Related papers: Balancing Inexactness in Mixed Precision Matrix Co…

Hierarchical matrix computations have attracted significant attention in the science and engineering community as exploiting data-sparse structures can significantly reduce the computational complexity of many important kernels. One…

Matrix seriation, the problem of permuting the rows and columns of a matrix to uncover latent structure, is a fundamental technique in data science, particularly in the visualization and analysis of relational data. Applications span…

Matrix multiplication is a fundamental operation in both training of neural networks and inference. To accelerate matrix multiplication, Graphical Processing Units (GPUs) provide it implemented in hardware. Due to the increased throughput…

Machine learning for molecular property prediction has focused largely on pure compounds, even though many practical applications depend on mixtures with intermolecular interactions. Recent work has expanded the availability of mixture…

Our interest lies in the robust and efficient solution of large sparse linear least-squares problems. In recent years, hardware developments have led to a surge in interest in exploiting mixed precision arithmetic within numerical linear…

Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time…

Neural network quantization is frequently used to optimize model size, latency and power consumption for on-device deployment of neural networks. In many cases, a target bit-width is set for an entire network, meaning every layer get…

Inaccurate circuits make possible the conservation of limited resources, such as energy. But effective design of such circuits requires an understanding of resulting tradeoffs between accuracy and design parameters, such as voltages and…

Modern technologies are generating ever-increasing amounts of data. Making use of these data requires methods that are both statistically sound and computationally efficient. Typically, the statistical and computational aspects are treated…

Accuracy-driven computation is a strategy widely used in exact-decisions number types for robust geometric algorithms. This work provides an overview on the usage of error bounds in accuracy-driven computation, compares different approaches…

With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the…

We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…

We present a scheme to automatically set the precision of floating point variables in an application. We design a framework that profiles applications to measure undesirable numerical behavior at the floating point operation level. We use…

In recent years, a new kind of accelerated hardware has gained popularity in the Artificial Intelligence (AI) and Machine Learning (ML) communities which enables extremely high-performance tensor contractions in reduced precision for deep…

Matrix concentration inequalities and their recently discovered sharp counterparts provide powerful tools to bound the spectrum of random matrices whose entries are linear functions of independent random variables. However, in many…

Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…

Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…

Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…

We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…

A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid excessive rounding error propagation of conventional…