One Analog Neuron Cannot Recognize Deterministic Context-Free Languages

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F19%3A00505945" target="_blank" >RIV/67985807:_____/19:00505945 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.springer.com/gp/book/9783030367176" target="_blank" >https://www.springer.com/gp/book/9783030367176</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-36718-3_7" target="_blank" >10.1007/978-3-030-36718-3_7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

One Analog Neuron Cannot Recognize Deterministic Context-Free Languages

Popis výsledku v původním jazyce

We analyze the computational power of discrete-time recurrent neural networks (NNs) with the saturated-linear activation function within the Chomsky hierarchy. This model restricted to integer weights coincides with binary-state NNs with the Heaviside activation function, which are equivalent to finite automata (Chomsky level 3), while rational weights make this model Turing complete even for three analog-state units (Chomsky level 0). For an intermediate model alphaANN of a binary-state NN that is extended with alpha>=0 extra analog-state neurons with rational weights, we have established the analog neuron hierarchy 0ANNs subset 1ANNs subset 2ANNs subseteq 3ANNs. The separation 1ANNs subsetneq 2ANNs has been witnessed by the deterministic context-free language (DCFL) L_#={0^n1^n|n>=1} which cannot be recognized by any 1ANN even with real weights, while any DCFL (Chomsky level 2) is accepted by a 2ANN with rational weights. In this paper, we generalize this result by showing that any non-regular DCFL cannot be recognized by 1ANNs with real weights, which means (DCFLs-REG) subset (2ANNs-1ANNs), implying 0ANNs = 1ANNs cap DCFLs. For this purpose, we show that L_# is the simplest non-regular DCFL by reducing L_# to any language in this class, which is by itself an interesting achievement in computability theory.

Název v anglickém jazyce

One Analog Neuron Cannot Recognize Deterministic Context-Free Languages

Popis výsledku anglicky

We analyze the computational power of discrete-time recurrent neural networks (NNs) with the saturated-linear activation function within the Chomsky hierarchy. This model restricted to integer weights coincides with binary-state NNs with the Heaviside activation function, which are equivalent to finite automata (Chomsky level 3), while rational weights make this model Turing complete even for three analog-state units (Chomsky level 0). For an intermediate model alphaANN of a binary-state NN that is extended with alpha>=0 extra analog-state neurons with rational weights, we have established the analog neuron hierarchy 0ANNs subset 1ANNs subset 2ANNs subseteq 3ANNs. The separation 1ANNs subsetneq 2ANNs has been witnessed by the deterministic context-free language (DCFL) L_#={0^n1^n|n>=1} which cannot be recognized by any 1ANN even with real weights, while any DCFL (Chomsky level 2) is accepted by a 2ANN with rational weights. In this paper, we generalize this result by showing that any non-regular DCFL cannot be recognized by 1ANNs with real weights, which means (DCFLs-REG) subset (2ANNs-1ANNs), implying 0ANNs = 1ANNs cap DCFLs. For this purpose, we show that L_# is the simplest non-regular DCFL by reducing L_# to any language in this class, which is by itself an interesting achievement in computability theory.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

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

Projekt

<a href="/cs/project/GA19-05704S" target="_blank" >GA19-05704S: FoNeCo: Analytické základy neurovýpočtů</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název statě ve sborníku

Neural Information Processing. Proceedings, Part III

ISBN

978-3-030-36717-6

ISSN

—

e-ISSN

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Počet stran výsledku

13

Strana od-do

77-89

Název nakladatele

Springer

Místo vydání

Heidelberg

Místo konání akce

Sydney

Datum konání akce

12. 12. 2019

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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