan / Zheng, Peng

    Chemical communications (Cambridge, England)

    2023  Volume 59, Issue 75, Page(s) 11268–11271

    Abstract: The emergence of SARS-CoV-2 variants has further raised concerns about viral transmission. A fundamental understanding of the intermolecular interactions between the coronavirus and different surfaces is needed to address the transmission of SARS-CoV-2 ... ...

    Abstract The emergence of SARS-CoV-2 variants has further raised concerns about viral transmission. A fundamental understanding of the intermolecular interactions between the coronavirus and different surfaces is needed to address the transmission of SARS-CoV-2 through respiratory droplet-contaminated surfaces or fomites. The receptor-binding domain (RBD) of the spike protein is a key target for the adhesion of SARS-CoV-2 on the surface. To understand the effect of mutations on adhesion, atomic force microscopy-based single-molecule force spectroscopy (AFM-SMFS) was used to quantify the interactions between wild-type, Omicron, and XBB with several surfaces. The measurement revealed that RBD exhibits relatively higher forces on paper and gold surfaces, with the average force being 1.5 times greater compared to that on plastic surface. In addition, the force elevation on paper and gold surfaces for the variants can reach ∼28% relative to the wild type. These findings enhance our understanding of the nanomechanical interactions of the virus on common surfaces.
    MeSH term(s) Humans ; COVID-19 ; SARS-CoV-2/genetics ; Gold ; Microscopy, Atomic Force
    Chemical Substances Gold (7440-57-5)
    Language English
    Publishing date 2023-09-19
    Publishing country England
    Document type Journal Article
    ZDB-ID 1472881-3
    ISSN 1364-548X ; 1359-7345 ; 0009-241X
    ISSN (online) 1364-548X
    ISSN 1359-7345 ; 0009-241X
    DOI 10.1039/d3cc02721j
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  6. Article: Corneal Sub-Basal Nerve Plexus Regeneration Pattern following Implantable Collamer Lens Implantation for Myopia: A Prospective Longitudinal In Vivo Confocal Microscopy Study.

    Wei, Qiaoling / Ding, Xuan / Chang, Weiteng / Zhou, Xianjin / Jiang, Rui / Zhou, Xingtao / Yu, Zhiqiang

    Biomedicines

    2024  Volume 12, Issue 3

    Abstract: Implantable Collamer Lens (ICL) surgery has increasingly been adopted for myopia correction in recent decades. This study, employing in vivo confocal microscopy (IVCM), aimed to assess the impact of corneal incision during ICL surgery on the corneal sub- ... ...

    Abstract Implantable Collamer Lens (ICL) surgery has increasingly been adopted for myopia correction in recent decades. This study, employing in vivo confocal microscopy (IVCM), aimed to assess the impact of corneal incision during ICL surgery on the corneal sub-basal nerve plexus (SNP) and adjacent immune dendritiform cells (DCs). In this longitudinal study, eyes from 53 patients undergoing ICL surgery were assessed preoperatively and postoperatively over a twelve-month period. Quantification of seven SNP parameters was performed using ACCMetrics V.2 software. Ultimately, the final analysis was restricted to one eye from each of the 37 patients who completed a minimum of three months' postoperative follow-up. Preoperative investigations revealed a positive correlation of DC density with patient age and a negative association with corneal nerve fiber density (CNFD). Additionally, both DCs and CNFD were positively linked to spherical equivalent refraction (SER) and inversely related to axial length (AL). Intriguingly, preoperative DC density demonstrated an indirect relationship with both baseline and postoperative CNFD changes. Post-surgery, an initial surge in DC density was observed, which normalized subsequently. Meanwhile, parameters like CNFD, corneal nerve fiber length (CNFL), and corneal nerve fractal dimension (CNFrD) initially showed a decline following surgery. However, at one-year follow-up, CNFL and CNFrD displayed significant recovery, while CNFD did not return to its baseline level. This study thus delineates the regeneration pattern of SNP and alterations in DC density post-ICL surgery, highlighting that CNFD in the central cornea does not completely revert to preoperative levels within a year. Given these findings, practitioners are advised to exercise caution in older patients, those with high myopia, or elevated preoperative DCs who may undergo delayed SNP regeneration.
    Language English
    Publishing date 2024-03-01
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2720867-9
    ISSN 2227-9059
    ISSN 2227-9059
    DOI 10.3390/biomedicines12030555
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  7. Article ; Online: Literacy and attitude of Asian youths on dengue and its prevention in an endemic developed community.

    Soo, Wern Fern / Gunasekaran, Kalaipriya / Ng, Ding Xuan / Kwek, Kylie / Tan, Ngiap Chuan

    Frontiers in public health

    2024  Volume 12, Page(s) 1361717

    Abstract: Background: Over the past few decades, the incidence of dengue fever has considerably increased. Effective vector control strategies and specific protection using dengue vaccine are thought to be the key elements to combat dengue. The dengue incidence ... ...

    Abstract Background: Over the past few decades, the incidence of dengue fever has considerably increased. Effective vector control strategies and specific protection using dengue vaccine are thought to be the key elements to combat dengue. The dengue incidence among the Singapore youths (15-24 years) was second only to that of adults (25-44 years). This study evaluated the knowledge and attitude of Singapore youths on dengue and its preventive measures.
    Methods: A cross-sectional study using online-based questionnaire survey was conducted among Singapore youths from September to November 2022. Data were analyzed for descriptive statistics whereas Chi-squared test, linear regression analysis and Pearson correlation were used to determine the association between demographic factors and youth's attitude on dengue prevention using Rstudio.
    Results: A total of 624 respondents completed the survey out of 1822 surveys distributed nation-wide, with a response rate of 34.2% (mean age 17.4 years
    Conclusion: The overall knowledge of the youths on dengue and its prevention was satisfactory. Future health promotion campaigns targeting the youths should focus on transforming the knowledge into practice.
    MeSH term(s) Young Adult ; Humans ; Adolescent ; Female ; Male ; Literacy ; Cross-Sectional Studies ; Dengue/epidemiology ; Dengue/prevention & control ; Surveys and Questionnaires ; Regression Analysis
    Language English
    Publishing date 2024-03-08
    Publishing country Switzerland
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 2711781-9
    ISSN 2296-2565 ; 2296-2565
    ISSN (online) 2296-2565
    ISSN 2296-2565
    DOI 10.3389/fpubh.2024.1361717
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  8. Article ; Online: Effect of different iron ratios on interaction and thermodynamic stability of bound whey protein isolate.

    Ding, Xuan / Liu, Yujia / Zheng, Liyuan / Chang, Qiushuo / Chen, Xing / Xi, Chunyu

    Food research international (Ottawa, Ont.)

    2024  Volume 182, Page(s) 114198

    Abstract: Whey protein isolates (WPI) are known to have mineral-binding capacity to promote iron absorption. The aim of this study was to investigate the effect of iron ratio on the conformational structure of iron-bound whey protein isolate (WPI-Fe) and its ... ...

    Abstract Whey protein isolates (WPI) are known to have mineral-binding capacity to promote iron absorption. The aim of this study was to investigate the effect of iron ratio on the conformational structure of iron-bound whey protein isolate (WPI-Fe) and its thermodynamic stability. It was shown that the iron to protein ratio affects both the iron binding capacity of WPI and the iron valence state on the surface of WPI-Fe complexes. As the iron content increases, aggregation between protein molecules occurs. In addition, WPI-Fe nanoparticles have thermodynamic stability and Fe
    MeSH term(s) Whey Proteins/chemistry ; Iron ; Nanoparticles ; Thermodynamics
    Chemical Substances Whey Proteins ; Iron (E1UOL152H7)
    Language English
    Publishing date 2024-03-05
    Publishing country Canada
    Document type Journal Article
    ZDB-ID 1111695-x
    ISSN 1873-7145 ; 0963-9969
    ISSN (online) 1873-7145
    ISSN 0963-9969
    DOI 10.1016/j.foodres.2024.114198
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    In stock of ZB MED Bonn / Germany

    Z 2972: Show issues

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  9. Article ; Online: Low-Electronegativity Cationic High-Entropy Doping to Trigger Stable Anion Redox Activity for High-Ni Co-Free Layered Cathodes in Li-Ion Batteries.

    Liang, Pengrui / Qi, Kaiwen / Chen, Shiyuan / Ding, Xuan / Wu, Xiaojun / Wu, Changzheng / Zhu, Yongchun

    Angewandte Chemie (International ed. in English)

    2024  Volume 63, Issue 10, Page(s) e202318186

    Abstract: ... ...

    Abstract LiNi
    Language English
    Publishing date 2024-01-22
    Publishing country Germany
    Document type Journal Article
    ZDB-ID 2011836-3
    ISSN 1521-3773 ; 1433-7851
    ISSN (online) 1521-3773
    ISSN 1433-7851
    DOI 10.1002/anie.202318186
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  10. Article ; Online: Generalization Analysis of Pairwise Learning for Ranking With Deep Neural Networks.

    Huang, Shuo / Zhou, Junyu / Feng, Han / Zhou, Ding-Xuan

    Neural computation

    2023  Volume 35, Issue 6, Page(s) 1135–1158

    Abstract: Pairwise learning is widely employed in ranking, similarity and metric learning, area under the ROC curve (AUC) maximization, and many other learning tasks involving sample pairs. Pairwise learning with deep neural networks was considered for ranking, ... ...

    Abstract Pairwise learning is widely employed in ranking, similarity and metric learning, area under the ROC curve (AUC) maximization, and many other learning tasks involving sample pairs. Pairwise learning with deep neural networks was considered for ranking, but enough theoretical understanding about this topic is lacking. In this letter, we apply symmetric deep neural networks to pairwise learning for ranking with a hinge loss ϕh and carry out generalization analysis for this algorithm. A key step in our analysis is to characterize a function that minimizes the risk. This motivates us to first find the minimizer of ϕh-risk and then design our two-part deep neural networks with shared weights, which induces the antisymmetric property of the networks. We present convergence rates of the approximation error in terms of function smoothness and a noise condition and give an excess generalization error bound by means of properties of the hypothesis space generated by deep neural networks. Our analysis is based on tools from U-statistics and approximation theory.
    Language English
    Publishing date 2023-04-10
    Publishing country United States
    Document type Journal Article
    ZDB-ID 1025692-1
    ISSN 1530-888X ; 0899-7667
    ISSN (online) 1530-888X
    ISSN 0899-7667
    DOI 10.1162/neco_a_01585
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