
The Computational Power of Neural Networks and Representations of Numbers in NonInteger Bases.
Šíma, Jiří
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 integerweight neural networks with an extra analog rationalweight neuron (1ANN). We show a representation theorem which characterizes the classification problems solvable by 1ANNs, by using socalled cut languages. Our analysis reveals an interesting link to an active research field on nonstandard positional numeral systems with noninteger bases. Within this framework, we introduce a new concept of quasiperiodic numbers which is used to classify the computational power of 1ANNs within the Chomsky hierarchy.


The Computational Power of Neural Networks and Representations of Numbers in NonInteger Bases
Šíma, Jiří
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 integerweight neural networks with an extra analog rationalweight neuron (1ANN). We show a representation theorem which characterizes the classification problems solvable by 1ANNs, by using socalled cut languages. Our analysis reveals an interesting link to an active research field on nonstandard positional numeral systems with noninteger bases. Within this framework, we introduce a new concept of quasiperiodic numbers which is used to classify the computational power of 1ANNs within the Chomsky hierarchy.


The Computational Power of Neural Networks and Representations of Numbers in NonInteger Bases
Šíma, Jiří
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 integerweight neural networks with an extra analog rationalweight neuron (1ANN). We show a representation theorem which characterizes the classification problems solvable by 1ANNs, by using socalled cut languages. Our analysis reveals an interesting link to an active research field on nonstandard positional numeral systems with noninteger bases. Within this framework, we introduce a new concept of quasiperiodic numbers which is used to classify the computational power of 1ANNs within the Chomsky hierarchy.
