11 citations · 32 across the 15 of their papers we have counts for
15 papers
Least-Squares Neural Network (LSNN) Method for Scalar Hyperbolic Partial Differential Equations
Min Liu, Zhiqiang Cai
This chapter offers a comprehensive introduction to the least-squares neural network (LSNN) method introduced in [14,16], for solving scalar first-order hyperbolic partial differen…
ReLU neural network approximation to piecewise constant functions
Zhiqiang Cai, Junpyo Choi, Min Liu
This paper studies the approximation property of ReLU neural networks (NNs) to piecewise constant functions with unknown interfaces in bounded regions in . Under the…
A Structure-Guided Gauss-Newton Method for Shallow ReLU Neural Network
Zhiqiang Cai, Tong Ding, Min Liu +2
In this paper, we propose a structure-guided Gauss-Newton (SgGN) method for solving least squares problems using a shallow ReLU neural network. The method effectively takes advanta…
Least-Squares Neural Network (LSNN) Method For Linear Advection-Reaction Equation: Non-constant Jumps
Zhiqiang Cai, Junpyo Choi, Min Liu
The least-squares ReLU neural network (LSNN) method was introduced and studied for solving linear advection-reaction equation with discontinuous solution in \cite{Cai2021linear,cai…
Least-Squares Neural Network (LSNN) Method For Linear Advection-Reaction Equation: Discontinuity Interface
Zhiqiang Cai, Junpyo Choi, Min Liu
We studied the least-squares ReLU neural network (LSNN) method for solving linear advection-reaction equation with discontinuous solution in [Cai, Zhiqiang, Jingshuang Chen, and Mi…
Just Least Squares: Binary Compressive Sampling with Low Generative Intrinsic Dimension
Yuling Jiao, Dingwei Li, Min Liu +2
In this paper, we consider recovering dimensional signals from binary measurements corrupted by noises and sign flips under the assumption that the target signals have low…
Least-Squares Neural Network (LSNN) Method For Scalar Nonlinear Hyperbolic Conservation Laws: Discrete Divergence Operator
Zhiqiang Cai, Jingshuang Chen, Min Liu
A least-squares neural network (LSNN) method was introduced for solving scalar linear and nonlinear hyperbolic conservation laws (HCLs) in [7, 6]. This method is based on an equiva…
Coordinate Descent for MCP/SCAD Penalized Least Squares Converges Linearly
Yuling Jiao, Dingwei Li, Min Liu +1
Recovering sparse signals from observed data is an important topic in signal/imaging processing, statistics and machine learning. Nonconvex penalized least squares have been attrac…
Self-adaptive deep neural network: Numerical approximation to functions and PDEs
Zhiqiang Cai, Jingshuang Chen, Min Liu
Designing an optimal deep neural network for a given task is important and challenging in many machine learning applications. To address this issue, we introduce a self-adaptive al…
Adaptive Two-Layer ReLU Neural Network: II. Ritz Approximation to Elliptic PDEs
Min Liu, Zhiqiang Cai
In this paper, we study adaptive neuron enhancement (ANE) method for solving self-adjoint second-order elliptic partial differential equations (PDEs). The ANE method is a self-adap…
Adaptive Two-Layer ReLU Neural Network: I. Best Least-squares Approximation
Min Liu, Zhiqiang Cai, Jingshuang Chen
In this paper, we introduce adaptive neuron enhancement (ANE) method for the best least-squares approximation using two-layer ReLU neural networks (NNs). For a given function f(x),…
Deep Tiny Network for Recognition-Oriented Face Image Quality Assessment
Baoyun Peng, Min Liu, Zhaoning Zhang +2
Face recognition has made significant progress in recent years due to deep convolutional neural networks (CNN). In many face recognition (FR) scenarios, face images are acquired fr…
Least-Squares ReLU Neural Network (LSNN) Method For Scalar Nonlinear Hyperbolic Conservation Law
Zhiqiang Cai, Jingshuang Chen, Min Liu
We introduced the least-squares ReLU neural network (LSNN) method for solving the linear advection-reaction problem with discontinuous solution and showed that the method outperfor…
Learning generic feature representation with synthetic data for weakly-supervised sound event detection by inter-frame distance loss
Yuxin Huang, Liwei Lin, Xiangdong Wang +4
Due to the limitation of strong-labeled sound event detection data set, using synthetic data to improve the sound event detection system performance has been a new research focus.…
Guided multi-branch learning systems for sound event detection with sound separation
Yuxin Huang, Liwei Lin, Shuo Ma +5
In this paper, we describe in detail our systems for DCASE 2020 Task 4. The systems are based on the 1st-place system of DCASE 2019 Task 4, which adopts weakly-supervised framework…