128 citations · 540 across the 44 of their papers we have counts for
17 papers · 1 filter
A Provable Splitting Approach for Symmetric Nonnegative Matrix Factorization
Xiao Li, Zhihui Zhu, Qiuwei Li +1
The symmetric Nonnegative Matrix Factorization (NMF), a special but important class of the general NMF, has found numerous applications in data analysis such as various clustering…
Are All Losses Created Equal: A Neural Collapse Perspective
Jinxin Zhou, Chong You, Xiao Li +4
While cross entropy (CE) is the most commonly used loss to train deep neural networks for classification tasks, many alternative losses have been developed to obtain better empiric…
Neural Collapse with Normalized Features: A Geometric Analysis over the Riemannian Manifold
Can Yaras, Peng Wang, Zhihui Zhu +2
When training overparameterized deep networks for classification tasks, it has been widely observed that the learned features exhibit a so-called "neural collapse" phenomenon. More…
Error Analysis of Tensor-Train Cross Approximation
Zhen Qin, Alexander Lidiak, Zhexuan Gong +3
Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensional…
On the Optimization Landscape of Neural Collapse under MSE Loss: Global Optimality with Unconstrained Features
Jinxin Zhou, Xiao Li, Tianyu Ding +3
When training deep neural networks for classification tasks, an intriguing empirical phenomenon has been widely observed in the last-layer classifiers and features, where (i) the c…
Robust Training under Label Noise by Over-parameterization
Sheng Liu, Zhihui Zhu, Qing Qu +1
Recently, over-parameterized deep networks, with increasingly more network parameters than training samples, have dominated the performances of modern machine learning. However, wh…
Only Train Once: A One-Shot Neural Network Training And Pruning Framework
Tianyi Chen, Bo Ji, Tianyu Ding +7
Structured pruning is a commonly used technique in deploying deep neural networks (DNNs) onto resource-constrained devices. However, the existing pruning methods are usually heuris…
A Geometric Analysis of Neural Collapse with Unconstrained Features
Zhihui Zhu, Tianyu Ding, Jinxin Zhou +4
We provide the first global optimization landscape analysis of -- an intriguing empirical phenomenon that arises in the last-layer classifiers and features of ne…
Robust Recovery via Implicit Bias of Discrepant Learning Rates for Double Over-parameterization
Chong You, Zhihui Zhu, Qing Qu +1
Recent advances have shown that implicit bias of gradient descent on over-parameterized models enables the recovery of low-rank matrices from linear measurements, even with no prio…
Recovery and Generalization in Over-Realized Dictionary Learning
Jeremias Sulam, Chong You, Zhihui Zhu
In over two decades of research, the field of dictionary learning has gathered a large collection of successful applications, and theoretical guarantees for model recovery are know…
Finding the Sparsest Vectors in a Subspace: Theory, Algorithms, and Applications
Qing Qu, Zhihui Zhu, Xiao Li +3
The problem of finding the sparsest vector (direction) in a low dimensional subspace can be considered as a homogeneous variant of the sparse recovery problem, which finds applicat…
Analysis of the Optimization Landscapes for Overcomplete Representation Learning
Qing Qu, Yuexiang Zhai, Xiao Li +2
We study nonconvex optimization landscapes for learning overcomplete representations, including learning (i) sparsely used overcomplete dictionaries and (ii) convolutional dictiona…
Compressed Sensing with Probability-based Prior Information
Q. Jiang, S. Li, Z. Zhu +3
This paper deals with the design of a sensing matrix along with a sparse recovery algorithm by utilizing the probability-based prior information for compressed sensing system. With…
Dual Principal Component Pursuit: Probability Analysis and Efficient Algorithms
Zhihui Zhu, Yifan Wang, Daniel P. Robinson +3
Recent methods for learning a linear subspace from data corrupted by outliers are based on convex and nuclear norm optimization and require the dimension of the subspace a…
Dropping Symmetry for Fast Symmetric Nonnegative Matrix Factorization
Zhihui Zhu, Xiao Li, Kai Liu +1
Symmetric nonnegative matrix factorization (NMF), a special but important class of the general NMF, is demonstrated to be useful for data analysis and in particular for various clu…
The Global Optimization Geometry of Shallow Linear Neural Networks
Zhihui Zhu, Daniel Soudry, Yonina C. Eldar +1
We examine the squared error loss landscape of shallow linear neural networks. We show---with significantly milder assumptions than previous works---that the corresponding optimiza…
An Efficient Method for Robust Projection Matrix Design
Tao Hong, Zhihui Zhu
Our objective is to efficiently design a robust projection matrix for the Compressive Sensing (CS) systems when applied to the signals that are not exactly sparse. The optimal…