Related papers: Deterministic and Probabilistic Rounding Error Ana…

Stochastic Rounding is a probabilistic rounding mode that is surprisingly effective in large-scale computations and low-precision arithmetic. Its random nature promotes error cancellation rather than error accumulation, resulting in slower…

The advent of data-driven real-time applications requires the implementation of Deep Neural Networks (DNNs) on Machine Learning accelerators. Google's Tensor Processing Unit (TPU) is one such neural network accelerator that uses systolic…

The growing demands of the worldwide IT infrastructure stress the need for reduced power consumption, which is addressed in so-called transprecision computing by improving energy efficiency at the expense of precision. For example, reducing…

Compression of floating-point data will play an important role in high-performance computing as data bandwidth and storage become dominant costs. Lossy compression of floating-point data is powerful, but theoretical results are needed to…

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

We consider the problem of precision matrix estimation where, due to extraneous confounding of the underlying precision matrix, the data are independent but not identically distributed. While such confounding occurs in many scientific…

Stochastic rounding (SR) is a probabilistic method used to round numbers to floating-point and fixed-point representations. In length $n$ summation, the worst-case error of SR grows as $\sqrt{n}$ with high probability, unlike for standard…

1) We introduce random discrete Morse theory as a computational scheme to measure the complicatedness of a triangulation. The idea is to try to quantify the frequence of discrete Morse matchings with a certain number of critical cells. Our…

In this paper, we use reduced precision checking (RPC) to detect errors in floating point arithmetic. Prior work explored RPC for addition and multiplication. In this work, we extend RPC to a complete floating point unit (FPU), including…

The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…

Randomized algorithms are overwhelming methods for low-rank approximation that can alleviate the computational expenditure with great reliability compared to deterministic algorithms. A crucial thought is generating a standard Gaussian…

Multi-target tracking (MTT) serves as a cornerstone technology in information fusion, yet faces significant challenges in robustness and efficiency when dealing with model uncertainties, clutter interference, and target interactions.…

The present research builds on a recently proposed spatial prediction method for discretized two-dimensional data, based on a suitably modified planar rotator (MPR) spin model from statistical physics. This approach maps the measured data…

Efficient mixed-precision matrix multiply accumulate (MMA) operations are critical for accelerating deep learning workloads on GPGPUs. However, existing open-source dot product implementations for Tensor Cores rely on discrete arithmetic…

Training of large-scale deep neural networks is often constrained by the available computational resources. We study the effect of limited precision data representation and computation on neural network training. Within the context of…

NVIDIA Tensor Cores and AMD Matrix Cores (together called Matrix Accelerators) are of growing interest in high-performance computing and machine learning owing to their high performance. Unfortunately, their numerical behaviors are not…

Finite-precision arithmetic computations face an inherent tradeoff between accuracy and efficiency. The points in this tradeoff space are determined, among other factors, by different data types but also evaluation orders. To put it simply,…

We introduce a novel algorithm that leverages stochastic sampling techniques to compute the perturbative triples correction in the coupled-cluster (CC) framework. By combining elements of randomness and determinism, our algorithm achieves a…

We present a second-order recursive Fermi-operator expansion scheme using mixed precision floating point operations to perform electronic structure calculations using tensor core units. A performance of over 100 teraFLOPs is achieved for…

We describe various issues caused by the lack of round-to-nearest mode in the \textit{gcc} compiler implementation of the fixed-point arithmetic data types and operations. We demonstrate that round-to-nearest is not performed in the…