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Analog neuron hierarchy.

Jiří Šíma1

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

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|May 25, 2020
PubMed
Summary
This summary is machine-generated.

Researchers explored intermediate models of neural networks (NNs) to understand their computational power. They established a hierarchy of analog-state NNs, showing that 2ANNs can simulate deterministic pushdown automata, bridging the gap between finite automata and Turing machines.

Keywords:
Analog neuron hierarchyChomsky hierarchyDeterministic context-free languageRecurrent neural networkTuring machine

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Area of Science:

  • Computational Neuroscience
  • Theoretical Computer Science
  • Artificial Intelligence

Background:

  • Discrete-time recurrent neural networks (NNs) computational power ranges from finite automata (Chomsky level 3) to Turing-complete analog-state NNs (Chomsky level 0).
  • Understanding intermediate models is crucial for refining this analysis.

Purpose of the Study:

  • To analyze the computational power of intermediate neural network models.
  • To establish and differentiate an analog neuron hierarchy.
  • To determine the capabilities of these models concerning formal language recognition.

Main Methods:

  • Introduced an intermediate model, αANN, extending binary-state NNs with analog neurons.
  • Established a hierarchy for analog neuron networks (ANNs) with rational weights: 0ANNs ⊂ 1ANNs ⊂ 2ANNs ⊆ 3ANNs.
  • Proved limitations of 1ANNs in recognizing specific deterministic languages and demonstrated 2ANNs' ability to simulate deterministic pushdown automata.

Main Results:

  • 0ANNs are equivalent to binary-state NNs (Chomsky level 3).
  • 1ANNs accept languages up to Chomsky level 1 (context-sensitive), including some above level 2, but cannot recognize L#={0n1n∣n≥1}.
  • 2ANNs with rational weights can simulate deterministic pushdown automata, forming a proper superset of 1ANNs.
  • 3ANNs with rational weights can simulate any Turing machine with linear-time overhead, collapsing the hierarchy.

Conclusions:

  • The analog neuron hierarchy provides a refined understanding of neural network computational power.
  • 2ANNs represent a significant computational leap, capable of recognizing deterministic context-free languages.
  • The full hierarchy collapses to 3ANNs, demonstrating their Turing completeness.