• 许志钦

    Zhiqin John Xu  

    Curriculum Vitae

    Research Areas

    Publication List



    Contact:

    Courant Institute
    New York University
    251 Mercer Street
    New York, NY 10012-1185


    Email:

    zhiqinxu at nyu dot edu

    I am currently a Visiting Member in the Courant Institute of Mathematical Sciences at New York University and a Postdoc Associate at New York University Abu Dhabi, working with Prof. David W. McLaughlin in mathematical and computational neuroscience. I obtained my B.S. in Physics (Zhiyuan College) and a Ph.D. degree in Mathematics from Shanghai Jiao Tong University in China under the supervision of Profs. David Cai and Douglas Zhou.

    My research interests lie in computational neuroscience, ranging from theoretical study and simulation to data analysis. I have collaborated actively with theoretical and experimental neuroscientists. Directly from experimental data, we have found a common dynamical state (Probability Polling state or p-polling state) underlying neuronal coding, which reveals a mechanism underlying the application of low order Maximum Entropy Principle (MEP) in neuronal networks. Our study on the effective interactions of the MEP model also shows how a sparse coupling structure can lead to a sparse coding scheme.

    My another interest is to study deep learning theoretically. Empirically, we found a Frequency Principle (F-Principle) that deep neural networks (DNNs) often capture target functions from low frequency to high frequency in order during the training. We then develop a theoretical framework by Fourier analysis to understand the F-Principle. In addition, our theory can understand when and how F-Principle can hold or fail. Our theory provides an understanding to why DNNs can have a large capacity to memorize randomly labeled dataset, but still, possess good generalization in real dataset.

    Education arrow right

    • 2016   Ph.D. in Mathematics, School of Mathematical Sciences, Shanghai Jiao Tong University, China.
    • 2012    B.S. in Physics (major) and Mathematics (minor), Zhiyuan College, Shanghai Jiao Tong University, China.

    Research Visitings arrow right

    • New York University Abu Dhabi, United Arab Emirates:
    •         Aug. 01-Sep. 01, 2013; Jan. 19-Feb. 19, 2014; Jan. 27-Feb. 27, 2015
    • Courant Institute, New York University, U.S.:
    •         Sep. 1st-Dec. 20th, 2015; Sep. 15th-Dec. 20th, 2016; Sep. 10th-Dec. 20th, 2017; Mar. 1st-Dec. 31st, 2018.

    Publications & Preprints arrow right

      Fourier analysis in Deep Learning
    • Z.-Q. J. Xu*, "Understanding training and generalization in deep learning by Fourier analysis", arXiv preprint: 1808.04295, (2018). [arXiv][CODE][Note: theoretical framework]
    • Z.-Q. J. Xu*, Y. Zhang, and Y. Xiao, "Training behavior of deep neural network in frequency domain", arXiv preprint: 1807.01251, (2018).[arXiv] [CODE][Note: F-Principle]
    • Computational Neuroscience
    • Z.-Q. J. Xu, Jennifer Crodelle, D. Zhou, and D. Cai, "Maximum Entropy Principle Analysis in Network Systems with Short-time Recordings", arXiv preprint:1808.10506, (2018). [.pdf][arXiv]
    • Z.-Q. J. Xu, D. Zhou, and D. Cai, "Dynamical and Coupling Structure of Pulse-Coupled Networks in Maximum Entropy Analysis", arXiv preprint:1808.04499, (2018). [.pdf][arXiv]
    • Z.-Q. J. Xu, G. Bi, D. Zhou, and D. Cai, "A dynamical state underlying the second order maximum entropy principle in neuronal networks", Communications in Mathematical Sciences, 15 (2017), pp. 665–692. [.pdf]
    • D. Zhou, Y. Xiao, Y. Zhang, Z. Xu, and D. Cai, "Granger causality network reconstruction of conductance-based integrate-and-fire neuronal systems", PloS one, 9 (2014) [.pdf]
    • D. Zhou, Y. Xiao, Y. Zhang, Z. Xu, and D. Cai, "Causal and structural connectivity of pulse-coupled nonlinear networks", Physical review letters, 111 (2013) [.pdf]
    • (∗ indicates the corresponding author)

    Teaching & Course information arrow right

    • Fall 2014 and Spring 2015 Recitation Instructor: Mathematical Analysis.
    • Spring 2014 Teaching Assistant: Probability.
    • Fall 2013 Teaching Assistant: Analysis.
    • Spring 2013 Teaching Assistant: Asymptotic Analysis.
    • Fall 2012 Teaching Assistant: Mathematical Physics.

    Selected Conferences & Talks arrow right

    • Sep 20, 2018 Clements Scientific Computing Seminar Series, Southern Methodist University.
    • Aug 7, 2018 In memory of David Cai, SIAM Conference on Life Sciences, Minneapolis, Minnesota.
    • Aug 3, 2018 Seminar, Zhejiang University.
    • Jun 12, 2018 INS Colloquia, Shanghai Jiao Tong University.
    • May 9, 2018 Data Science Seminar at NYU Shanghai.
    • May 7, 2018 Math-Neuroscience Seminar at NYU Shanghai.
    • Apr 17, 2018 Seminar at Rensselaer Polytechnic Institute.
    • Nov 28, 2017 Seminar at Rensselaer Polytechnic Institute.
    • Nov 11-15, 2017 Society for Neuroscience, Washington, DC.
    • Jun 26, 2017 Seminar at Wuhan University.
    • Jun 27, 2017 Seminar at Wuhan University.
    • Jun 16, 2017 Workshop on Data Analysis and Nonlinear Dynamic System at Shanghai Lixin University of Accounting and Finance.
    • Jun 7, 2017 Workshop on Data Assimilation and Information Theory at Fudan University.
    • May 25, 2017 SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah.
    • Feb 10, 2017 Colloquium at the University of North Carolina at Chapel Hill.
    • Nov 15, 2016 Seminar at Rensselaer Polytechnic Institute.
    • Nov 8, 2016 Colloquium at Courant Institute, New York University.
    • Aug 8-11, 2016 SIAM Conference on Nonlinear Waves and Coherent Structures, Philadelphia, Pennsylvania.
    • Nov 5, 2015 Seminar at Rensselaer Polytechnic Institute.
    • 2015 -- 2018 Organizer, The INS-ZY Student Workshop on Natural Sciences, Shanghai Jiao Tong University.

    Awards & Fellowships arrow right

    • 2012 Outstanding Graduate Award, At Shanghai Jiao Tong University.
    • 2011 President’s Award At Shanghai Jiao Tong University.
    • 2010 Meritourious Award in The Mathematical Contest in Modeling, 2010. With Di Qi and Qiu Yang.