Deep Learning Generalization

[8] K. Chen^, C. Wang^, H. Yang^*.  Let Data Talk: Data-Regularized Operator Learning Theory for Inverse Problems. [pdf]

[7] H. Liu, H. Yang*, M. Chen, T. Zhao, W. Liao*. Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces. Journal of Machine Learning Research, 2024. [pdf] [doi]

[6] Y. Yang, H. Yang*. Y. Xiang. Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivatives. 37th Conference on Neural Information Processing Systems (NeurIPS 2023). [pdf] [doi]

[5] Y. Jiao^, Y. Lai^, Y. Wang^, H. Yang^, Y. Yang^*. Convergence Analysis of the Deep Galerkin Method for Weak Solutions. In Patricia Alonso Ruiz, Michael Hinz, Kasso A. Okoudjou, Luke G. Rogers, Alexander Teplyaev, From Classical Analysis to Analysis on Fractals, A Tribute to Robert Strichartz, Volume 1, 2023 [pdf] [doi]

[4] K. Chen^, C. Wang^, H. Yang^*. Deep Operator Learning Lessens the Curse of Dimensionality for PDEs. Transactions on Machine Learning Research, 2023. [pdf] [doi]

[3] Y. Gu^, J. Harlim^, S. Liang^*, H. Yang^, Stationary Density Estimation of Itô Diffusions Using Deep Learning. SIAM Journal on Numerical Analysis, 2022. [pdf] [doi]

[2] F. Liu, H. Yang, S. Hayou, Q. Li*,  . From Optimization Dynamics to Generalization Bounds via Łojasiewicz Gradient Inequality. Transactions on Machine Learning Research, 2022. [pdf] [doi]

[1] T. Luo^, H. Yang^*. Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory. Submitted. [pdf] 

^: Equal contribution; *: Corresponding author.