The Power of Extra Analog Neuron

Šíma, Jiří

doi:10.1007/978-3-319-13749-0_21

Cited by 5 publications

(2 citation statements)

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“…We have previously shown that 1ANN is computationally equivalent to a finite automaton with a rationalvalued register whose domain is partitioned into a finite number of intervals, each associated with a local state-transition function [35]. We now characterize the class of problems solvable by 1ANNs in the following representation theorem (cf.…”

Section: Neural Network and The Chomsky Hierarchymentioning

confidence: 99%

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The Computational Power of Neural Networks and Representations of Numbers in Non-Integer Bases

Šíma¹

2017

mendel

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We briefly survey the basic concepts and results concerning the computational power of neural net-orks which basically depends on the information content of eight parameters. In particular, recurrent neural networks with integer, rational, and arbitrary real weights are classi ed within the Chomsky and finer complexity hierarchies. Then we re ne 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.

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Section: Neural Network and The Chomsky Hierarchymentioning

confidence: 99%

“…Acknowledgement: This paper is an extended abstract of an invited talk which is based on author's previous work [35,39,36]. The research was done with institutional support RVO: 67985807 and partially supported by the grant of the Czech Science Foundation No.…”

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confidence: 99%