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We show that a coherent network of lasers exhibits emergent neural computing capabilities. The proposed scheme is built on harnessing the collective behavior of laser networks for storing a number of phase patterns as stable fixed points of…

We present a fast direct solver for structured linear systems based on multilevel matrix compression. Using the recently developed interpolative decomposition of a low-rank matrix in a recursive manner, we embed an approximation of the…

Clique tree conversion solves large-scale semidefinite programs by splitting an $n\times n$ matrix variable into up to $n$ smaller matrix variables, each representing a principal submatrix of up to $\omega\times\omega$. Its fundamental…

We propose a protocol for solving systems of linear algebraic equations via quantum mechanical methods using the minimal number of qubits. We show that $(M+1)$-qubit system is enough to solve a system of $M$ equations for one of the…

The Transformer architecture has revolutionized deep learning on sequential data, becoming ubiquitous in state-of-the-art solutions for a wide variety of applications. Yet vanilla Transformers are notoriously resource-expensive, requiring…

This work aims at estimating inverse autocovariance matrices of long memory processes admitting a linear representation. A modified Cholesky decomposition is used in conjunction with an increasing order autoregressive model to achieve this…

We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…

We assume the permutation $\pi$ is given by an $n$-element array in which the $i$-th element denotes the value $\pi(i)$. Constructing its inverse in-place (i.e. using $O(\log{n})$ bits of additional memory) can be achieved in linear time…

A decision tree recursively splits a feature space $\mathbb{R}^{d}$ and then assigns class labels based on the resulting partition. Decision trees have been part of the basic machine-learning toolkit for decades. A large body of work treats…

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

Disentanglement of constituent factors of a sensory signal is central to perception and cognition and hence is a critical task for future artificial intelligence systems. In this paper, we present a compute engine capable of efficiently…

Matrix computations have become increasingly significant in many data-driven applications. However, Moores law for digital computers has been gradually approaching its limit in recent years. Moreover, digital computers encounter substantial…

An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…

We first describe three algorithms for computing the Lyndon array that have been suggested in the literature, but for which no structured exposition has been given. Two of these algorithms execute in quadratic time in the worst case, the…

This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the workshop Linear Systems and Eigenvalue Problems, which was…

We show that the three-dimensional layers-of-maxima problem can be solved in $o(n\log n)$ time in the word RAM model. Our algorithm runs in $O(n(\log \log n)^3)$ deterministic time or $O(n(\log\log n)^2)$ expected time and uses O(n) space.…

We show that a simple algorithm for computing a matching on a graph runs in a logarithmic number of phases incurring work linear in the input size. The algorithm can be adapted to provide efficient algorithms in several models of…

We consider the classical sensor scheduling problem for linear systems where only one sensor is activated at each time. We show that the sensor scheduling problem has a close relation to the sensor design problem and the solution of a…

Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…

We describe a model that enables us to analyze the running time of an algorithm in a computer with a memory hierarchy with limited associativity, in terms of various cache parameters. Our model, an extension of Aggarwal and Vitter's I/O…