Polynomial-Computable Representation of Neural Networks in Semantic Programming
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-compu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | J |
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| Online Access: | https://www.mdpi.com/2571-8800/6/1/4 |
| _version_ | 1827749380230217728 |
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| author | Sergey Goncharov Andrey Nechesov |
| author_facet | Sergey Goncharov Andrey Nechesov |
| author_sort | Sergey Goncharov |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T06:23:17Z |
| format | Article |
| id | doaj.art-a1a34c2bf92f4ef9b4d228bc0af62f25 |
| institution | Directory Open Access Journal |
| issn | 2571-8800 |
| language | English |
| last_indexed | 2024-03-11T06:23:17Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | J |
| spelling | doaj.art-a1a34c2bf92f4ef9b4d228bc0af62f252023-11-17T11:47:01ZengMDPI AGJ2571-88002023-01-0161485710.3390/j6010004Polynomial-Computable Representation of Neural Networks in Semantic ProgrammingSergey Goncharov0Andrey Nechesov1Sobolev Institute of Mathematics, Academician Koptyug Ave., 4, 630090 Novosibirsk, RussiaSobolev Institute of Mathematics, Academician Koptyug Ave., 4, 630090 Novosibirsk, RussiaA 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.https://www.mdpi.com/2571-8800/6/1/4polynomialitypolynomial algorithmlogical programming languagesemantic programmingAIneural networks |
| spellingShingle | Sergey Goncharov Andrey Nechesov Polynomial-Computable Representation of Neural Networks in Semantic Programming J polynomiality polynomial algorithm logical programming language semantic programming AI neural networks |
| title | Polynomial-Computable Representation of Neural Networks in Semantic Programming |
| title_full | Polynomial-Computable Representation of Neural Networks in Semantic Programming |
| title_fullStr | Polynomial-Computable Representation of Neural Networks in Semantic Programming |
| title_full_unstemmed | Polynomial-Computable Representation of Neural Networks in Semantic Programming |
| title_short | Polynomial-Computable Representation of Neural Networks in Semantic Programming |
| title_sort | polynomial computable representation of neural networks in semantic programming |
| topic | polynomiality polynomial algorithm logical programming language semantic programming AI neural networks |
| url | https://www.mdpi.com/2571-8800/6/1/4 |
| work_keys_str_mv | AT sergeygoncharov polynomialcomputablerepresentationofneuralnetworksinsemanticprogramming AT andreynechesov polynomialcomputablerepresentationofneuralnetworksinsemanticprogramming |