Related papers: An Accelerated Alternating Partial Bregman Algorit…

In this paper, we present a novel approach to the low rank matrix recovery (LRMR) problem by casting it as a group sparsity problem. Specifically, we propose a flexible group sparse regularizer (FLGSR) that can group any number of matrix…

In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…

Nonconvex optimization problems arise in different research fields and arouse lots of attention in signal processing, statistics and machine learning. In this work, we explore the accelerated proximal gradient method and some of its…

Thresholding iterative methods are recently successfully applied to image deblurring problems. In this paper, we investigate the modified linearized Bregman algorithm (MLBA) used in image deblurring problems, with a proper treatment of the…

We introduce a novel approach for analyzing the training dynamics of ReLU networks by examining the characteristic activation boundaries of individual ReLU neurons. Our proposed analysis reveals a critical instability in common neural…

This paper proposes a new framework for computing low-rank solutions to nonlinear matrix equations arising from spatial discretization of nonlinear partial differential equations: low-rank Anderson acceleration (lrAA). lrAA is an adaptation…

This paper introduces scalable, sampling-based algorithms that optimize trained neural networks with ReLU activations. We first propose an iterative algorithm that takes advantage of the piecewise linear structure of ReLU neural networks…

We consider the problem of estimating the inverse covariance matrix by maximizing the likelihood function with a penalty added to encourage the sparsity of the resulting matrix. We propose a new approach based on the split Bregman method to…

The efficacy of deep neural networks is heavily reliant on the design of non-linear activation functions, yet existing approaches often struggle to balance optimization stability with computational efficiency. While piecewise linear…

Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…

In this work, we present randomized compression algorithms for flat rank-structured matrices with shared bases, termed uniform Block Low-Rank (BLR) matrices. Our main contribution is a technique called tagging, which improves upon the…

The explicit low-rank regularization, e.g., nuclear norm regularization, has been widely used in imaging sciences. However, it has been found that implicit regularization outperforms explicit ones in various image processing tasks. Another…

This work proposes a general learned proximal alternating minimization algorithm, LPAM, for solving learnable two-block nonsmooth and nonconvex optimization problems. We tackle the nonsmoothness by an appropriate smoothing technique with…

The low-rank matrix approximation problems within a threshold are widely applied in information retrieval, image processing, background estimation of the video sequence problems and so on. This paper presents an adaptive randomized…

A matrix algorithm runs superfast (aka at sublinear cost) if it involves much fewer flops and memory cells than an input matrix has entries. Big Data are frequently represented by matrices of immense sizes that cannot be handled directly…

Important workloads, such as machine learning and graph analytics applications, heavily involve sparse linear algebra operations. These operations use sparse matrix compression as an effective means to avoid storing zeros and performing…

Fully connected layers are a primary source of memory and computational overhead in deep neural networks due to their dense, often redundant parameterization. While various compression techniques exist, they frequently introduce complex…

Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…

The training of deep neural networks predominantly relies on a combination of gradient-based optimisation and back-propagation for the computation of the gradient. While incredibly successful, this approach faces challenges such as…

This paper considers the problem of minimizing the sum of a smooth function and the Schatten-$p$ norm of the matrix. Our contribution involves proposing accelerated iteratively reweighted nuclear norm methods designed for solving the…