People

Title

Assistant Professor

Degree

PhD Applied Mathematics, Princeton University, USA
BA Mathematics, University of Cambridge, UK

Research Interests

Deep Learning Theory and Applications, Optimization Methods for Machine Learning, Applied Dynamical Systems, Numerical Analysis, Scientific Computing

Office Location

S17, #07-23, 10 Lower Kent Ridge Rd, National University of Singapore

Biography

Qianxiao Li is an assistant professor (NUS presidential young professor) in the Department of Mathematics, National University of Singapore. He graduated with a BA in mathematics from University of Cambridge and a PhD in applied mathematics from Princeton University. His research interests include the interplay of machine learning and dynamical systems, stochastic gradient algorithms and the application of data-driven methods to scientific problems. He is a recipient of the NRF fellowship, class of 2021.

Selected Publications

• Z. Li, J. Han, W. E, and Q. Li, “Approximation and Optimization Theory for Linear Continuous-Time Recurrent Neural Networks,” Journal of Machine Learning Research, vol. 23, no. 42, pp. 1–85, 2022.
• H. Yu, X. Tian, W. E, and Q. Li, “OnsagerNet: Learning stable and interpretable dynamics using a generalized Onsager principle,” Phys. Rev. Fluids, vol. 6, no. 11, p. 114402, Nov. 2021.
• Z. Li, H. Jiang, and Q. Li, “On the approximation properties of recurrent encoder-decoder architectures,” International Conference on Learning Representations, Sep. 2021.
• H. Jiang, Z. Li, and Q. Li, “Approximation Theory of Convolutional Architectures for Time Series Modelling,” in Proceedings of the 38th International Conference on Machine Learning, Jul. 2021, pp. 4961–4970.
• Z. Li, J. Han, W. E, and Q. Li, “On the Curse of Memory in Recurrent Neural Networks: Approximation and Optimization Analysis,” International Conference on Learning Representations, Sep. 2020.
• Q. Li, C. Tai, and W. E, “Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations,” Journal of Machine Learning Research, vol. 20, no. 40, pp. 1–47, 2019.
• Q. Li and S. Hao, “An Optimal Control Approach to Deep Learning and Applications to Discrete-Weight Neural Networks,” in Proceedings of the 35th international conference on machine learning, 2018, vol. 80, pp. 2985–2994.
• Q. Li, C. Tai, and W. E, “Stochastic Modified Equations and Adaptive Stochastic Gradient Algorithms,” in Proceedings of the 34th International Conference on Machine Learning, Jul. 2017, pp. 2101–2110.
• Q. Li, F. Dietrich, E. M. Bollt, and I. G. Kevrekidis, “Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 27, no. 10, p. 103111, 2017.
• Q. Li, L. Chen, C. Tai, and W. E, “Maximum principle based algorithms for deep learning,” The Journal of Machine Learning Research, vol. 18, no. 1, pp. 5998–6026, 2017.