Related papers: How to Fake Multiply by a Gaussian Matrix

The textbook algorithm for single-source shortest paths with real-valued edge weights runs in $O(m n)$ time on a graph with $m$ edges and $n$ vertices. A recent breakthrough algorithm by Fineman [Fin24] takes $\tilde O(m n^{8/9})$…

Inspired by a recent paper of I. Grama, E. Le Page and M. Peign\'e, we consider a sequence $(g_n)_{n \geq 1}$ of i.i.d. random $d\times d$-matrices with non-negative entries and study the fluctuations of the process $(\log \vert g_n\cdots…

We consider the spectrum of additive, polynomially vanishing random perturbations of deterministic matrices, as follows. Let $M_N$ be a deterministic $N\times N$ matrix, and let $G_N$ be a complex Ginibre matrix. We consider the matrix…

We use lookup tables to design faster algorithms for important algebraic problems over finite fields. These faster algorithms, which only use arithmetic operations and lookup table operations, may help to explain the difficulty of…

Given a matrix A \in R^{m x n}, we present a randomized algorithm that sparsifies A by retaining some of its elements by sampling them according to a distribution that depends on both the square and the absolute value of the entries. We…

In a recent work we presented a recursive algorithm to compute the matrix elements of a generic Gaussian transformation in the photon-number basis. Its purpose was to evolve a quantum state by building the transformation matrix and…

This paper proposes new factorizations for computing the Neumann series. The factorizations are based on fast algorithms for small prime sizes series and the splitting of large sizes into several smaller ones. We propose a different basis…

In this paper, we present algorithms to solve matrix multiplication problems in the MPC model. In particular, we consider the problem under various processor/memory constraints in the MPC model and prove the following results. 1.…

Given a time-evolving tensor with missing entries, how can we effectively factorize it for precisely predicting the missing entries? Tensor factorization has been extensively utilized for analyzing various multi-dimensional real-world data.…

We exploit the truncated singular value decomposition and the recently proposed circulant decomposition for an efficient first-order approximation of the multiplication of large dense matrices. A decomposition of each matrix into a sum of a…

Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…

Let $R_n$ be a $n \times n$ random matrix with i.i.d. subgaussian entries. Let $M$ be a $n \times n$ deterministic matrix with norm $\lVert M \rVert \le n^\gamma$ where $1/2<\gamma<1$. The goal of this paper is to give a general estimate of…

We present a technique for significantly speeding up Alternating Least Squares (ALS) and Gradient Descent (GD), two widely used algorithms for tensor factorization. By exploiting properties of the Khatri-Rao product, we show how to…

Non-negative matrix factorization (NMF) has become a popular machine learning approach to many problems in text mining, speech and image processing, bio-informatics and seismic data analysis to name a few. In NMF, a matrix of non-negative…

In the total least squares problem, one is given an $m \times n$ matrix $A$, and an $m \times d$ matrix $B$, and one seeks to "correct" both $A$ and $B$, obtaining matrices $\hat{A}$ and $\hat{B}$, so that there exists an $X$ satisfying the…

This paper presents an efficient method for implementing the Gaussian elimination technique for an nxm (m>=n) matrix, using a 2D SIMD array of nxm processors. The described algorithm consists of 2xn-1=O(n) iterations, which provides an…

This paper introduces the Gaussian multi-Graphical Model, a model to construct sparse graph representations of matrix- and tensor-variate data. We generalize prior work in this area by simultaneously learning this representation across…

Let $G$ be an $N \times N$ real matrix whose entries are independent identically distributed standard normal random variables $G_{ij} \sim \mathcal{N}(0,1)$. The eigenvalues of such matrices are known to form a two-component system…

Let $\mathcal{M}$ be a smooth $d$-dimensional submanifold of $\mathbb{R}^N$ with boundary that's equipped with the Euclidean (chordal) metric, and choose $m \leq N$. In this paper we consider the probability that a random matrix $A \in…

Given an $n$-vertex $m$-edge digraph $G = (V,E)$ and a subset $S \subseteq V$ of $|S| = n^{\sigma}$ (for some $0 \le \sigma \le 1$) designated sources, the $S \times V$ reachability problem is to compute the sets $\mathcal V_s$ of vertices…