Wenjing Liao  Associate Professor School of Mathematics Georgia Institute of Technology Office: Skiles 115 Email: wliao60@gatech.edu

My research interests are imaging, signal processing,  high dimensional data analysis and machine learning. I finished my Ph.D. in Mathematics under the supervision of Prof. Albert Fannjiang at University of California, Davis. I was a visiting assistant professor at Duke University and an assistant research scientist at Johns Hopkins University before joining Georgia Tech. I worked with Prof. Mauro Maggioni at Duke and JHU. My research is supported by NSF and DOE,  including NSF CAREER and DOE CAREER awards. Here is my CV.

My group has PhD and postdoc openings to start in Fall 2027.  Please send me an email if you are interested.

Teaching at Georgia Tech: 

• Math 3235 in Fall 2026
  
• Math4803 Data Science in Fall 2019: This course becomes Math 4210.
  

Research Workshop:

• 2025 Georgia Scientific Computing Symposium (GSCS), 2025
  
• IPAM on Sampling, Inference, and Data-Driven Physical Modeling in Scientific Machine Learning, July 14 -18, 2025
  

Student Workshop:

• Southeast Florida-Georgia Applied Computational Math Student Workshop: 2023 at FSU, 2024 at Georgia Tech, 2025 at Auburn Univ. 2026 at Emory Univ
• Data Science Bootcamp for undergraduates and high school students: 1st in Emory in 2025, 2nd at Georgia Tech in 2026
  

• Generalization Guarantees for Multi-Input Neural Operator Learning in Sobolev Spaces, arXiv, 2026.
  Yahong Yang, Zecheng Zhang, Wei Zhu, Wenjing Liao, Hao Liu
  
• Learning Theory of Transformers: Local-to-Global Approximation via Softmax Partition of Unity, arXiv, 2026.
  Zhongjie Shi, Wenjing Liao
• Understanding In-Context Learning for Nonlinear Regression with Transformers: Attention as Featurizer, arXiv, 2026.
  Alex Hsu, Zhaiming Shen, Wenjing Liao, Rongjie Lai
  

• Data-Driven Model Reduction Using WeldNet: Windowed Encoders for Learning Dynamics, arXiv, 2025.
  Biraj Dahal, Jiahui Cheng, Hao Liu, Rongjie Lai, Wenjing Liao
• Understanding In-Context Learning on Structured Manifolds: Bridging Attention to Kernel Methods, ICLR, 2026.
  Zhaiming Shen, Alex Hsu, Rongjie Lai, Wenjing Liao
• IDENT Review: Recent Advances in Identification of Differential Equations from Noisy Data, Handbook of Numerical Analysis, 2025.
  Roy He, Hao Liu, Wenjing Liao, Sung Ha Kang
  
• Identification of Differential Equations by Dynamics-Guided Weighted Weak From with Voting, accepted by Communication in Computational Physics, 2025.
  Jiahui Cheng, Sung Ha Kang, Haomin Zhou, Wenjing Liao
• Single-Shot Prediction of Parametric  Partial Differential Equations, arXiv, 2025.
  Khalid Rafiq, Wenjing Liao, Aditya G. Nair
  
• Transformers for Learning on Noisy and Task-Level Manifold: Approximation and Generalization Insights, arXiv, 2025.
  Zhaiming Shen, Alex Havrilla, Rongjie Lai, Alex Cloninger, Wenjing Liao
• Optimality of Gradient-MUSIC for Spectral Estimation, accepted by IMA Information and Inference.
  Albert Fannjiang, Weilin Li, Wenjing Liao
• Coefficient-to-Basis Network: A Fine-Tunable Operator Learning Framework for Inverse Problems with Adaptive Discretizations and Theoretical Guarantees, Philosophical Transactions A, 2025.
  Zecheng Zhang, Hao Liu, Wenjing Liao, Guang Lin

• Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study, revision in Journal of Machine Learning Research, 2024.
  Hao Liu, Zecheng Zhang, Wenjing Liao, Hayden Schaeffer
  
• Understanding Scaling Laws with Statistical and Approximation Theory for Transformer Neural Networks on Intrinsically Low-Dimensional Data, NeurIPS, 2024.
  Alex Havrilla, Wenjing Liao
• Deep Neural Networks Are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation, Journal of Machine Learning Research, 2024.
  Hao Liu, Jiahui Cheng, Wenjing Liao
• Generalization Error Guaranteed Auto-Encoder-Based Nonlinear Model Reduction for Operator Learning, Applied and Computational Harmonic Analysis, 2024.
  Hao Liu, Biraj Dahal, Rongjie Lai, Wenjing Liao
• Learning Functions Varying along a Central Subspace, SIAM Journal on Mathematics of Data Science, 2024.
  Hao Liu, Wenjing Liao

• DFU: Scale-Robust Diffusion Model for Zero-Shot Super-Resolution Image Generation, NeurIPS Workshop on Diffusion Models, 2023.
  Alex Havrilla, Kevin Rojas, Wenjing Liao, Molei Tao
• Fourier Features for Identifying Differential Equations (FourierIdent), accepted by Journal of Scientific Computing, 2023.
  Mengyi Tang, Hao Liu, Wenjing Liao, Sung Ha Kang
• Effective Minkowski Dimension of Deep Nonparametric Regression, ICML, 2023.
  Zixuan Zhang, Minshuo Chen, Mengdi Wang, Wenjing Liao, Tuo Zhao
  
• Group Projected Subspace Pursuit for Identification of Variable Coefficient Differential Equations (GP-IDENT), Journal of Computational Physics, 2023.
  Yuchen He, Sung Ha Kang, Wenjing Liao, Hao Liu, Yingjie Liu
  
• Deep Nonparametric Estimation of Intrinsic Data Structures by Chart Autoencoders: Generalization Error and Robustness, Applied and Computational Harmonic Analysis, 2023.
  Hao Liu, Alex Havrilla, Rongjie Lai, Wenjing Liao

• On Deep Generative Models for Approximation and Estimation of Distributions on Manifolds, NeurIPS 2022.
  Biraj Dahal*, Alex Havrilla*, Minshuo Chen, Tuo Zhao, Wenjing Liao
• A Manifold Two-Sample Test Study: Integral Probability Metric with Neural Networks, IMA Information and Inference, 2023.
  Jie Wang, Minshuo Chen, Tuo Zhao, Wenjing Liao, Yao Xie
• Benefits of Overparametrized Convolutional Residual Networks: Function Approximation under Smoothness Constraint, ICML 2022.
  Hao Liu, Minshuo Chen, Siawpeng Er, Wenjing Liao, Tong Zhang, Tuo Zhao
• Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces, Journal of Machine Learning Research, 2024.
  Hao Liu, Haizhao Yang, Minshuo Chen, Tuo Zhao, Wenjing Liao
• WeakIdent: Weak formulation for Identifying Differential Equations using Narrow-fit and Trimming, Journal of Computational Physics, 2023
  Mengyi Tang, Wenjing Liao, Rachel Kuske, Sung Ha Kang
• High Dimensional Binary Classification under Label Shift: Phase Transition and Regularization, Sampling Theory, Signal Processing, and Data Analysis, 2023.
  Jiahui Cheng*, Minshuo Chen*, Hao Liu, Tuo Zhao, Wenjing Liao
  

• Nonparametric Regression on Low-Dimensional Manifolds Using Deep ReLU Networks, IMA Information and Inference, 2022.
  Minshuo Chen, Haoming Jiang, Wenjing Liao, Tuo Zhao
• Doubly Robust Off-Policy Learning on Low-Dimensional Manifolds by Deep Neural Networks, accepted by Mathematics of Operation Research.
  Minshuo Chen*, Hao Liu*, Wenjing Liao, Tuo Zhao
  
• Besov Function Approximation and Binary Classification on Low-Dimensional Manifolds Using Convolutional Residual Networks, ICML, 2021.
  Hao Liu, Minshuo Chen, Tuo Zhao, Wenjing Liao
• Statistical Guarantees of Generative Adversarial Networks for Distribution Estimation, arXiv, 2020.
  Minshuo Chen, Wenjing Liao, Hongyuan Zha, Tuo Zhao
• Efficient Approximation of Deep ReLU Networks for Functions on Low-Dimensional Manifolds, NeurIPS 2019.
  Minshuo Chen, Haoming Jiang, Wenjing Liao, Tuo Zhao
  

• Multiscale Regression on Unknown Manifolds, Mathematics in Engineering, 2022.
  Wenjing Liao, Mauro Maggioni, Stefano Vigogna
• Adaptive Geometric Multiscale Approximations for Intrinsically Low-Dimensional Data, Journal of Machine Learning Research, 2020.
  Wenjing Liao, Mauro Maggioni
• Learning Adaptive Multiscale Approximations to Data and Functions near Low-Dimensional Sets, Proceedings of the IEEE Information Theory Workshop 2016
  Wenjing Liao, Mauro Maggioni, Stefano Vigogna

• Robust Identification of Differential Equations by Numerical Techniques from A Single Set of Noisy Observation, SIAM Journal on Scientific Computing, 2022.
  Yuchen He, Sung Ha Kang, Wenjing Liao, Hao Liu, Yingjie Liu
• Identifying Differential Equations with Numerical Time Evolution, Journal of Scientific Computing, 2021.
  Sung Ha Kang, Wenjing Liao, Yingjie Liu
• Numerical Identification of Nonlocal Potential Aggregation, Communication in Computational Physics, 2022.
  Yuchen He, Sung Ha Kang, Wenjing Liao, Hao Liu, Yingjie Liu

• Stability and Super-Resolution of MUSIC and ESPRIT for Multi-Snapshot Spectral Estimation, IEEE Transactions on Signal Processing, 2022.
  Weilin Li, Zengying Zhu, Weiguo Gao, Wenjing Liao
  
• Super-Resolution Limit of the ESPRIT Algorithm, IEEE Transactions on Information Theory 2020.
  Weilin Li, Wenjing Liao, Albert Fannjiang
  
• Conditioning of Restricted Fourier Matrices and Super-Resolution of MUSIC, Proceeding of the Sampling Theory and Applications, 2019.
  Weilin Li, Wenjing Liao
• Stable Super-Resolution Limit and Smallest Singular Value of Restricted Fourier Matrices, Applied and Computational Harmonic Analysis (ACHA), 2020. [ACHA 2021 Charles Chui Young Researcher Best Paper Award]
  Weilin Li, Wenjing Liao
• Sensor Calibration for Off-the-Grid Spectral Estimation, Applied and Computational Harmonic Analysis, 2018.
  Yonina Eldar, Wenjing Liao, Sui Tang
  
• MUSIC for Single-Snapshot Spectral Estimation: Stability and Super-Resolution, Applied and Computational Harmonic Analysis (ACHA), 2016.
  Wenjing Liao, Albert Fannjiang
  
• MUSIC for Multidimensional Spectral Estimation: Stability and Super-Resolution, IEEE Transactions on Signal Processing, 2015
  Weilin Li, Wenjing Liao
• MUSIC for Joint Frequency Estimation: Stability with Compressive Measurements, Proceedings of the IEEE Global Conference on Signal and Information Processing, 2014.
  Wenjing Liao
  
• Coherence-Pattern Guided Compressive Sensing with Unresolved Grids, SIAM Journal on Imaging Sciences, 2012.
  Albert Fannjiang, Wenjing Liao
  
• Super-Resolution by Compressive Sensing Algorithms, 2012 Asilomar Conference on Signals, Systems and Computers.
  Albert Fannjiang, Wenjing Liao
• Mismatch and Resolution in Compressive Imaging, Wavelets and Sparsity XIV, Proceedings of SPIE, 2011.
  Albert Fannjiang, Wenjing Liao

• Fourier Phasing with Phase-Uncertain Mask, Inverse Problems, 2013. [Matlab code]
  Albert Fannjiang, Wenjing Liao
  
• Phase Retrieval with Random Phase Illumination, Journal of the Optical Society of America, 2012. Top 5 of the most downloaded articles on image processing from JOSA A and Optical Express over 2012 and 2013. [Matlab code]
  Albert Fannjiang, Wenjing Liao
• Compressed Sensing Phase Retrieval, 2011 Asilomar Conference on Signals, Systems and Computers.
  Albert Fannjiang, Wenjing Liao

• Haoran Yan, 2025 - now
  

Postdoc

• Zhongjie Shi, 2025 - now
  

Student Alumni

• Biraj Dahal, 2021 - 2026
  
• First and current job: Postdoc at Purdue University
  
• Alex Havrilla, ML PhD student, Georgia Tech in 2021 - 2025
  
• First and current job: Research Scientist at Google DeepMind
• Jiahui Cheng, CSE PhD student, Georgia Tech in 2020 - 2025
  
• First and current job: Machine Learning Scientist at Meta
• Minshuo Chen, ML PhD student, Georgia Tech in 2018 - 2023, co-advised with Prof. Tuo Zhao in ISyE
  
• First job: Postdoc at Princeton University
• Current job: Assistant Professor at Northwestern University

• Zhaiming Shen, 2024 - 2026
• First and current job: Assistant Professor at Utah State University
  
• Hao Liu, postdoc at Georgia Tech in 2018 - 2021
• First and current job: Assistant Professor at Hong Kong Baptist University