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

0486446 - ÚI 2018 RIV CZ eng C - Conference Paper (international conference)
Šíma, Jiří
The Computational Power of Neural Networks and Representations of Numbers in Non-Integer Bases.
Mendel 2017. Brno: University of Technology, 2017, s. 103-110. Mendel Journal Series, 23. ISSN 1803-3814.
[MENDEL 2017. International Conference on Soft Computing /23./. Brno (CZ), 20.06.2017-22.06.2017]
R&D Projects: GA ČR GBP202/12/G061
Institutional support: RVO:67985807
Keywords : neural network * Chomsky hierarchy * beta-expansion * cut language
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
http://www.mendel-conference.org/?link=invited17

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.
Permanent Link: http://hdl.handle.net/11104/0281255