activity
20202026
most citedSelf-adaptive deep neural network: Numerical approximation to functions and PDEs

11 citations · 32 across the 15 of their papers we have counts for

collaborators

15 papers

math.NA2026

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…

math.FA2024

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…

cs.LG2024

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…

math.NA2023

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…

math.NA2023★ 5 cited

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…

cs.LG2021

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…

math.NA2021★ 2 cited

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…

stat.ML2021

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…

math.NA2021★ 11 cited

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…

math.NA2021★ 1 cited

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…

math.NA2021★ 1 cited

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),…

cs.CV2021

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…

math.NA2021★ 4 cited

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…

cs.SD2020★ 2 cited

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.…

cs.SD2020★ 6 cited

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…