Related papers: Spiky Rank and Its Applications to Rigidity and Ci…

We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…

When factorizing binary matrices, we often have to make a choice between using expensive combinatorial methods that retain the discrete nature of the data and using continuous methods that can be more efficient but destroy the discrete…

Low-rank training methods reduce the number of trainable parameters by re-parameterizing the weights with matrix decompositions (e.g., singular value decomposition). However, enforcing a fixed low-rank structure caps the rank of the weight…

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…

Accurate estimation of camera matrices is an important step in structure from motion algorithms. In this paper we introduce a novel rank constraint on collections of fundamental matrices in multi-view settings. We show that in general, with…

Block full rank pencils introduced in [Dopico et al., Local linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problems, Linear Algebra Appl., 2020] allow us to obtain local information…

A new approach to solving eigenvalue optimization problems for large structured matrices is proposed and studied. The class of optimization problems considered is related to computing structured pseudospectra and their extremal points, and…

In many machine learning and data related applications, it is required to have the knowledge of approximate ranks of large data matrices at hand. In this paper, we present two computationally inexpensive techniques to estimate the…

The critical state is assumed to be optimal for any computation in recurrent neural networks, because criticality maximizes a number of abstract computational properties. We challenge this assumption by evaluating the performance of a…

We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…

Saturating sets are combinatorial objects in projective spaces over finite fields that have been intensively investigated in the last three decades. They are related to the so-called covering problem of codes in the Hamming metric. In this…

The spectral moments of ensembles of sparse random block matrices are analytically evaluated in the limit of large order. The structure of the sparse matrix corresponds to the Erd\"os-Renyi random graph. The blocks are i.i.d. random…

We determine the rank of a random matrix over an arbitrary field with prescribed numbers of non-zero entries in each row and column. As an application we obtain a formula for the rate of low-density parity check codes. This formula…

We introduce the Lipschitz matrix: a generalization of the scalar Lipschitz constant for functions with many inputs. Among the Lipschitz matrices compatible a particular function, we choose the smallest such matrix in the Frobenius norm to…

We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use…

Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…

In this paper we study the rank of planar rigidity matrix of 4-valent graphs, both in case of generic realizations and configurations in general position, under various connectivity assumptions on the graphs. For each case considered, we…

Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly…

Many algorithms for processing probabilistic networks are dependent on the topological properties of the problem's structure. Such algorithms (e.g., clustering, conditioning) are effective only if the problem has a sparse graph captured by…

On-chip edge intelligence has necessitated the exploration of algorithmic techniques to reduce the compute requirements of current machine learning frameworks. This work aims to bridge the recent algorithmic progress in training Binary…