Related papers: Compressed Modular Matrix Multiplication
To alleviate the problem of information explosion, recommender systems are widely deployed to provide personalized information filtering services. Usually, embedding tables are employed in recommender systems to transform high-dimensional…
Motivated by applications in machine learning, such as subset selection and data summarization, we consider the problem of maximizing a monotone submodular function subject to mixed packing and covering constraints. We present a tight…
The modular composite representation (MCR) is a computing model that represents information with high-dimensional integer vectors using modular arithmetic. Originally proposed as a generalization of the binary spatter code model, it aims to…
This article describes lossless compression algorithms for multisets of sequences, taking advantage of the multiset's unordered structure. Multisets are a generalisation of sets where members are allowed to occur multiple times. A multiset…
The ability to find short representations, i.e. to compress data, is crucial for many intelligent systems. We present a theory of incremental compression showing that arbitrary data strings, that can be described by a set of features, can…
A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector is proposed. The method is based on factorization of a tensor and using the factors for building computational structures performing fast…
Two decades ago, a breakthrough in indexing string collections made it possible to represent them within their compressed space while at the same time offering indexed search functionalities. As this new technology permeated through…
Compressing integer keys is a fundamental operation among multiple communities, such as database management (DB), information retrieval (IR), and high-performance computing (HPC). Recent advances in \emph{learned indexes} have inspired the…
Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…
Efficiently processing basic linear algebra subroutines is of great importance for a wide range of computational problems. In this paper, we consider techniques to implement matrix functions on a quantum computer, which are composed of…
In neural network-based models for natural language processing (NLP), the largest part of the parameters often consists of word embeddings. Conventional models prepare a large embedding matrix whose size depends on the vocabulary size.…
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…
We consider the problem of producing compact architectures for text classification, such that the full model fits in a limited amount of memory. After considering different solutions inspired by the hashing literature, we propose a method…
Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…
The BMR16 circuit garbling scheme introduces gadgets that allow for ciphertext-free modular addition, while the multiplication of private inputs modulo a prime p can be done with 2(p - 1) ciphertexts as described in Malkin, Pastro, and…
This article presents a vertical multiplication formula for calculating the multiplication of any two multi-digit integers, which may be not only used to design the multiplier but also to the mental multiplication. Our algorithm is a…
Accelerators for sparse matrix multiplication are important components in emerging systems. In this paper, we study the main challenges of accelerating Sparse Matrix Multiplication (SpMM). For the situations that data is not stored in the…
Today's PCs can directly manipulate numbers not longer than 64 bits because the size of the CPU registers and the data-path are limited. Consequently, arithmetic operations such as addition, can only be performed on numbers of that length.…
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 tight $\Omega((n/\sqrt{M})^{\log_2 7}M)$ lower bound is derived on the \io complexity of Strassen's algorithm to multiply two $n \times n$ matrices, in a two-level storage hierarchy with $M$ words of fast memory. A proof technique is…