Original title: The Computational Power of Neural Networks and Representations of Numbers in Non-Integer Bases.
Authors: Šíma, Jiří
Document type: Papers
Conference/Event: MENDEL 2017. International Conference on Soft Computing /23./, Brno (CZ), 20170620
Year: 2017
Language: eng
Abstract: We briefly survey the basic concepts and results concerning the computational power of neural networks which basically depends on the information content of weight parameters. In particular, recurrent neural networks with integer, rational, and arbitrary real weights are classified within the Chomsky and finer complexity hierarchies. Then we refine the analysis between integer and rational weights by investigating an intermediate model of integer-weight neural networks with an extra analog rational-weight neuron (1ANN). We show a representation theorem which characterizes the classification problems solvable by 1ANNs, by using so-called cut languages. Our analysis reveals an interesting link to an active research field on non-standard positional numeral systems with non-integer bases. Within this framework, we introduce a new concept of quasi-periodic numbers which is used to classify the computational power of 1ANNs within the Chomsky hierarchy.
Keywords: beta-expansion; Chomsky hierarchy; cut language; neural network
Project no.: GBP202/12/G061 (CEP)
Funding provider: GA ČR
Host item entry: Mendel 2017, ISSN 1803-3814
Note: Související webová stránka: http://www.mendel-conference.org/?link=invited17

Institution: Institute of Computer Science AS ČR (web)
Document availability information: Fulltext is available at the institute of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0281255

Permalink: http://www.nusl.cz/ntk/nusl-371581


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