Related papers: Arbitrarily Substantial Number Representation for …
Partial differential equations have a wide range of applications in modeling multiple physical, biological, or social phenomena. Therefore, we need to approximate the solutions of these equations in computationally feasible terms. Nowadays,…
This paper introduces the Adaptive Base Representation (ABR) Theorem and proposes a novel number system that offers a structured alternative to the binary number system for digital computers. The ABR number system enables each decimal…
In this paper an extension of the sparse decomposition problem is considered and an algorithm for solving it is presented. In this extension, it is known that one of the shifted versions of a signal s (not necessarily the original signal…
How best to quantify the information of an object, whether natural or artifact, is a problem of wide interest. A related problem is the computability of an object. We present practical examples of a new way to address this problem. By…
Many NP-complete problems take integers as part of their input instances. These input integers are generally binarized, that is, provided in the form of the "binary" numeral representation, and the lengths of such binary forms are used as a…
How much can pruning algorithms teach us about the fundamentals of learning representations in neural networks? And how much can these fundamentals help while devising new pruning techniques? A lot, it turns out. Neural network pruning has…
NLP systems rarely give special consideration to numbers found in text. This starkly contrasts with the consensus in neuroscience that, in the brain, numbers are represented differently from words. We arrange recent NLP work on numeracy…
Recently the authors presented a matrix representation approach to real Appell polynomials essentially determined by a nilpotent matrix with natural number entries. It allows to consider a set of real Appell polynomials as solution of a…
This paper advocates the use of complex variables to represent votes in the Hough transform for circle detection. Replacing the positive numbers classically used in the parameter space of the Hough transforms by complex numbers allows…
How data is represented and operationalized is critical for building computational solutions that are both effective and efficient. A common approach is to represent data objects as binary vectors, denoted \textit{hash codes}, which require…
Anomalous cancellation of fractions is a mathematically inaccurate method where cancelling the common digits of the numerator and denominator correctly reduces it. While it appears to be accidentally successful, the property of anomalous…
Developing meaningful and efficient representations that separate the fundamental structure of the data generation mechanism is crucial in representation learning. However, Disentangled Representation Learning has not fully shown its…
We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative…
Despite the frequent challenges posed by ambiguity when representing meaning via natural language, it is often ignored or deliberately removed in tasks mapping language to formally-designed representations, which generally assume a…
Literature considers under the name \emph{unimaginable numbers} any positive integer going beyond any physical application, with this being more of a vague description of what we are talking about rather than an actual mathematical…
Probabilistic numerics casts numerical tasks, such the numerical solution of differential equations, as inference problems to be solved. One approach is to model the unknown quantity of interest as a random variable, and to constrain this…
Previous studies have found that an adversary attacker can often infer unintended input information from intermediate-layer features. We study the possibility of preventing such adversarial inference, yet without too much accuracy…
For a real function, automatic differentiation is such a standard algorithm used to efficiently compute its gradient, that it is integrated in various neural network frameworks. However, despite the recent advances in using complex…
Unsupervised extraction of objects from low-level visual data is an important goal for further progress in machine learning. Existing approaches for representing objects without labels use structured generative models with static images.…
Throughout history, recreational mathematics has always played a prominent role in advancing research. Following in this tradition, in this paper we extend some recent work with crazy sequential representations of numbers- equations made of…