Publications

Ph.D. Dissertation:

Oscillatory Data Analysis and Fast Algorithms for Integral Operators, Stanford University, 2015. [pdf] 

Preprints:

[S16] K. Chen, C. Yi, H. Yang. Towards Better Generalization: Weight Decay Induces Low-rank Bias for Neural Networks. [pdf]

[S15] G. Hardwick^, S. Liang^, H. Yang*. Solving High-Dimensional Partial Integral Differential Equations: The Finite Expression Method. [pdf]

[S14] L. Liang^, C. Austin^, H. Yang*. Accelerating Multi-Block Constrained Optimization Through Learning to Optimize. [pdf]

[S13] L. Liang, H. Yang*. PNOD: An Efficient Projected Newton Framework for Exact Optimal Experimental Designs. [pdf]

[S12] A. Maiti^, M. Michelle^*, H. Yang^. Optimal Neural Network Approximation for High-Dimensional Continuous Functions. [pdf]

[S11] L. Liang*, Q. Pang, K. Toh, H. Yang. Vertex Exchange Method for a Class of Quadratic Programming Problems. [pdf]

[S10] L. Liang, Q. Pang, K. Toh, H. Yang*. Nesterov's Accelerated Jacobi-Type Methods for Large-scale Symmetric Positive Semidefinite Linear Systems. [pdf]

[S9] Z. Song^, J. Yuan^, H. Yang*. FMint: Bridging Human Designed and Data Pretrained Models for Differential Equation Foundation Model. [pdf]

[S8] J. Aftab*, H. Yang. Approximating Korobov Functions via Quantum Circuits. [pdf]

[S7] K. Chen^, C. Wang^, H. Yang^*.  Let Data Talk: Data-Regularized Operator Learning Theory for Inverse Problems. [pdf]

[S6] Y. Yang, Y. Wu, H. Yang*, Y. Xiang*. Nearly Optimal Approximation Rates for Deep Super ReLU Networks on Sobolev Spaces. Submitted. [pdf]

[S5] Z. Song, C. Wang, H. Yang. A Fast Algorithm for the Finite Expression Method in Learning Dynamics on Complex Networks. Submitted. [pdf]

[S4] Z. Jiang, C. Wang, H. Yang*. Finite Expression Methods for Discovering Physical Laws from Data. Submitted. [pdf]

[S3] Q. Pang, H. Yang*. Spectral Clustering via Orthogonalization-Free Methods. Submitted. [pdf]

[S2] W. Hao^, C. Wang^*, X. Xu^, H. Yang^. Deep Learning via Neural Energy Descent. Submitted. [pdf]

[S1] S. Liang^, H. Yang^*. Finite Expression Method for Solving High-Dimensional Partial Differential Equations. Submitted. [pdf]

Journal Publications:

2024

[70] L. Liang*, H. Yang. On the Stochastic (Variance-Reduced) Proximal Gradient Method for Regularized Expected Reward Optimization. Transaction on Machine Learning Research, 2024 [pdf] [doi]

[69] Z. Song, M. Cameron, H. Yang*. A Finite Expression Method for Solving High-Dimensional Committor Problems. SIAM Journal of Scientific Computing, 2024. [pdf]

[68] H. Jiang^*, Y. Khoo^, H. Yang^. Reinforced Inverse Scattering. SIAM Journal of Scientific Computing, 2024. [pdf] 

[67] S. Zheng, H. Yang, X. Zhang*. On the Convergence of Orthogonalization-Free Conjugate Gradient Method for Extreme Eigenvalues of Hermitian Matrices: a Riemannian Optimization Interpretation. Journal of Computational and Applied Mathematics, 2024. [pdf] [doi]

[66] S. Liang*, S. W. Jiang, J. Harlim, H. Yang, Solving PDEs on Unknown Manifolds with Machine Learning. Applied and Computational Harmonic Analysis, 2024. [pdf] [doi]

[65] S. Han, S. Su, S. He, S. Han, H. Yang, S. Zou, F. Miao*. What is the Solution for State-Adversarial Multi-Agent Reinforcement Learning? Transaction on Machine Learning Research, 2024 [pdf] [doi]

[64] 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]

[63] Q. Pang, H. Yang*, A Distributed Block Chebyshev-Davidson Algorithm for Parallel Spectral Clustering. Journal of Scientific Computing, 2024. [pdf] [doi]

[62] S. Liang^, L. Lyu^, C. Wang ^, H. Yang^*. Reproducing Activation Function for Deep Learning. Communication in Mathematical Sciences, 2024. [pdf] [doi]

[61] Y. Tu, Z. Xu*, H. Yang. Hierarchical Interpolative Factorization for Self Green's Function in 3D Modified Poisson-Boltzmann Equations. Communications on Applied Mathematics and Computation, 2024. [pdf] [doi]

2023

[60] Z. Huang, S. Liang, H. Zhang, H. Yang, L. Lin*, On Fast Simulation of Dynamical System with Neural Vector Enhanced Numerical Solver. Scientific Report, 2023  [pdf] [doi]

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

[58] J. Xu, Y. Li, H. Yang*, D. Dunson, I. Daubechies, PiPs: a Kernel-based Optimization Scheme for Analyzing Non-Stationary 1D Signals. Applied and Computational Harmonic Analysis. [pdf] [doi]

[57] F. Chen^, J. Huang^, C. Wang ^, H. Yang^*. Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning. SIAM Journal of Scientific Computing, 2023. [pdf] [doi]

[56] Y. Gu^, J. Harlim^, S. Liang^*, H. Yang^. Stationary Density Estimation of Itô Diffusions Using Deep Learning. SIAM Journal on Numerical Analysis, 2023. [pdf] [doi]

2022

[55] 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]

[54] Y. Ong^, Z. Shen^, H. Yang^*. Integral Autoencoder Network for Discretization-Invariant Learning. Journal of Machine Learning Research, 2022.  [pdf] [doi]

[53] Z. Shen^, H. Yang^, S. Zhang^*. Deep Network Approximation:  Achieving Arbitrary Accuracy with  Fixed Number of Neurons. Journal of Machine Learning Research, 2022.  [pdf] [doi]

[52] S. Hon^*, H. Yang^. Simultaneous Neural Network Approximations for Smooth Functions. Neural Networks, 2022.  [pdf] [doi]

[51]  Q. Du^, Y. Gu^, H. Yang^*, C. Zhou^. The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation. SIAM Journal on Numerical Analysis. [pdf]  [doi]

[50] J. Hu^*, X. Huang^, J. Shen^, H. Yang^. A Fast Petrov-Galerkin Spectral Method for the Multi-Dimensional Boltzmann Equation Using Mapped Chebyshev Functions. SIAM Journal on Scientific Computing, 2022. [pdf] [doi]

[49] Y. Tu, Q. Pang, H. Yang*, Z. Xu. Linear-Scaling Selected Inversion based on Hierarchical Interpolative Factorization for Self Green's Function for Modified Poisson-Boltzmann Equation in Two Dimensions. Journal of Computational Physics, 2022. [pdf] [doi]

[48] Y. Ong, H. Yang*, Generative Imaging and Image Processing via Generative Encoder. Inverse Problems and Imaging, 2022 [pdf] [doi]

[47] Z. Shen^*, H. Yang^, S. Zhang^. Optimal Approximation Rate of ReLU Networks in terms of Width and Depth. Journal de Mathématiques Pures et Appliquées, 2022. [pdf] [doi]

2021

[46] J. Bremer^, Z. Chen^, H. Yang^*. Rapid Application of the Spherical Harmonic Transform via Interpolative Decomposition Butterfly Factorization. SIAM Journal on Scientific Computing, 2021. [pdf] [doi]

[45] L. Li, C. Goodrich, H. Yang, J. Zhong, K. R. Phillips, Z. Jia, H. Chen, L. Wang, J. Zhong, A. Liu, J. Lu, J. Shuai, M. P Brenner, F. Spaepen, J. Aizenberg. Microscopic Origins of the Crystallographically Preferred Growth in Evaporation-Induced Colloidal Crystals. Proceedings of the National Academy of Sciences of the United States of America (PNAS), 2021. [doi]

[44] J. Lu^, Z. Shen^, H. Yang^*, S. Zhang^. Deep Network Approximation for Smooth Functions. SIAM Journal on Mathematical Analysis, 2021. [pdf] [doi]

[43] Y. Gu, H. Yang*, C. Zhou. SelectNet: Self-Paced Learning for High-dimensional Partial Differential Equations. Journal of Computational Physics, 2021. [pdf] [doi]

[42] Z. Shen^, H. Yang^*, S. Zhang^. Neural Network Approximation: Three Hidden Layers Are Enough. Neural Networks, 2021. [pdf] [doi] 

[41] Y. Gu^, C. Wang ^, H. Yang^*. Structure Probing Neural Network Deflation. Journal of Computational Physics, 2021.  [pdf] [doi]

[40] Y. Li^, and H. Yang^*, Interior Eigensolver for Sparse Hermitian Definite Matrices Based on Zolotarevs Functions. Communication in Mathematical Sciences, 2021. [pdf] [doi]

[39] H. Montanelli, H. Yang*, Q. Du, Deep ReLU Networks Overcome the Curse of Dimensionality for Bandlimited Functions. Journal of Computational Mathematics, 2021. [pdf] [doi]

[38] J. Bremer^, Q. Pang^, H. Yang^*, Fast Algorithms for Multi-dimensional Jacobi Polynomial Transforms. Applied and Computational Harmonic Analysis, 2021. [pdf] [doi]

[37] H. Yang*, Multiresolution Mode Decomposition for Adaptive Time Series Analysis. Applied and Computational Harmonic Analysis, 2021. [pdf] [doi]

[36] Z. Shen^, H. Yang^*, S. Zhang^. Deep Network with Approximation Error Being Reciprocal of Width to Power of Square Root of Depth. Neural Computation, 2021. [pdf]  [doi]

[35] J. Harlim^*, S. W. Jiang^, S. Liang^, H. Yang^. Machine Learning for Prediction with Missing Dynamics. Journal of Computational Physics, 2021. [pdf] [doi]

2020

[34] Z. Shen^, H. Yang^*, S. Zhang^. Deep Network Approximation Characterized by Number of Neurons. Communications in Computational Physics, 2020. [pdf] [doi]

[33] J. Huang^, H. Wang^, H. Yang^*. Int-Deep: A Deep Learning Initialized Iterative Method for Nonlinear Problems. Journal of Computational Physics, 2020. [pdf] [doi]

[32] X. Zhu, H. Yang, Z. Zhang*, J. Gao, N. Liu. Frequency-Chirprate Reassignment. Digital Signal Processing, 2020. [pdf] [doi]

[31] S. Liang, Y. Kwoo, H. Yang*, Drop-Activation: Implicit Parameter Reduction and Harmonic Regularization. Communications on Applied Mathematics and Computation, 2020. [pdf] [doi]

[30] H. Montanelli^*, H. Yang^, Error Bounds for Deep ReLU Networks using the Kolmogorov--Arnold Superposition Theorem. Neural Networks, 2020. [pdf] [doi]

[29] Z. Chen, J. Zhang, K. Ho, H. Yang*, Multidimensional Phase Recovery and Interpolative Decomposition Butterfly Factorization. Journal of Computational Physics, 2020. [pdf] [doi]

[28] G. Tang, H. Yang*, A Fast Algorithm for Multiresolution Mode Decomposition. SIAM Multiscale Modeling and Simulation, 2020. [pdf] [doi]

[27] Q. Pang, K. Ho, H. Yang*, Interpolative Decomposition Butterfly Factorization. SIAM Journal of Scientific Computing, 2020. [pdf] [doi]

[26] Y. Liu^, H. Yang^*. A Hierarchical Butterfly LU Preconditioner for Two-Dimensional Electromagnetic Scattering Problems Involving Open Surfaces. Journal of Computational Physics, 2020. [pdf] [doi]

2019

[25] T. Zhang, L. Li, H. Yang*, 3D Crystal Image Analysis based on Fast Synchrosqueezed Transforms. Communication in Mathematical Sciences, 2019. [pdf] [doi]

[24] K. R. Phillips, C. T. Zhang, T. Yang, T. Kay, C. Gao, S. Brandt, L. Liu, H. Yang, Y. Li,  J. Aizenberg, L. Li*. Fabrication of Photonic Microbricks via Crack Engineering of Colloidal Crystals. Advanced Functional Materials, 2019. Frontispiece article. [doi]   

[23] Z. Shen^, H. Yang^*, S. Zhang^. Nonlinear Approximation via Compositions. Neural Networks, Volume 119, November 2019, Pages 74-84. [pdf] [doi]

[22] J. Bremer^*, H. Yang^, Fast Algorithms for Jacobi Expansions via Nonoscillatory Phase Functions. IMA Journal of Numerical Analysis, 2019.  [pdf] [doi]

[21] H. Yang*, A Unified Framework for Oscillatory Integral Transform: When to use NUFFT or Butterfly Factorization? Journal of Computational Physics, 2019. [pdf] [doi]

2018

[20] V. W-z Yu, F. Corsetti, A. García, W. P Huhn, M. Jacquelin, W. Jia, B. Lange, L. Lin, J. Lu, W. Mi, A. Seifitokaldani, Á. Vázquez-Mayagoitia, C. Yang, H. Yang, V. Blum*, ELSI: A Unified Software Interface for Kohn-Sham Electronic Structure Solvers. Computer Physics Communications, Volume 222, January 2018, Pages 267-285. [pdf] [doi]

[19] J. Lu^ and H. Yang^*, Phase Space Sketching for Crystal Image Analysis based on Synchrosqueezed Transforms.  SIAM Journal on Imaging Science, 11(3), 1954–1978, 2018. [pdf] [doi]

[18] J. Xu, H. Yang*, and I. Daubechies, Recursive Diffeomorphism-Based Regression for Shape Functions. SIAM Journal on Mathematical Analysis, 50(1), 5-32, 2018. [pdf] [doi]

[17] H. Yang*, Statistical Analysis of Synchrosqueezed Transforms, Applied and Computational Harmonic Analysis, 2018. Codes. [pdf] [doi]

2017

[16] J. Lu^, and H. Yang^*, A Cubic Scaling Algorithm to Calculate Excited States Based on Particle-Particle Random Phase Approximation,  Journal of Computational Physics, Volume 340, 1 July 2017, Pages 297-308. [pdf]  [doi]

[15] J. Harlim^* and H. Yang^, Diffusion Forecasting Model with Basis Functions from QR Decomposition. Journal of Nonlinear Science, 2017. [pdf] [doi]

[14] Y. Li^, and H. Yang^*,  Interpolative Butterfly Factorization, SIAM Journal on Scientific Computing, 2017. [pdf] [doi]

[13] Y. Li^, H. Yang^*, and L. Ying^, Multidimensional Butterfly Factorization, Applied and Computational Harmonic Analysis, 2017. [pdf] [doi]

2016

[12] J. Lu^, and H. Yang^*, Preconditioning Orbital Minimization Method for Planewave Discretization, SIAM Multiscale Modeling and Simulation, 2016. [pdf] [doi]

[11] B. Cornelis, H. Yang*, A. Goodfriend, N. Ocon, J. Lu, and I. Daubechies, Removal of Canvas Patterns in Digital Acquisitions of Paintings, IEEE Transactions on Image Processing, 2016. [pdf] [doi]

[10] J. Lu^, B. Wirth^, H. Yang^*, Combining 2D synchrosqueezed Wave Packet Transform with Optimization for Crystal Image Analysis, Journal of the Mechanics and Physics of Solids, 2016. [pdf] [doi]

2015 and forwards

[9] Y. Li, H. Yang, E. Martin, K. Ho and L. Ying*, Butterfly Factorization, SIAM Multiscale Modeling and Simulation, 2015. [pdf] [doi]

[8] Y. Li^, H. Yang^* and L. Ying^, A Multiscale Butterfly Algorithm for Multidimensional Fourier Integral Operators, SIAM Multiscale Modeling and Simulation, 2015. [pdf] [doi]

[7] H. Yang*, J. Lu and L. Ying, Crystal Image Analysis Using 2D Synchrosqueezed Transforms, SIAM Multiscale Modeling and Simulation, 2015. [pdf] [doi]

[6] H. Yang, J. Lu*, W. P. Brown, I. Daubechies, and L. Ying, Quantitative Canvas Weave Analysis Using 2D Synchrosqueezed Transforms, IEEE Signal Processing Magazine, 2015. [pdf] [doi]

[5] H. Yang*, Synchrosqueezed Wave Packet Transforms and Diffeomorphism Based Spectral Analysis for 1D General Mode Decompositions. Applied and Computational Harmonic Analysis, 2015. [pdf]  [doi]

[4] H. Yang^* and L. Ying^, Synchrosqueezed Curvelet Transform for 2D Mode Decomposition, SIAM Journal of Mathematical Analysis, 2014. [pdf] [doi]

[3] H. Yang^* and L. Ying^, Synchrosqueezed Wave Packet Transform for 2D Mode Decomposition, SIAM Journal on Imaging Science, 2013. [pdf] [doi]

[2] H. Yang^ and L. Ying^*, A Fast Algorithm for Multilinear Operators, Applied and Computational Harmonic Analysis, 2012. [pdf] [doi]

[1] Z. Xu*, X. Cheng and H. Yang, Treecode-based generalized Born method, Journal of Chemical Physics, 2011. [pdf] [doi]

Conference Proceedings:

2024

[C11] Z. Huang, S. Liang, M. Liang, H. Yang, L. Lin*.  The Lottery Ticket Hypothesis for Self-attention Networks in Computer Vision. IEEE Conference on Multimedia Expo 2024, Oral. [pdf]

[C10] D. Wu, Y. Jiao, L. Shen, H. Yang*, X. Lu*. Neural Network Approximation for Pessimistic Offline Reinforcement Learning. The 38th AAAI Conference on Artificial Intelligence (AAAI 2024). [pdf]

2023

[C9] 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]

[C8] S. Han, S. Su, S. He, S. Han, H. Yang, F. Miao*. What is the Solution for State-Adversarial Multi-Agent Reinforcement Learning? ICML Workshop on New Frontiers in Learning, Control, and Dynamical Systems, 2023 [pdf]

2022

[C7] Z. Shen^, H. Yang^, S. Zhang^*. Neural Network Architecture Beyond Width and Depth. 36th Conference on Neural Information Processing Systems (NeurIPS 2022).  [pdf] [doi]

[C6] Z. Shen^,  H. Yang^, S. Zhang^*. Deep Network Approximation in Terms of Intrinsic Parameters. The 39th International Conference on Machine Learning (ICML 2022), Spotlight. [pdf] [doi]

2021

[C5] W. He^, Z. Huang^, M. Liang, S. Liang, H. Yang*. Blending Pruning Criteria for Efficient Convolutional Neural Networks. 30th International Conference on Artificial Neural Networks, ICANN, 2021. [pdf] [doi]

2020

[C4] Y. Ong*, N. You, Y. E. Li, H. Yang. Digital Rock Image Inpainting using GANs. In 90-th Annual International Meeting, SEG, Expanded Abstracts, Houston, 2020. [pdf] [doi]

[C3] Y. Liu, T. Gao, H. Yang*, SelectNet: Learning to Sample from the Wild for Imbalanced Data Training. Mathematical and Scientific Machine Learning Conference 2020. [pdf] [doi]

[C2] S. Liang^, Z. Huang^, M. Liang, H. Yang*, Instance Enhancement Batch Normalization: an Adaptive Regulator of Batch Noise. Proceedings of the AAAI Conference on Artificial Intelligence, 2020. [pdf] [doi]

[C1] Z. Huang^, S. Liang^, M. Liang, H. Yang*, DIANet: Dense-and-Implicit Attention Network. Proceedings of the AAAI Conference on Artificial Intelligence, 2020. [pdf] [doi]

^: Equal contribution; *: Corresponding author.

Book Chapters:

2024

[B2] T. Luo^, H. Yang^*. Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory. In Siddhartha Mishra, Alex Townsend, Numerical Analysis meets Machine Learning (Handbook of Numerical Analysis, Volume 25), 1st Edition, 2024. [pdf] [doi]

2023

[B1] 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]

^: Equal contribution; *: Corresponding author.