• 2022-2026: City University of Hong Kong, Ph.D. Degree (Full-time)
• 2013-2017: Shandong University, Bachelor’s Degree (Full-time)

工作经历：

• 2026-Present: Shenzhen Loop Area Institute, Research Assistant Professor
• 2023-2026: King Abdullah University of Science and Technology, Postdoctoral Researcher
• 2022-2023: Claremont Graduate University, Postdoctoral Researcher
• 2017-2018: City University of Hong Kong, Research Assistant

My research lies at the intersection of approximation theory, harmonic analysis, and the mathematical foundations of machine learning. I study neural networks from the perspective of nonlinear approximation theory, focusing on how architectural structures—including convolutional architectures, activation regularity, parameterization strategies, and linearized feature representations—govern their expressive power, approximation accuracy, and stability. The overarching goal of my research is to develop rigorous mathematical frameworks for understanding the behavior of modern neural networks and to establish connections with functional approximation, operator theory, and numerical analysis. These theoretical developments aim to provide principled guidance for the design of deep learning models and learning-based methods in scientific computing.

I welcome students with a strong mathematical background, a deep interest in the theoretical foundations of deep learning, and a long-term ambition to pursue an academic research career.

1. X. Liu, T. Mao*, J. Xu. Integral Representations of Sobolev Spaces via ReLUk Activation Function and Optimal Error Estimates for Linearized Networks. Mathematics of Computation, accepted.”
2. T. Mao, J. W. Siegel*, J. Xu. Approximation Rates for Shallow ReLUk Neural Networks on Sobolev Spaces via the Radon Transform. SIAM Journal on Mathematical Analysis, 58(2):1171–1186, 2026.
3. T. Mao, D.-X. Zhou*. Rates of Approximation by ReLU Shallow Neural Networks. Journal of Complexity, 79:101784, 2023.
4. T. Mao, Z. Shi, D.-X. Zhou*. Theory of Deep Convolutional Neural Networks III: Approximating Radial Functions. Neural Networks, 144:778–790, 2021.
5. T. Mao, Z. Shi, D.-X. Zhou*. Approximating Functions with Multi-Features by Deep Convolutional Neural Networks. Analysis and Applications, 21(1):93–125, 2023.
6. X. Liu, T. Mao*, J. Xu. Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples. preprint, arXiv: 2608.06687
7. X. Liu, T. Mao*, J. Xu. Condition Numbers and Eigenvalue Spectra of Shallow Networks on Spheres. preprint, arXiv:2511.02625, 2025.
8. T. Mao, D.-X. Zhou*. Approximation of Functions from Korobov Spaces by Deep Convolutional Neural Networks. Advances in Computational Mathematics, 48:84, 2022.
9. T. Mao, J. Xu, X. Xu*. Solving High-Dimensional PDEs Using Linearized Neural Networks. preprint, arXiv:2601.11771, 2026.
10. T. Mao*, J. Xu. Sharp Lower Bounds for Linearized ReLUk Approximation on the Sphere. preprint, arXiv:2510.04060, 2025.
11. T. Mao*, J. Xu. Do Neural Networks Really Beat the Curse of Dimensionality? A Bit-Complexity View. preprint arXiv:2608.01357
12. J. Li*, T. Mao, J. Xu. Sharp Sobolev Approximation on General Domains by Linearized Shallow Networks with Analytic Activations. preprint arXiv:2608.18520