Related papers: Time complexity of in-memory solution of linear sy…

In this work, we study the relative hardness of fundamental problems with state-of-the-art word RAM algorithms that take $O(n\sqrt{\log n})$ time for instances described in $\Theta(n)$ machine words ($\Theta(n\log n)$ bits). This complexity…

Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of…

The original softmax-based attention mechanism (regular attention) in the extremely successful Transformer architecture computes attention between $N$ tokens, each embedded in a $D$-dimensional head, with a time complexity of $O(N^2D)$.…

In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…

Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…

Many important multiple-objective decision problems can be cast within the framework of ranking under constraints and solved via a weighted bipartite matching linear program. Some of these optimization problems, such as personalized content…

This paper presents a new approach to solve linear and nonlinear model predictive control (MPC) problems that requires small memory footprint and throughput and is particularly suitable when the model and/or controller parameters change at…

Networks with memristive elements (resistors with memory) are being explored for a variety of applications ranging from unconventional computing to models of the brain. However, analytical results that highlight the role of the graph…

Computationally efficient classification system architecture is proposed. It utilizes fast tensor-vector multiplication algorithm to apply linear operators upon input signals . The approach is applicable to wide variety of recognition…

Component separation is one of the key stages of any modern, cosmic microwave background (CMB) data analysis pipeline. It is an inherently non-linear procedure and typically involves a series of sequential solutions of linear systems with…

In breakthrough work, Tardos (Oper. Res. '86) gave a proximity based framework for solving linear programming (LP) in time depending only on the constraint matrix in the bit complexity model. In Tardos's framework, one reduces solving the…

We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes…

We revisit the classic combinatorial pattern matching problem of finding a longest common subsequence (LCS). For strings $x$ and $y$ of length $n$, a textbook algorithm solves LCS in time $O(n^2)$, but although much effort has been spent,…

Compute in-memory (CIM) is a promising technique that minimizes data transport, the primary performance bottleneck and energy cost of most data intensive applications. This has found wide-spread adoption in accelerating neural networks for…

Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…

Despite their tremendous success and versatility, Deep Neural Networks (DNNs) such as Large Language Models (LLMs) suffer from inference inefficiency and rely on advanced computational infrastructure. To address these challenges and make…

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…

Motivated by recent progress on symmetry breaking problems such as maximal independent set (MIS) and maximal matching in the low-memory Massively Parallel Computation (MPC) model (e.g., Behnezhad et al.~PODC 2019; Ghaffari-Uitto SODA 2019),…

Training and inference in Gaussian processes (GPs) require solving linear systems with $n\times n$ kernel matrices. To address the prohibitive $\mathcal{O}(n^3)$ time complexity, recent work has employed fast iterative methods, like…

Large, sparse linear systems are pervasive in modern science and engineering, and Krylov subspace solvers are an established means of solving them. Yet convergence can be slow for ill-conditioned matrices, so practical deployments usually…