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Subrecursive Neural Networks
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SYSNO ASEP 0490203 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Subrecursive Neural Networks Tvůrce(i) Šíma, Jiří (UIVT-O) RID, SAI, ORCID Zdroj.dok. Neural Networks. - : Elsevier - ISSN 0893-6080
Roč. 116, August (2019), s. 208-223Poč.str. 16 s. Jazyk dok. eng - angličtina Země vyd. GB - Velká Británie Klíč. slova recurrent neural network ; Chomsky hierarchy ; cut language ; quasi-periodic number Vědní obor RIV IN - Informatika Obor OECD Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) CEP GA19-05704S GA ČR - Grantová agentura ČR Způsob publikování Omezený přístup Institucionální podpora UIVT-O - RVO:67985807 UT WOS 000471669900018 EID SCOPUS 85065759931 DOI 10.1016/j.neunet.2019.04.019 Anotace 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. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2020 Elektronická adresa http://dx.doi.org/10.1016/j.neunet.2019.04.019
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