Název: The Computational Power of Neural Networks and Representations of Numbers in Non-Integer Bases
Autoři: Šíma, Jiří
Typ dokumentu: Příspěvky z konference
Konference/Akce: MENDEL 2017. International Conference on Soft Computing /23./, Brno (CZ), 20170620
Jazyk: eng
Abstrakt: 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.
Klíčová slova: beta-expansion; Chomsky hierarchy; cut language; neural network
Číslo projektu: GBP202/12/G061 (CEP)
Poskytovatel projektu: GA ČR
Zdrojový dokument: Mendel - Soft Computing Journal, ISSN 1803-3814

Instituce: Ústav informatiky AV ČR (web)
Informace o dostupnosti dokumentu: Dokument je dostupný v příslušném ústavu Akademie věd ČR.
Původní záznam: http://hdl.handle.net/11104/0272441

Trvalý odkaz NUŠL: http://www.nusl.cz/ntk/nusl-358337


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