Xiuyuan Cheng


Assistant Professor of Mathematics

As an applied analyst, I develop theoretical and computational techniques to solve problems in high-dimensional statistics, signal processing and machine learning.

Appointments and Affiliations

  • Assistant Professor of Mathematics

Contact Information

  • Office Location: 120 Science Drive, 293 Physics Building, Durham, NC 27708
  • Email Address: xiuyuan.cheng@duke.edu
  • Websites:


  • Ph.D. Princeton University, 2013

Research Interests

Theory and computation of spectral methods, geometrical data analysis, high dimensional statistics, mathematical analysis of deep neural networks.

Courses Taught

  • K_MATH 302: Numerical Analysis
  • K_MATH 405: Mathematics of Data Analysis and Machine Learning
  • MATH 393: Research Independent Study
  • MATH 493: Research Independent Study
  • MATH 532: Basic Analysis II
  • MATH 561: Numerical Linear Algebra, Optimization and Monte Carlo Simulation
  • MATH 790-90: Minicourse in Advanced Topics

Representative Publications

  • Cheng, X; Cloninger, A; Coifman, RR, Two-sample statistics based on anisotropic kernels, Information and Inference (2019) [10.1093/imaiai/iaz018] [abs].
  • Cheng, X; Qiu, Q; Calderbank, R; Sapiro, G, RotDCF: Decomposition of convolutional filters for rotation-equivariant deep networks (2019) [abs].
  • Cheng, X; Rachh, M; Steinerberger, S, On the diffusion geometry of graph Laplacians and applications, Applied and Computational Harmonic Analysis, vol 46 no. 3 (2019), pp. 674-688 [10.1016/j.acha.2018.04.001] [abs].
  • Yan, B; Sarkar, P; Cheng, X, Provable estimation of the number of blocks in block models, Proceedings of the Twenty First International Conference on Artificial Intelligence and Statistics (Aistats'18), vol 84 (2018), pp. 1185-1194 [abs].
  • Cheng, X; Mishne, G; Steinerberger, S, The geometry of nodal sets and outlier detection, Journal of Number Theory, vol 185 (2018), pp. 48-64 [10.1016/j.jnt.2017.09.021] [abs].