Related papers: On the Significance of Digits in Interval Notation
The interplay of optimizers and architectures in neural networks is complicated and hard to understand why some optimizers work better on some specific architectures. In this paper, we find that the traditionally used sharpness metric does…
Statistical depth measures the centrality of a point with respect to a given distribution or data cloud. It provides a natural center-outward ordering of multivariate data points and yields a systematic nonparametric multivariate analysis…
The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…
Definition of the number of prime numbers in the given interval
Quantifying errors and losses due to the use of Floating-Point (FP) calculations in industrial scientific computing codes is an important part of the Verification, Validation and Uncertainty Quantification (VVUQ) process. Stochastic…
We present information value, a measure which quantifies the predictability of an utterance relative to a set of plausible alternatives. We introduce a method to obtain interpretable estimates of information value using neural text…
The field of computational complexity is concerned both with the intrinsic hardness of computational problems and with the efficiency of algorithms to solve them. Given such a problem, normally one designs an algorithm to solve it and sets…
Language models struggle with handling numerical data and performing arithmetic operations. We hypothesize that this limitation can be partially attributed to non-intuitive textual numbers representation. When a digit is read or generated…
Confidence intervals provide a way to determine plausible values for a population parameter. They are omnipresent in research articles involving statistical analyses. Appropriately, a key statistical literacy learning objective is the…
We address the task of identifying anomalous observations by analyzing digits under the lens of Benford's law. Motivated by the crucial objective of providing reliable statistical analysis of customs declarations, we answer one major and…
We propose here a number of approaches to implement constraint propagation for arithmetic constraints on integer intervals. To this end we introduce integer interval arithmetic. Each approach is explained using appropriate proof rules that…
Digital System Research has pioneered the mathematics and design for a new class of computing machine using residue numbers. Unlike prior art, the new breakthrough provides methods and apparatus for general purpose computation using several…
We describe a new algorithm for calculating the topological degree deg (f, B, 0) where B \subseteq Rn is a product of closed real intervals and f : B \rightarrow Rn is a real-valued continuous function given in the form of arithmetical…
All data are digitized, and hence are essentially integers rather than true real numbers. Ordinarily this causes no difficulties since the truncation or rounding usually occurs below the noise level. However, in some instances, when the…
Convergence bounds are one of the main tools to obtain information on the performance of a distributed machine learning task, before running the task itself. In this work, we perform a set of experiments to assess to which extent, and in…
Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all.…
Differentiation is a cornerstone of computing and data analysis in every discipline of science and engineering. Indeed, most fundamental physics laws are expressed as relationships between derivatives in space and time. However, derivatives…
The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…
Many AI researchers argue that probability theory is only capable of dealing with uncertainty in situations where a full specification of a joint probability distribution is available, and conclude that it is not suitable for application in…
The signal to noise ratio, which plays such an important role in information theory, is shown to become pointless in digital communications where - symbols are modulating carriers, which are solutions of linear differential equations with…