47 citations · 106 across the 22 of their papers we have counts for
25 papers
Near-Optimal Nonconvex Matrix Completion
Jian-Feng Cai, Xiliang Lu, Juntao You
We study nonconvex methods for matrix completion, the problem of recovering a low-rank matrix from a subset of its entries. Convex methods achieve sample complexity linear in the m…
Off-Grid Point-Scatterer Localization from Sparse Limited-Aperture Data via Hankel Completion
Jingzhi Li, Xiliang Lu, Juntao You
We study the localization of distinct planar point scatterers from sparsely sampled single-incidence, single-frequency acoustic far-field data over a limited receiver aperture.…
Approximation Error Upper and Lower Bounds for Hölder Class with Transformers
Xin He, Yuling Jiao, Xiliang Lu +1
We explore the expressive power of Transformers by establishing precise approximation error upper and lower bounds for Hölder class. Specifically, a new approximation upper bound i…
Near-optimal Prediction Error Estimation for Quantum Machine Learning Models
Qiuhao Chen, Yuling Jiao, Yinan Li +2
Understanding the theoretical capabilities and limitations of quantum machine learning (QML) models to solve machine learning tasks is crucial to advancing both quantum software an…
GraHTP: A Provable Newton-like Algorithm for Sparse Phase Retrieval
Licheng Dai, Xiliang Lu, Juntao You
This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-conv…
Quantum Compiling with Reinforcement Learning on a Superconducting Processor
Z. T. Wang, Qiuhao Chen, Yuxuan Du +16
To effectively implement quantum algorithms on noisy intermediate-scale quantum (NISQ) processors is a central task in modern quantum technology. NISQ processors feature tens to a…
Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descent
HanQin Cai, Longxiu Huang, Xiliang Lu +1
This paper studies the robust Hankel recovery problem, which simultaneously removes the sparse outliers and fulfills missing entries from the partial observation. We propose a nove…
Numerical Recovery of the Diffusion Coefficient in Diffusion Equations from Terminal Measurement
Bangti Jin, Xiliang Lu, Qimeng Quan +1
In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigo…
On the robustness of double-word addition algorithms
Yuanyuan Yang, XinYu Lyu, Sida He +3
We demonstrate that, even when there are moderate overlaps in the inputs of sloppy or accurate double-word addition algorithms in the QD library, these algorithms still guarantee e…
Neural Network Approximation for Pessimistic Offline Reinforcement Learning
Di Wu, Yuling Jiao, Li Shen +2
Deep reinforcement learning (RL) has shown remarkable success in specific offline decision-making scenarios, yet its theoretical guarantees are still under development. Existing wo…
Sampling via Föllmer Flow
Zhao Ding, Yuling Jiao, Xiliang Lu +2
We introduce a novel unit-time ordinary differential equation (ODE) flow called the preconditioned Föllmer flow, which efficiently transforms a Gaussian measure into a desired targ…
Non-asymptotic Approximation Error Bounds of Parameterized Quantum Circuits
Zhan Yu, Qiuhao Chen, Yuling Jiao +4
Parameterized quantum circuits (PQCs) have emerged as a promising approach for quantum neural networks. However, understanding their expressive power in accomplishing machine learn…
Current density impedance imaging with PINNs
Chenguang Duan, Yuling Jiao, Xiliang Lu +1
In this paper, we introduce CDII-PINNs, a computationally efficient method for solving CDII using PINNs in the framework of Tikhonov regularization. This method constructs a physic…
Deep Neural Network Approximation of Composition Functions: with application to PINNs
Chenguang Duan, Yuling Jiao, Xiliang Lu +2
In this paper, we focus on approximating a natural class of functions that are compositions of smooth functions. Unlike the low-dimensional support assumption on the covariate, we…
GAS: A Gaussian Mixture Distribution-Based Adaptive Sampling Method for PINNs
Yuling Jiao, Di Li, Xiliang Lu +2
With the recent study of deep learning in scientific computation, the Physics-Informed Neural Networks (PINNs) method has drawn widespread attention for solving Partial Differentia…
Efficient and practical quantum compiler towards multi-qubit systems with deep reinforcement learning
Qiuhao Chen, Yuxuan Du, Qi Zhao +3
Efficient quantum compiling tactics greatly enhance the capability of quantum computers to execute complicated quantum algorithms. Due to its fundamental importance, a plethora of…
Sample-Efficient Sparse Phase Retrieval via Stochastic Alternating Minimization
Jian-Feng Cai, Yuling Jiao, Xiliang Lu +1
In this work we propose a nonconvex two-stage \underline{s}tochastic \underline{a}lternating \underline{m}inimizing (SAM) method for sparse phase retrieval. The proposed algorithm…
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…
A Data-Driven Line Search Rule for Support Recovery in High-dimensional Data Analysis
Peili Li, Yuling Jiao, Xiliang Lu +1
In this work, we consider the algorithm to the (nonlinear) regression problems with penalty. The existing algorithms for based optimization problem are often carr…
Analysis of Deep Ritz Methods for Laplace Equations with Dirichlet Boundary Conditions
Chenguang Duan, Yuling Jiao, Yanming Lai +3
Deep Ritz methods (DRM) have been proven numerically to be efficient in solving partial differential equations. In this paper, we present a convergence rate in norm for dee…
Global Optimization via Schr{ö}dinger-F{ö}llmer Diffusion
Yin Dai, Yuling Jiao, Lican Kang +2
We study the problem of finding global minimizers of approximately via sampling from a probability distribution with density $p_σ(x)=…
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…
A rate of convergence of Physics Informed Neural Networks for the linear second order elliptic PDEs
Yuling Jiao, Yanming Lai, Dingwei Li +4
In recent years, physical informed neural networks (PINNs) have been shown to be a powerful tool for solving PDEs empirically. However, numerical analysis of PINNs is still missing…
Deep Neural Networks with ReLU-Sine-Exponential Activations Break Curse of Dimensionality in Approximation on Hölder Class
Yuling Jiao, Yanming Lai, Xiliang Lu +3
In this paper, we construct neural networks with ReLU, sine and as activation functions. For general continuous defined on with continuity modulus ,…