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Exploring the impact of post-training rounding in regression models

Jan Kalina (2024)

Applications of Mathematics

Post-training rounding, also known as quantization, of estimated parameters stands as a widely adopted technique for mitigating energy consumption and latency in machine learning models. This theoretical endeavor delves into the examination of the impact of rounding estimated parameters in key regression methods within the realms of statistics and machine learning. The proposed approach allows for the perturbation of parameters through an additive error with values within a specified interval. This...

Extended Ramsey theory for words representing rationals

Vassiliki Farmaki, Andreas Koutsogiannis (2013)

Fundamenta Mathematicae

Ramsey theory for words over a finite alphabet was unified in the work of Carlson, who also presented a method to extend the theory to words over an infinite alphabet, but subject to a fixed dominating principle. In the present work we establish an extension of Carlson's approach to countable ordinals and Schreier-type families developing an extended Ramsey theory for dominated words over a doubly infinite alphabet (in fact for ω-ℤ*-located words), and we apply this theory, exploiting the Budak-Işik-Pym...

Extending Full Text Search Engine for Mathematical Content

Mišutka, Jozef, Galamboš, Leo (2008)

Towards Digital Mathematics Library. Birmingham, United Kingdom, July 27th, 2008

The WWW became the main resource of mathematical knowledge. Currently available full text search engines can be used on these documents but they are deficient in almost all cases. By applying axioms, equal transformations, and by using different notation each formula can be expressed in numerous ways. Most of these documents do not contain semantic information; therefore, precise mathematical interpretation is impossible. On the other hand, semantic information can help to give more precise information....

Extending regular expressions with homomorphic replacement

Henning Bordihn, Jürgen Dassow, Markus Holzer (2010)

RAIRO - Theoretical Informatics and Applications

We define H- and EH-expressions as extensions of regular expressions by adding homomorphic and iterated homomorphic replacement as new operations, resp. The definition is analogous to the extension given by Gruska in order to characterize context-free languages. We compare the families of languages obtained by these extensions with the families of regular, linear context-free, context-free, and EDT0L languages. Moreover, relations to language families based on patterns, multi-patterns,...

Extending the lambda-calculus with unbind and rebind

Mariangiola Dezani-Ciancaglini, Paola Giannini, Elena Zucca (2011)

RAIRO - Theoretical Informatics and Applications

We extend the simply typed λ-calculus with unbind and rebind primitive constructs. That is, a value can be a fragment of open code, which in order to be used should be explicitly rebound. This mechanism nicely coexists with standard static binding. The motivation is to provide an unifying foundation for mechanisms of dynamic scoping, where the meaning of a name is determined at runtime, rebinding, such as dynamic updating of resources and exchange of mobile code, and delegation, where an alternative...

Extending the lambda-calculus with unbind and rebind

Mariangiola Dezani-Ciancaglini, Paola Giannini, Elena Zucca (2011)

RAIRO - Theoretical Informatics and Applications

We extend the simply typed λ-calculus with unbind and rebind primitive constructs. That is, a value can be a fragment of open code, which in order to be used should be explicitly rebound. This mechanism nicely coexists with standard static binding. The motivation is to provide an unifying foundation for mechanisms of dynamic scoping, where the meaning of a name is determined at runtime, rebinding, such as dynamic updating of resources and exchange of mobile code, and delegation, where an alternative...

Extending the UML for modelling variability for system families

Silva Robak, Bogdan Franczyk, Silva Robak (2002)

International Journal of Applied Mathematics and Computer Science

The process of modelling and developing commonality and variability for system families should be supported by suitable methods and notations. The object-oriented methods and their notations, which are used at present, focus on the development of a single system at a time. In this paper we analyse feature models as a representation of the common parts and variants contained in a system family, and propose using a feature diagram as a basic representation of commonality, variability and dependencies....

Extracting Precise Data on the Mathematical Content of PDF Documents

Baker, Josef B., Sexton, Alan P., Sorge, Volker (2008)

Towards Digital Mathematics Library. Birmingham, United Kingdom, July 27th, 2008

As more and more scientific documents become available in PDF format, their automatic analysis becomes increasingly important. We present a procedure that extracts mathematical symbols from PDF documents by examining both the original PDF file and a rasterized version. This provides more precise information than is available either directly from the PDF file or by traditional character recognition techniques. The data can then be used to improve mathematical parsing methods that transform the mathematics...

Extraction of fuzzy logic rules from data by means of artificial neural networks

Martin Holeňa (2005)

Kybernetika

The extraction of logical rules from data has been, for nearly fifteen years, a key application of artificial neural networks in data mining. Although Boolean rules have been extracted in the majority of cases, also methods for the extraction of fuzzy logic rules have been studied increasingly often. In the paper, those methods are discussed within a five-dimensional classification scheme for neural-networks based rule extraction, and it is pointed out that all of them share the feature of being...

Extraction of fuzzy rules using deterministic annealing integrated with ε-insensitive learning

Robert Czabański (2006)

International Journal of Applied Mathematics and Computer Science

A new method of parameter estimation for an artificial neural network inference system based on a logical interpretation of fuzzy if-then rules (ANBLIR) is presented. The novelty of the learning algorithm consists in the application of a deterministic annealing method integrated with ε-insensitive learning. In order to decrease the computational burden of the learning procedure, a deterministic annealing method with a "freezing" phase and ε-insensitive learning by solving a system of linear inequalities...

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