Related papers: Customizing Number Representation and Precision

This invention addresses fixed-point representations of convolutional neural networks (CNN) in integrated circuits. When quantizing a CNN for a practical implementation there is a trade-off between the precision used for operations between…

Major advancements in building general-purpose and customized hardware have been one of the key enablers of versatility and pervasiveness of machine learning models such as deep neural networks. To sustain this ubiquitous deployment of…

Most state-of-the-art branch-and-bound solvers for mixed-integer linear programming rely on limited-precision floating-point arithmetic and use numerical tolerances when reasoning about feasibility and optimality during their search. While…

Modern computer architectures support low-precision arithmetic, which present opportunities for the adoption of mixed-precision algorithms to achieve high computational throughput and reduce energy consumption. As a growing number of…

Thanks to the computational power of modern cluster machines, numerical simulations can provide, with an unprecedented level of details, new insights into fluid mechanics. However, taking full advantage of this hardware remains challenging…

Methods for learning feature representations for Offline Handwritten Signature Verification have been successfully proposed in recent literature, using Deep Convolutional Neural Networks to learn representations from signature pixels. Such…

Low-precision formats have proven to be an efficient way to reduce not only the memory footprint but also the hardware resources and power consumption of deep learning computations. Under this premise, the posit numerical format appears to…

We give an exposition of Natural Topology (NToP), which highlights its advantages for exact computation. The NToP-definition of the real numbers (and continuous real functions) matches recent expert recommendations for exact real…

We investigate the use of half-precision floating-point numbers (FP16) in mixed-precision linear solvers for lattice QCD simulations. Since the emergence of GPUs for general-purpose, mixed-precision algorithms that combine single-precision…

Analog mixed-signal (AMS) devices promise faster, more energy-efficient deep neural network (DNN) inference than their digital counterparts. However, recent studies show that DNNs on AMS devices with fixed-point numbers can incur an…

Scientific computing programs often undergo aggressive compiler optimization to achieve high performance and efficient resource utilization. While performance is critical, we also need to ensure that these optimizations are correct. In this…

The problem of exactly summing n floating-point numbers is a fundamental problem that has many applications in large-scale simulations and computational geometry. Unfortunately, due to the round-off error in standard floating-point…

With the increasing application of machine learning (ML) algorithms in embedded systems, there is a rising necessity to design low-cost computer arithmetic for these resource-constrained systems. As a result, emerging models of computation,…

Deep neural networks have enabled progress in a wide variety of applications. Growing the size of the neural network typically results in improved accuracy. As model sizes grow, the memory and compute requirements for training these models…

Diffusion models are emerging models that generate images by iteratively denoising random Gaussian noise using deep neural networks. These models typically exhibit high computational and memory demands, necessitating effective post-training…

From a theoretical point of view, finding the solution set of a system of inequalities in only two variables is easy. However, if we want to get rigorous bounds on this set with floating point arithmetic, in all possible cases, then things…

Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularization is typically necessary to ensure accurate and stable…

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 consider the problem of accurate computation of the finite difference $f(\x+\s)-f(\x)$ when $\Vert\s\Vert$ is very small. Direct evaluation of this difference in floating point arithmetic succumbs to cancellation error and yields 0 when…

Fast Fourier Transform (FFT) is an essential tool in scientific and engineering computation. The increasing demand for mixed-precision FFT has made it possible to utilize half-precision floating-point (FP16) arithmetic for faster speed and…