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Deep Neural Networks for Image-Based Dietary Assessment
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Subrecursive neural networks.

Jiří Šíma1

  • 1Institute of Computer Science of the Czech Academy of Sciences, P.O. Box 5, 18207 Prague 8, Czech Republic.

Neural Networks : the Official Journal of the International Neural Network Society
|May 24, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a novel neural network model (1ANN) capable of recognizing languages at Chomsky level 1, bridging the gap between finite automata and Turing-complete systems. The 1ANN model demonstrates context-sensitive language recognition, expanding the capabilities of neural networks.

Keywords:
Chomsky hierarchyCut languageQuasi-periodic numberRecurrent neural network

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Area of Science:

  • Theoretical Computer Science
  • Artificial Intelligence
  • Computational Linguistics

Background:

  • Discrete-time recurrent neural networks (NNs) with binary states and Heaviside activation are equivalent to finite automata (Chomsky level 3).
  • Analog-state NNs with rational weights and saturated-linear activation are Turing complete (Chomsky level 0), even with three units.
  • The existence of sub-Turing neural network models on Chomsky levels 1 or 2 remained an open question.

Purpose of the Study:

  • To introduce and analyze a novel neural network model, the 1-unit analog neural network (1ANN), capable of sub-Turing computation.
  • To syntactically characterize the languages accepted by 1ANNs.
  • To determine the Chomsky hierarchy level of languages recognized by 1ANNs.

Main Methods:

  • Development of a 1ANN model, a binary-state neural network augmented with one analog unit.
  • Syntactic characterization of accepted languages using 'cut languages' and standard operations.
  • Analysis of language complexity based on the 1ANN model's computational capabilities.

Main Results:

  • The 1ANN model provides a concrete example of a sub-Turing neural network operating on Chomsky levels 1 or 2.
  • Languages accepted by 1ANNs with rational weights are proven to be context-sensitive (Chomsky level 1).
  • Explicit examples of languages recognized by 1ANNs are presented that are not context-free (above Chomsky level 2).

Conclusions:

  • The 1ANN model successfully bridges the gap between finite automata and Turing-complete systems, demonstrating sub-Turing computational power.
  • The study establishes a syntactic characterization for languages recognized by 1ANNs, linking them to context-sensitive languages.
  • A sufficient condition for 1ANNs to recognize regular languages (Chomsky level 3) is formulated, involving quasi-periodicity of parameters related to Pisot numbers.