Related papers: Efficient Mixed-Precision Matrix Factorization of …
Solving and visualizing the potential roots of complex functions is essential in both theoretical and applied domains, yet often computationally intensive. We present a hardware-accelerated algorithm for complex function roots density graph…
Architectures with multiple classes of memory media are becoming a common part of mainstream supercomputer deployments. So called multi-level memories offer differing characteristics for each memory component including variation in…
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…
Firms earning prediction plays a vital role in investment decisions, dividends expectation, and share price. It often involves multiple tensor-compatible datasets with non-linear multi-way relationships, spatiotemporal structures, and…
Deep neural networks employ specialized architectures for vision, sequential and language tasks, yet this proliferation obscures their underlying commonalities. We introduce a unified matrix-order framework that casts convolutional,…
Factorization and multiplication of dense matrices and tensors are critical, yet extremely expensive pieces of the scientific toolbox. Careful use of low rank approximation can drastically reduce the computation and memory requirements of…
In todays world, high-power computing applications such as image processing, digital signal processing, graphics, and robotics require enormous computing power. These applications use matrix operations, especially matrix multiplication.…
The evolution of quantization and mixed-precision techniques has unlocked new possibilities for enhancing the speed and energy efficiency of NNs. Several recent studies indicate that adapting precision levels across different parameters can…
Hardware accelerations of deep learning systems have been extensively investigated in industry and academia. The aim of this paper is to achieve ultra-high energy efficiency and performance for hardware implementations of deep neural…
We develop quaternion--native iterative methods for computing the Moore--Penrose (MP) pseudoinverse of quaternion matrices and analyze their convergence. Our starting point is a damped Newton--Schulz (NS) iteration tailored to…
Deploying mixed-precision neural networks on edge devices is friendly to hardware resources and power consumption. To support fully mixed-precision neural network inference, it is necessary to design flexible hardware accelerators for…
Matrix completion constantly receives tremendous attention from many research fields. It is commonly applied for recommender systems such as movie ratings, computer vision such as image reconstruction or completion, multi-task learning such…
This study was aimed at simultaneously achieving sufficient accuracy and high performance for general matrix multiplications. Recent architectures, such as NVIDIA GPUs, feature high-performance units designed for low-precision matrix…
In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
In this paper we propose a mixed precision algorithm in the context of the semi-Lagrangian discontinuous Galerkin method. The performance of this approach is evaluated on a traditional dual socket workstation as well as on a Xeon Phi and an…
We have repurposed Google Tensor Processing Units (TPUs), application-specific chips developed for machine learning, into large-scale dense linear algebra supercomputers. The TPUs' fast inter-core interconnects (ICI)s, physically…
Standard rank-revealing factorizations such as the singular value decomposition and column pivoted QR factorization are challenging to implement efficiently on a GPU. A major difficulty in this regard is the inability of standard algorithms…
How can we compute the pseudoinverse of a sparse feature matrix efficiently and accurately for solving optimization problems? A pseudoinverse is a generalization of a matrix inverse, which has been extensively utilized as a fundamental…
The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer…