Related papers: Compressed Matrix Computations
Many scientific applications opt for particles instead of meshes as their basic primitives to model complex systems composed of billions of discrete entities. Such applications span a diverse array of scientific domains, including molecular…
Data compression plays a key role in reducing storage and I/O costs. Traditional lossy methods primarily target data on rectilinear grids and cannot leverage the spatial coherence in unstructured mesh data, leading to suboptimal compression…
For minimization problems without 2nd derivative information, methods that estimate Hessian matrices can be very effective. However, conventional techniques generate dense matrices that are prohibitive for large problems. Limited-memory…
We explore an error-bounded lossy compression approach for reducing scientific data associated with 2D/3D unstructured meshes. While existing lossy compressors offer a high compression ratio with bounded error for regular grid data,…
Coupled decompositions are a widely used tool for data fusion. As the volume of data increases, so does the dimensionality of matrices and tensors, highlighting the need for more efficient coupled decomposition algorithms. This paper…
This paper presents error-bounded lossy compression tailored for particle datasets from diverse scientific applications in cosmology, fluid dynamics, and fusion energy sciences. As today's high-performance computing capabilities advance,…
While Deep Neural Networks (DNNs) push the state-of-the-art in many machine learning applications, they often require millions of expensive floating-point operations for each input classification. This computation overhead limits the…
A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation…
Efficient number representation is essential for federated learning, natural language processing, and network measurement solutions. Due to timing, area, and power constraints, such applications use narrow bit-width (e.g., 8-bit) number…
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…
Traditional optimization methods rely on the use of single-precision floating point arithmetic, which can be costly in terms of memory size and computing power. However, mixed precision optimization techniques leverage the use of both…
At the core of any inference procedure in deep neural networks are dot product operations, which are the component that require the highest computational resources. A common approach to reduce the cost of inference is to reduce its memory…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
Lossy compression is widely used to reduce storage and I/O costs for large-scale particle datasets in scientific applications such as cosmology, molecular dynamics, and fluid dynamics, where clustering structures (e.g., single-linkage or…
At the present scenario of the internet, there exist many optimization techniques to improve the Web speed but almost expensive in terms of bandwidth. So after a long investigation on different techniques to compress the data without any…
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…
A new approach to data compression is developed and applied to multimedia content. This method separates messages into components suitable for both lossless coding and 'lossy' or statistical coding techniques, compressing complex objects by…
Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction,…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
We propose basic and natural assumptions under which iterative optimization methods with compressed iterates can be analyzed. This problem is motivated by the practice of federated learning, where a large model stored in the cloud is…