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Polynomial-Computable Representation of Neural Networks in Semantic Programming

Author

Listed:
  • Sergey Goncharov

    (Sobolev Institute of Mathematics, Academician Koptyug Ave., 4, 630090 Novosibirsk, Russia
    These authors contributed equally to this work.)

  • Andrey Nechesov

    (Sobolev Institute of Mathematics, Academician Koptyug Ave., 4, 630090 Novosibirsk, Russia
    These authors contributed equally to this work.)

Abstract

A lot of libraries for neural networks are written for Turing-complete programming languages such as Python, C++, PHP, and Java. However, at the moment, there are no suitable libraries implemented for a p-complete logical programming language L. This paper investigates the issues of polynomial-computable representation neural networks for this language, where the basic elements are hereditarily finite list elements, and programs are defined using special terms and formulas of mathematical logic. Such a representation has been shown to exist for multilayer feedforward fully connected neural networks with sigmoidal activation functions. To prove this fact, special p-iterative terms are constructed that simulate the operation of a neural network. This result plays an important role in the application of the p-complete logical programming language L to artificial intelligence algorithms.

Suggested Citation

  • Sergey Goncharov & Andrey Nechesov, 2023. "Polynomial-Computable Representation of Neural Networks in Semantic Programming," J, MDPI, vol. 6(1), pages 1-10, January.
    • Handle: RePEc:gam:jjopen:v:6:y:2023:i:1:p:4-57:d:1027858
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