TY - GEN
TI - The Computational Power of Neural Networks and Representations of Numbers in Non-Integer Bases
T3 - MENDEL 2017. International Conference on Soft Computing /23./
AU - Šíma, Jiří
AB - 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.
SN - 000000000
SN - 1803-3814
UR - http://www.nusl.cz/ntk/nusl-317284
UR - http://hdl.handle.net/11104/0271950
LA - eng
KW - Chomsky hierarchy
KW - beta-expansion
KW - cut language
KW - neural network
PY - 2017
PB - Ústav informatiky, Pod vodárenskou věží 2, 182 07 Praha 8, http://www.cs.cas.cz/
ER -