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Currently, the dominating constraint in many high performance computing applications is data capacity and bandwidth, in both inter-node communications and even more-so in on-node data motion. A new approach to address this limitation is to…
This research investigates using a mixed-precision iterative refinement method using posit numbers instead of the standard IEEE floating-point format. The method is applied to solve a general linear system represented by the equation $Ax =…
Boundary element methods for the Helmholtz equation lead to large dense matrices that can only be handled if efficient compression techniques are used. Directional compression techniques can reach good compression rates even for…
In this thesis, we describe a new, practical approach to integrating hardware-based data compression within the memory hierarchy, including on-chip caches, main memory, and both on-chip and off-chip interconnects. This new approach is fast,…
Sequence model based NLP applications can be large. Yet, many applications that benefit from them run on small devices with very limited compute and storage capabilities, while still having run-time constraints. As a result, there is a need…
Many common types of data can be represented as functions that map coordinates to signal values, such as pixel locations to RGB values in the case of an image. Based on this view, data can be compressed by overfitting a compact neural…
Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statis- tics face tremendous challenges due to the prohibitive…
Weighted low rank approximation (WLRA) is an important yet computationally challenging primitive with applications ranging from statistical analysis, model compression, and signal processing. To cope with the NP-hardness of this problem,…
Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…
Reduced-rank decompositions provide descriptions of the variation among the elements of a matrix or array. In such decompositions, the elements of an array are expressed as products of low-dimensional latent factors. This article presents a…
The singular value decomposition is widely used to approximate data matrices with lower rank matrices. Feng and He [Ann. Appl. Stat. 3 (2009) 1634-1654] developed tests on dimensionality of the mean structure of a data matrix based on the…
One of the main difficulties of scaling current localization systems to large environments is the on-board storage required for the maps. In this paper we propose to learn to compress the map representation such that it is optimal for the…
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…
Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…
Binarization is an extreme network compression approach that provides large computational speedups along with energy and memory savings, albeit at significant accuracy costs. We investigate the question of where to binarize inputs at…
Despite their high accuracy, complex neural networks demand significant computational resources, posing challenges for deployment on resource constrained devices such as mobile phones and embedded systems. Compression algorithms have been…
Low-rank matrix approximation is one of the central concepts in machine learning, with applications in dimension reduction, de-noising, multivariate statistical methodology, and many more. A recent extension to LRMA is called low-rank…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
We consider the problem of approximating an affinely structured matrix, for example a Hankel matrix, by a low-rank matrix with the same structure. This problem occurs in system identification, signal processing and computer algebra, among…
Images are a substantial portion of the internet, making efficient compression important for reducing storage and bandwidth demands. This study investigates the use of Singular Value Decomposition and low-rank matrix approximations for…