Counting with Analog Neurons

Autoři: doc. RNDr. Jiří Šíma, DSc.
Rok vydání: 2019
Typ publikace: Konferenční příspěvek (mezinárodní konf.)
Periodikum: Artificial Neural Networks and Machine Learning – ICANN 2019: Theoretical Neural Computation. Proceedings, Part I
Projekty: FoNeCo: Analytické základy neurovýpočtů
Bibliografická citace: ŠÍMA, Jiří. Counting with Analog Neurons. In: TETKO, I. V., KŮRKOVÁ, V., KARPOV, P., THEIS, F., eds. Artificial Neural Networks and Machine Learning – ICANN 2019: Theoretical Neural Computation. Proceedings, Part I. Cham: Springer, 2019, S. 389-400. Lecture Notes in Computer Science, 11727. ISBN 978-3-030-30486-7. ISSN 0302-9743
Dostupné z: doi:10.1007/978-3-030-30487-4_31
DOI: 10.1007/978-3-030-30487-4_31
ID: 502583

Abstrakt

We refine the analysis of binary-state neural networks with alpha extra analog neurons (alpha-ANNs). For rational weights, it has been known that online 1ANNs accept context-sensitive languages including examples of non-context-free languages, while offline 3ANNs are Turing complete. We now prove that the deterministic (context-free) language containing the words of n zeros followed by n ones, cannot be recognized offline by any 1ANN with real weights. Hence, the offline 1ANNs are not Turing complete. On the other hand, we show that any deterministic language can be accepted by a 2ANN with rational weights. Thus, two extra analog units can count to any number which is not the case of one analog neuron.