Related papers: Compressed Modular Matrix Multiplication
Quantum-dot cellular automata (QCA) shows promise as a post silicon CMOS, low power computational technology. Nevertheless, to generalize QCA for next-generation digital devices, the ability to implement conventional programmable circuits…
Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor…
Scientific computations or measurements may result in huge volumes of data. Often these can be thought of representing a real-valued function on a high-dimensional domain, and can be conceptually arranged in the format of a tensor of high…
The problem of distributed matrix multiplication with straggler tolerance over finite fields is considered, focusing on field sizes for which previous solutions were not applicable (for instance, the field of two elements). We employ…
A variety of large-scale machine learning problems can be cast as instances of constrained submodular maximization. Existing approaches for distributed submodular maximization have a critical drawback: The capacity - number of instances…
We analyze the grammar generation algorithm of the RePair compression algorithm and show the relation between a grammar generated by RePair and maximal repeats. We reveal that RePair replaces step by step the most frequent pairs within the…
Sparse matrix multiplication is an important component of linear algebra computations. Implementing sparse matrix multiplication on an associative processor (AP) enables high level of parallelism, where a row of one matrix is multiplied in…
The complexity of matrix multiplication (hereafter MM) has been intensively studied since 1969, when Strassen surprisingly decreased the exponent 3 in the cubic cost of the straightforward classical MM to log 2 (7) $\approx$ 2.8074.…
An alternative to the matrix inverse procedure is presented. Given a bit register which is arbitrarily large, the matrix inverse to an arbitrarily large matrix can be peformed in ${\cal O}(N^2)$ operations, and to matrix multiplication on a…
We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows…
We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…
Storage systems often rely on multiple copies of the same compressed data, enabling recovery in case of binary data errors, of course, at the expense of a higher storage cost. In this paper we show that a wiser method of duplication entails…
Let $a,k\in\mathbb{N}$. For the $k-1$-th iterate of the exponential function $x\mapsto a^x$, also known as tetration, we write \[ ^k a:=a^{a^{.^{.^{.^{a}}}}}. \] In this paper, we show how an efficient algorithm for tetration modulo natural…
This paper presents arithmetic operations like addition, subtraction and multiplications in Modulo-4 arithmetic, and also addition, multiplication in Galois field, using multi-valued logic (MVL). Quaternary to binary and binary to…
Digital System Research has pioneered the mathematics and design for a new class of computing machine using residue numbers. Unlike prior art, the new breakthrough provides methods and apparatus for general purpose computation using several…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization…
Closed-form generating functions for counting one-face rooted hypermaps with a known number of darts by number of vertices and edges is found, using matrix integral expressions relating to the reduced density operator of a bipartite quantum…
We consider the problem of multiplying sparse matrices (over a semiring) where the number of non-zero entries is larger than main memory. In the classical paper of Hong and Kung (STOC '81) it was shown that to compute a product of dense $U…
Polynomial multiplication is known to have quasi-linear complexity in both the dense and the sparse cases. Yet no truly linear algorithm has been given in any case for the problem, and it is not clear whether it is even possible. This…
Binary quantization approaches, which replace weight matrices with binary matrices and substitute costly multiplications with cheaper additions, offer a computationally efficient approach to address the increasing computational and storage…