Related papers: Computable Compressed Matrices
Graphics Processing Units (GPUs) were once used solely for graphical computation tasks but with the increase in the use of machine learning applications, the use of GPUs to perform general-purpose computing has increased in the last few…
Sequential computation is well understood but does not scale well with current technology. Within the next decade, systems will contain large numbers of processors with potentially thousands of processors per chip. Despite this, many…
Multiplying matrices is among the most fundamental and compute-intensive operations in machine learning. Consequently, there has been significant work on efficiently approximating matrix multiplies. We introduce a learning-based algorithm…
Molecular dynamics simulations yield large amounts of trajectory data. For their durable storage and accessibility an efficient compression algorithm is paramount. State of the art domain-specific algorithms combine quantization, Huffman…
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…
Nowadays, the compression performance of neural-networkbased image compression algorithms outperforms state-of-the-art compression approaches such as JPEG or HEIC-based image compression. Unfortunately, most neural-network based compression…
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…
We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo. Modular Multiplication is not directly…
Directional interpolation is a fast and efficient compression technique for high-frequency Helmholtz boundary integral equations, but it requires a very large amount of storage in its original form. Algebraic recompression can significantly…
We develop and implement in this paper a fast sparse assembly algorithm, the fundamental operation which creates a compressed matrix from raw index data. Since it is often a quite demanding and sometimes critical operation, it is of…
Sorting is a fundamental operation across numerous computational domains. Traditionally, this process involves transferring data from main memory to a processing unit for sorting, followed by writing the sorted data back to memory. This…
This work focuses on reducing neural network size, which is a major driver of neural network execution time, power consumption, bandwidth, and memory footprint. A key challenge is to reduce size in a manner that can be exploited readily for…
Patch-based relaxation refers to a family of methods for solving linear systems which partitions the matrix into smaller pieces often corresponding to groups of adjacent degrees of freedom residing within patches of the computational…
Many emerging computer applications require the processing of large numbers, larger than what a CPU can handle. In fact, the top of the line PCs can only manipulate numbers not longer than 32 bits or 64 bits. This is due to the size of the…
Modern data compression methods are slowly reaching their limits after 80 years of research, millions of papers, and wide range of applications. Yet, the extravagant 6G communication speed requirement raises a major open question for…
We present memory-efficient and scalable algorithms for kernel methods used in machine learning. Using hierarchical matrix approximations for the kernel matrix the memory requirements, the number of floating point operations, and the…
Dense linear layers are the dominant computational bottleneck in foundation models. Identifying more efficient alternatives to dense matrices has enormous potential for building more compute-efficient models, as exemplified by the success…
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.…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
Large-sample data became prevalent as data acquisition became cheaper and easier. While a large sample size has theoretical advantages for many statistical methods, it presents computational challenges. Sketching, or compression, is a…