Related papers: Computing Spectra -- On the Solvability Complexity…
In this paper, we explore statistical versus computational trade-off to address a basic question in the application of a distributed algorithm: what is the minimal computational cost in obtaining statistical optimality? In smoothing spline…
Many AI synthesis problems such as planning or scheduling may be modelized as constraint satisfaction problems (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all…
Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…
We study the decision version of tensor spectral norm from the viewpoint of real algebraic complexity. For a rationally specified tensor, the tensor spectral threshold problem asks whether its spectral norm exceeds a prescribed rational…
An active topic in the study of random constraint satisfaction problems (CSPs) is the geometry of the space of satisfying or almost satisfying assignments as the function of the density, for which a precise landscape of predictions has been…
The bandwidth of a signal is an important physical property that is of relevance in many signal- and information-theoretic applications. In this paper we study questions related to the computability of the bandwidth of computable…
Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure…
For a large class of optimization problems, namely those that can be expressed as finite-valued constraint satisfaction problems (VCSPs), we establish a dichotomy on the number of levels of the Lasserre hierarchy of semi-definite programs…
We present a spectral analysis for matrix scaling and operator scaling. We prove that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear convergence. This implies that a simple gradient descent…
Understanding the singular value spectrum of a matrix $A \in \mathbb{R}^{n \times n}$ is a fundamental task in countless applications. In matrix multiplication time, it is possible to perform a full SVD and directly compute the singular…
Constraint Satisfaction Problems (CSPs, for short) make up a class of problems with applications in many areas of computer science. The first classification of these problems was given by Schaeffer who showed that every CSP over the domain…
Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely…
Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity,…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…
This document describes our freely distributed Maple library {\sc spectra}, for Semidefinite Programming solved Exactly with Computational Tools of Real Algebra. It solves linear matrix inequalities with symbolic computation in exact…
We address the computational spectral theory of Jacobi operators that are compact perturbations of the free Jacobi operator via the asymptotic properties of a connection coefficient matrix. In particular, for finite-rank perturbation we…
Given a countable structure $\mathcal{A}$, the degree spectrum of $\mathcal{A}$ is the set of all Turing degrees which can compute an isomorphic copy of $\mathcal{A}$. One of the major programs in computable structure theory is to determine…
We present a spectral approach to design approximation algorithms for network design problems. We observe that the underlying mathematical questions are the spectral rounding problems, which were studied in spectral sparsification and in…
In many high-dimensional problems, like sparse-PCA, planted clique, or clustering, the best known algorithms with polynomial time complexity fail to reach the statistical performance provably achievable by algorithms free of computational…
High-performance computing (HPC) is essential for tackling complex computational problems across various domains. As the scale and complexity of HPC applications continue to grow, the need for scalable systems and software architectures…