540 citations · 841 across the 27 of their papers we have counts for
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Fourier-domain Variational Formulation and Its Well-posedness for Supervised Learning
Tao Luo, Zheng Ma, Zhiwei Wang +2
A supervised learning problem is to find a function in a hypothesis function space given values on isolated data points. Inspired by the frequency principle in neural networks, we…
On the exact computation of linear frequency principle dynamics and its generalization
Tao Luo, Zheng Ma, Zhi-Qin John Xu +1
Recent works show an intriguing phenomenon of Frequency Principle (F-Principle) that deep neural networks (DNNs) fit the target function from low to high frequency during the train…
A regularized deep matrix factorized model of matrix completion for image restoration
Zhemin Li, Zhi-Qin John Xu, Tao Luo +1
It has been an important approach of using matrix completion to perform image restoration. Most previous works on matrix completion focus on the low-rank property by imposing expli…
Towards an Understanding of Residual Networks Using Neural Tangent Hierarchy (NTH)
Yuqing Li, Tao Luo, Nung Kwan Yip
Gradient descent yields zero training loss in polynomial time for deep neural networks despite non-convex nature of the objective function. The behavior of network in the infinite…
Phase diagram for two-layer ReLU neural networks at infinite-width limit
Tao Luo, Zhi-Qin John Xu, Zheng Ma +1
How neural network behaves during the training over different choices of hyperparameters is an important question in the study of neural networks. In this work, inspired by the pha…
Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory
Tao Luo, Haizhao Yang
The problem of solving partial differential equations (PDEs) can be formulated into a least-squares minimization problem, where neural networks are used to parametrize PDE solution…