Related papers: Precision-aware Deterministic and Probabilistic Er…
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 mechanize the fundamental properties of a rounding error model for floating-point arithmetic based on relative precision, a measure of error proposed as a substitute for relative error in rounding error analysis. A key property of…
For scientific computations on a digital computer the set of real number is usually approximated by a finite set F of "floating-point" numbers. We compare the numerical accuracy possible with difference choices of F having approximately the…
In basic computational physics classes, students often raise the question of how to compute a number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical…
This paper presents a deterministic algorithmic approach of exploring the solution space of the Subset Sum Problem. The algorithm presented is input-robust and structurally adaptive. Exploration is guided and narrows into areas in the…
When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship…
Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify…
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…
The use of reduced and mixed precision computing has gained increasing attention in high-performance computing (HPC) as a means to improve computational efficiency, particularly on modern hardware architectures like GPUs. In this work, we…
In this paper, we improve the usual relative error bound for the computation of x^n through iterated multiplications by x in binary floating-point arithmetic. The obtained error bound is only slightly better than the usual one, but it is…
With the increasing complexity of machine learning models, managing computational resources like memory and processing power has become a critical concern. Mixed precision techniques, which leverage different numerical precisions during…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…
In this paper, we study the accuracy of values aggregated over classes predicted by a classification algorithm. The problem is that the resulting aggregates (e.g., sums of a variable) are known to be biased. The bias can be large even for…
We introduce data structures and algorithms to count numerical inaccuracies arising from usage of floating numbers described in IEEE 754. Here we describe how to estimate precision for some collection of functions most commonly used for…
We describe algorithms and data structures to extend a neural network library with automatic precision estimation for floating point computations. We also discuss conditions to make estimations exact and preserve high computation…
Automated techniques for rigorous floating-point round-off error analysis are important in areas including formal verification of correctness and precision tuning. Existing tools and techniques, while providing tight bounds, fail to analyze…
Online learning methods yield sequential regret bounds under minimal assumptions and provide in-expectation risk bounds for statistical learning. However, despite the apparent advantage of online guarantees over their statistical…
IIn computational geometry, the construction of essential primitives like convex hulls, Voronoi diagrams and Delaunay triangulations require the evaluation of the signs of determinants, which are sums of products. The same signs are needed…
Numerical data processing is a key task across different fields of computer technology use. However, even simple summation of values is not precise due to the floating point representation use. This paper presents a practical algorithm for…
Belief updating in Bayes nets, a well known computationally hard problem, has recently been approximated by several deterministic algorithms, and by various randomized approximation algorithms. Deterministic algorithms usually provide…