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 532: Basic Analysis II
  • MATH 790-90: Minicourse in Advanced Topics

Representative Publications

  • Zhao, J; Jaffe, A; Li, H; Lindenbaum, O; Sefik, E; Jackson, R; Cheng, X; Flavell, RA; Kluger, Y, Detection of differentially abundant cell subpopulations in scRNA-seq data., Proceedings of the National Academy of Sciences of the United States of America, vol 118 no. 22 (2021) [10.1073/pnas.2100293118] [abs].
  • Zhang, Y; Cheng, X; Reeves, G, Convergence of Gaussian-smoothed optimal transport distance with sub-gamma distributions and dependent samples, 24th International Conference on Artificial Intelligence and Statistics (Aistats), vol 130 (2021) [abs].
  • Li, Y; Cheng, X; Lu, J, Butterfly-net: Optimal function representation based on convolutional neural networks, Communications in Computational Physics, vol 28 no. 5 (2020), pp. 1838-1885 [10.4208/CICP.OA-2020-0214] [abs].
  • Mhaskar, HN; Cheng, X; Cloninger, A, A Witness Function Based Construction of Discriminative Models Using Hermite Polynomials, Frontiers in Applied Mathematics and Statistics, vol 6 (2020) [10.3389/fams.2020.00031] [abs].
  • Cheng, X; Miao, Z; Qiu, Q, Graph Convolution with Low-rank Learnable Local Filters (2020) [abs].