Energy Scaling and Asymptotic Properties of Step Bunching in Epitaxial Growth with Elasticity Effects. - Tao Luo 012; Yang Xiang 002; Nung Kwan Yip (Multiscale Model. Simul., 2016)

Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks. - Zhi-Qin John Xu; Yaoyu Zhang; Tao Luo 012; Yanyang Xiao; Zheng Ma 009 (CoRR, 2019)

Explicitizing an Implicit Bias of the Frequency Principle in Two-layer Neural Networks. - Yaoyu Zhang; Zhi-Qin John Xu; Tao Luo 012; Zheng Ma 009 (CoRR, 2019)

Theory of the Frequency Principle for General Deep Neural Networks. - Tao Luo 012; Zheng Ma 009; Zhi-Qin John Xu; Yaoyu Zhang (CoRR, 2019)

A type of generalization error induced by initialization in deep neural networks. - Yaoyu Zhang; Zhi-Qin John Xu; Tao Luo 012; Zheng Ma 009 (MSML, 2020)

Towards an Understanding of Residual Networks Using Neural Tangent Hierarchy (NTH). - Yuqing Li; Tao Luo 012; Nung Kwan Yip (CoRR, 2020)

A regularized deep matrix factorized model of matrix completion for image restoration. - Zhemin Li; Zhi-Qin John Xu; Tao Luo 012; Hongxia Wang (CoRR, 2020)

Fourier-domain Variational Formulation and Its Well-posedness for Supervised Learning. - Tao Luo 012; Zheng Ma 009; Zhiwei Wang; Zhi-Qin John Xu; Yaoyu Zhang (CoRR, 2020)

Embedding Principle of Loss Landscape of Deep Neural Networks. - Yaoyu Zhang; Zhongwang Zhang; Tao Luo 012; Zhi-Qin John Xu (NeurIPS, 2021)

Linear Frequency Principle Model to Understand the Absence of Overfitting in Neural Networks. - Yaoyu Zhang; Tao Luo 012; Zheng Ma 009; Zhi-Qin John Xu (CoRR, 2021)

An Upper Limit of Decaying Rate with Respect to Frequency in Deep Neural Network. - Tao Luo 012; Zheng Ma 009; Zhiwei Wang; Zhi-Qin John Xu; Yaoyu Zhang (CoRR, 2021)

Towards Understanding the Condensation of Two-layer Neural Networks at Initial Training. - Zhi-Qin John Xu; Hanxu Zhou; Tao Luo 012; Yaoyu Zhang (CoRR, 2021)

MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs. - Lulu Zhang; Tao Luo 012; Yaoyu Zhang; Zhi-Qin John Xu; Zheng Ma 009 (CoRR, 2021)

Embedding Principle: a hierarchical structure of loss landscape of deep neural networks. - Yaoyu Zhang; Yuqing Li; Zhongwang Zhang; Tao Luo 012; Zhi-Qin John Xu (CoRR, 2021)

Phase Diagram for Two-layer ReLU Neural Networks at Infinite-width Limit. - Tao Luo 012; Zhi-Qin John Xu; Zheng Ma 009; Yaoyu Zhang (J. Mach. Learn. Res., 2021)

Energy Scaling and Asymptotic Properties of One-Dimensional Discrete System with Generalized Lennard-Jones (m, n) Interaction. - Tao Luo 012; Yang Xiang 002; Nung Kwan Yip (J. Nonlinear Sci., 2021)

Finite Temperature Cauchy-Born Rule and Stability of Crystalline Solids with Point Defects. - Tao Luo 012; Yang Xiang 002; Jerry Zhijian Yang (Multiscale Model. Simul., 2021)

An Upper Limit of Decaying Rate with Respect to Frequency in Linear Frequency Principle Model. - Tao Luo 012; Zheng Ma 010; Zhiwei Wang; Zhiqin John Xu; Yaoyu Zhang (MSML, 2022)

Empirical Phase Diagram for Three-layer Neural Networks with Infinite Width. - Hanxu Zhou; Qixuan Zhou; Zhenyuan Jin; Tao Luo 012; Yaoyu Zhang; Zhi-Qin John Xu (NeurIPS, 2022)

Towards Understanding the Condensation of Neural Networks at Initial Training. - Hanxu Zhou; Qixuan Zhou; Tao Luo 012; Yaoyu Zhang; Zhi-Qin John Xu (NeurIPS, 2022)

Overview frequency principle/spectral bias in deep learning. - Zhi-Qin John Xu; Yaoyu Zhang; Tao Luo 012 (CoRR, 2022)

An Experimental Comparison Between Temporal Difference and Residual Gradient with Neural Network Approximation. - Shuyu Yin; Tao Luo 012; Peilin Liu; Zhi-Qin John Xu (CoRR, 2022)

Embedding Principle in Depth for the Loss Landscape Analysis of Deep Neural Networks. - Zhiwei Bai; Tao Luo 012; Zhi-Qin John Xu; Yaoyu Zhang (CoRR, 2022)

Linear Stability Hypothesis and Rank Stratification for Nonlinear Models. - Yaoyu Zhang; Zhongwang Zhang; Leyang Zhang; Zhiwei Bai; Tao Luo 012; Zhi-Qin John Xu (CoRR, 2022)

A regularised deep matrix factorised model of matrix completion for image restoration. - Zhemin Li; Zhi-Qin John Xu; Tao Luo 012; Hongxia Wang (IET Image Process., 2022)

Nonlinear Weighted Directed Acyclic Graph and A Priori Estimates for Neural Networks. - Yuqing Li; Tao Luo 012; Chao Ma (SIAM J. Math. Data Sci., 2022)

On the Exact Computation of Linear Frequency Principle Dynamics and Its Generalization. - Tao Luo 012; Zheng Ma 009; Zhi-Qin John Xu; Yaoyu Zhang (SIAM J. Math. Data Sci., 2022)

Phase Diagram of Initial Condensation for Two-layer Neural Networks. - Zhengan Chen; Yuqing Li; Tao Luo 012; Zhangchen Zhou; Zhi-Qin John Xu (CoRR, 2023)

Optimistic Estimate Uncovers the Potential of Nonlinear Models. - Yaoyu Zhang; Zhongwang Zhang; Leyang Zhang; Zhiwei Bai; Tao Luo 012; Zhi-Qin John Xu (CoRR, 2023)

Structure and Gradient Dynamics Near Global Minima of Two-layer Neural Networks. - Leyang Zhang; Yaoyu Zhang; Tao Luo 012 (CoRR, 2023)

On Residual Minimization for PDEs: Failure of PINN, Modified Equation, and Implicit Bias. - Tao Luo 012; Qixuan Zhou (CoRR, 2023)

Limitation of Characterizing Implicit Regularization by Data-independent Functions. - Leyang Zhang; Zhi-Qin John Xu; Tao Luo 012; Yaoyu Zhang (Trans. Mach. Learn. Res., 2023)

Stochastic Modified Equations and Dynamics of Dropout Algorithm. - Zhongwang Zhang; Yuqing Li; Tao Luo 012; Zhi-Qin John Xu (ICLR, 2024)

A priori Estimates for Deep Residual Network in Continuous-time Reinforcement Learning. - Shuyu Yin; Qixuan Zhou; Fei Wen; Tao Luo 012 (CoRR, 2024)

Demystifying Lazy Training of Neural Networks from a Macroscopic Viewpoint. - Yuqing Li; Tao Luo 012; Qixuan Zhou (CoRR, 2024)

Geometry of Critical Sets and Existence of Saddle Branches for Two-layer Neural Networks. - Leyang Zhang; Yaoyu Zhang; Tao Luo 012 (CoRR, 2024)

Probing Implicit Bias in Semi-gradient Q-learning: Visualizing the Effective Loss Landscapes via the Fokker-Planck Equation. - Shuyu Yin; Fei Wen; Peilin Liu; Tao Luo 012 (CoRR, 2024)

Analyzing and Bridging the Gap between Maximizing Total Reward and Discounted Reward in Deep Reinforcement Learning. - Shuyu Yin; Fei Wen; Peilin Liu; Tao Luo 012 (CoRR, 2024)

Quantifying Training Difficulty and Accelerating Convergence in Neural Network-Based PDE Solvers. - Chuqi Chen; Qixuan Zhou; Yahong Yang; Yang Xiang 002; Tao Luo 012 (CoRR, 2024)