New York University

251 Mercer Street

New York, NY 10012-1185

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.

- 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.

- 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, 2017-Sep. 30th, 2019.

- Fourier analysis in Deep Learning [知乎上的科普] [Introduction on Quora]
- Zhi-Qin John Xu*,
*"Frequency Principle in Deep Learning with General Loss Functions and Its Potential Application"*, arXiv preprint, (2018). - Zhi-Qin John Xu*,
*"Understanding training and generalization in deep learning by Fourier analysis"*, arXiv preprint: 1808.04295, (2018). [arXiv][CODE][Note: theoretical framework] - Zhi-Qin John Xu*, Yaoyu Zhang, and Yanyang Xiao,
*"Training behavior of deep neural network in frequency domain"*, arXiv preprint: 1807.01251, (2018).[arXiv] [CODE][Note: F-Principle] (Submitted to IEEE transactions on neural networks and learning systems) - Computational Neuroscience
- Zhi-Qin John Xu et al.,
*"A Common Cortical State Underlying Neuronal Population Coding"*, (2018), in preparation - Zhi-Qin John Xu, Douglas Zhou, and David Cai,
*"Swift Two-sample Test on High-dimensional Neural Spiking Data"*, (2018), arXiv preprint - Zhi-Qin John Xu, Jennifer Crodelle, Douglas Zhou, and David Cai,
*"Maximum Entropy Principle Analysis in Network Systems with Short-time Recordings"*, arXiv preprint:1808.10506, (2018). [.pdf][arXiv] (Submitted to Physical Review E) - Zhi-Qin John Xu, Fang Xu, Guoqiang Bi, Douglas Zhou, David Cai,
*"A Cautionary Tale of Entropic Criteria in Assessing the Validity of Maximum Entropy Principle"*, (2018). (Submitted to Europhysics Letters) - Zhi-Qin John Xu, Douglas Zhou, and David Cai,
*"Dynamical and Coupling Structure of Pulse-Coupled Networks in Maximum Entropy Analysis"*, Entropy 2019, 21(1). - Zhi-Qin John Xu, Guoqiang Bi, Douglas Zhou, and David Cai,
*"A dynamical state underlying the second order maximum entropy principle in neuronal networks"*, Communications in Mathematical Sciences, 15 (2017), pp. 665–692. [.pdf] - Douglas Zhou, Yanyang Xiao, Yaoyu Zhang, Zhiqin Xu, and David Cai,
*"Granger causality network reconstruction of conductance-based integrate-and-fire neuronal systems"*, PloS one, 9 (2014) [.pdf] - Douglas Zhou, Yanyang Xiao, Yaoyu Zhang, Zhiqin Xu, and David Cai,
*"Causal and structural connectivity of pulse-coupled nonlinear networks"*, Physical review letters, 111 (2013) [.pdf] - (∗ indicates the corresponding author)

- 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.

- Nov 19, 2018
*Seminar at Center for Data Science, New York University* - Nov 13, 2018
*Seminar at Rensselaer Polytechnic Institute.* - Nov 3-7, 2018
*Poster, Society for Neuroscience, San Diego, CA.* - Oct 30, 2018
*Seminar at Purdue University.* - Oct 26, 2018
*Seminar at Illinois Institute of Technology.* - 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.*

- 2012 Outstanding Graduate Award, At Shanghai Jiao Tong University.
- 2011 President’s Award At Shanghai Jiao Tong University for organizing Zhiyuan Shuyuan (致远书院).
- 2010 Meritourious Award in The Mathematical Contest in Modeling, 2010. With Di Qi and Qiu Yang.