• 2018-2022：香港城市大学 博士（全日制）
• 2013-2017：山东大学 学士（全日制）

工作经历：

• 2026-至今：深圳河套学院 研究助理教授
• 2023-2026：阿卜杜拉国王科技大学 博士后
• 2022-2023：克莱蒙特研究大学 博士后
• 2017-2018：香港城市大学 助理研究员

我的研究方向主要位于近似理论、调和分析与机器学习数学基础的交叉领域。主要工作是将神经网络视为非线性逼近方法，研究网络结构（如卷积结构、激活函数正则性、参数化方式及线性化特征表示）对模型表达能力、逼近精度和稳定性的影响。目标是建立刻画现代神经网络行为的数学理论，并连接函数逼近、算子理论与数值分析，为深度学习模型设计和科学计算提供理论依据。招生方向面向具有良好数学基础、对深度学习理论研究具有浓厚兴趣，并希望以学术研究为职业发展方向的学生。

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