Related papers: Matrix Multiplication and Number On the Forehead C…
We show how to construct highly symmetric algorithms for matrix multiplication. In particular, we consider algorithms which decompose the matrix multiplication tensor into a sum of rank-1 tensors, where the decomposition itself consists of…
Reducing communication - either between levels of a memory hierarchy or between processors over a network - is a key component of performance optimization (in both time and energy) for many problems, including dense linear algebra, particle…
Algebraic matrix multiplication algorithms are designed by bounding the rank of matrix multiplication tensors, and then using a recursive method. However, designing algorithms in this way quickly leads to large constant factors: if one…
In 1981 Hong and Kung proved a lower bound on the amount of communication needed to perform dense, matrix-multiplication using the conventional $O(n^3)$ algorithm, where the input matrices were too large to fit in the small, fast memory. In…
We study an information-structure design problem (a.k.a. persuasion) with a single sender and multiple receivers with actions of a priori unknown types, independently drawn from action-specific marginal distributions. As in the standard…
Fast matrix multiplication can be described as searching for low-rank decompositions of the matrix--multiplication tensor. We design a neural architecture, \textsc{StrassenNet}, which reproduces the Strassen algorithm for $2\times 2$…
We give lower bounds on the communication complexity required to solve several computational problems in a distributed-memory parallel machine, namely standard matrix multiplication, stencil computations, comparison sorting, and the Fast…
In this article, we focus on the parallel communication cost of multiplying the same vector along two modes of a $3$-dimensional symmetric tensor. This is a key computation in the higher-order power method for determining eigenpairs of a…
Lifting theorems are one of the most powerful tools for proving communication lower bounds, with numerous downstream applications in proof complexity, monotone circuit lower bounds, data structures, and combinatorial optimization. However,…
Matrix multiplication (hereafter we use the acronym MM) is among the most fundamental operations of modern computations. The efficiency of its performance depends on various factors, in particular vectorization, data movement and arithmetic…
Multiplication is a fundamental operation in many applications, and multipliers are widely adopted in various circuits. However, optimizing multipliers is challenging due to the extensive design space. In this paper, we propose a multiplier…
Tensor operations, such as matrix multiplication, are central to large-scale machine learning applications. For user-driven tasks these operations can be carried out on a distributed computing platform with a master server at the user side…
A subset of the integer planar grid $[N] \times [N]$ is called corner-free if it contains no triple of the form $(x,y), (x+\delta,y), (x,y+\delta)$. It is known that such a set has a vanishingly small density, but how large this density can…
We study sequential language games in which two players, each with private information, communicate to achieve a common goal. In such games, a successful player must (i) infer the partner's private information from the partner's messages,…
We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different…
Determining the asymptotic algebraic complexity of matrix multiplication, succinctly represented by the matrix multiplication exponent $\omega$, is a central problem in algebraic complexity theory. The best upper bounds on $\omega$, leading…
Hella et al. (PODC 2012, Distributed Computing 2015) identified seven different models of distributed computing - one of which is the port-numbering model - and provided a complete classification of their computational power relative to…
This paper deals with distributed matrix multiplication. Each player owns only one row of both matrices and wishes to learn about one distinct row of the product matrix, without revealing its input to the other players. We first improve on…
We study nondeterministic multiparty quantum communication with a quantum generalization of broadcasts. We show that, with number-in-hand classical inputs, the communication complexity of a Boolean function in this communication model…
Naming game simulates the process of naming an objective by a population of agents organized in a certain communication network topology. By pair-wise iterative interactions, the population reaches a consensus state asymptotically. In this…