Subrecursive Neural Networks

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F19%3A00490203" target="_blank" >RIV/67985807:_____/19:00490203 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1016/j.neunet.2019.04.019" target="_blank" >http://dx.doi.org/10.1016/j.neunet.2019.04.019</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.neunet.2019.04.019" target="_blank" >10.1016/j.neunet.2019.04.019</a>

Result language

angličtina

Original language name

Subrecursive Neural Networks

Original language description

It has been known for discrete-time recurrent neural networks (NNs) that binary-state models using the Heaviside activation function (with Boolean outputs 0 or 1) are equivalent to finite automata (level 3 in the Chomsky hierarchy), while analog-state NNs with rational weights, employing the saturated-linear function (with real-number outputs in the interval ), are Turing complete (Chomsky level 0) even for three analog units. However, it is as yet unknown whether there exist subrecursive (i.e. sub-Turing) NN models which occur on Chomsky levels 1 or 2. In this paper, we provide such a model which is a binary-state NN extended with one extra analog unit (1ANN). We achieve a syntactic characterization of languages that are accepted online by 1ANNs in terms of so-called cut languages which are combined in a certain way by usual operations. We employ this characterization for proving that languages accepted by 1ANNs with rational weights are context-sensitive (Chomsky level 1) and we present explicit examples of such languages that are not context-free (i.e. are above Chomsky level 2). In addition, we formulate a sufficient condition when a 1ANN recognizes a regular language (Chomsky level 3) in terms of quasi-periodicity of parameters derived from its real weights, which is satisfied e.g. for rational weights provided that the inverse of the real self-loop weight of the analog unit is a Pisot number.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GA19-05704S" target="_blank" >GA19-05704S: FoNeCo: Analytical Foundations of Neurocomputing</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Neural Networks

ISSN

0893-6080

e-ISSN

—

Volume of the periodical

116

Issue of the periodical within the volume

August

Country of publishing house

GB - UNITED KINGDOM

Number of pages

16

Pages from-to

208-223

UT code for WoS article

000471669900018

EID of the result in the Scopus database

2-s2.0-85065759931