Related papers: Compressed Matrix Computations
Most data is automatically collected and only ever "seen" by algorithms. Yet, data compressors preserve perceptual fidelity rather than just the information needed by algorithms performing downstream tasks. In this paper, we characterize…
Today's scientific simulations, for example in the high-performance exascale sector, produce huge amounts of data. Due to limited I/O bandwidth and available storage space, there is the necessity to reduce scientific data of high…
Statistical computations are becoming increasingly important. These computations often need to be performed in log-space because probabilities become extremely small due to repeated multiplications. While using logarithms effectively…
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…
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…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
We describe a compression method for floating-point astronomical images that gives compression ratios of 6 -- 10 while still preserving the scientifically important information in the image. The pixel values are first preprocessed by…
In scientific fields such as quantum computing, physics, chemistry, and machine learning, high dimensional data are typically represented using sparse tensors. Tensor contraction is a popular operation on tensors to exploit meaning or alter…
Advanced algorithms for large-scale electronic structure calculations are mostly based on processing multi-dimensional sparse data. Examples are sparse matrix-matrix multiplications in linear-scaling Kohn-Sham calculations or the efficient…
We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
Cost-efficient compressive sensing is challenging when facing large-scale data, {\em i.e.}, data with large sizes. Conventional compressive sensing methods for large-scale data will suffer from low computational efficiency and massive…
Today's exponentially increasing data volumes and the high cost of storage make compression essential for the Big Data industry. Although research has concentrated on efficient compression, fast decompression is critical for analytics…
The computation of a matrix function $f(A)$ is an important task in scientific computing appearing in machine learning, network analysis and the solution of partial differential equations. In this work, we use only matrix-vector products…
The use of low-precision fixed-point arithmetic along with stochastic rounding has been proposed as a promising alternative to the commonly used 32-bit floating point arithmetic to enhance training neural networks training in terms of…
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…
The computation of scientific data can be very time consuming even if they are ultimately determined by a small number of parameters. The principle of compressed sampling suggests that we can achieve a considerable decrease in the…
Increasing data volumes from scientific simulations and instruments (supercomputers, accelerators, telescopes) often exceed network, storage, and analysis capabilities. The scientific community's response to this challenge is scientific…
This paper presents a new algorithm for the lossy compression of scalar data defined on 2D or 3D regular grids, with topological control. Certain techniques allow users to control the pointwise error induced by the compression. However, in…
The torrential influx of floating-point data from domains like IoT and HPC necessitates high-performance lossless compression to mitigate storage costs while preserving absolute data fidelity. Leveraging GPU parallelism for this task…