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On Correspondences between Feedforward Artificial Neural Networks on Finite Memory Automata and Classes of Primitive Recursive Functions

Author

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  • Vladimir A. Kulyukin

    (Department of Computer Science, Utah State University, Logan, UT 84322, USA)

Abstract

When realized on computational devices with finite quantities of memory, feedforward artificial neural networks and the functions they compute cease being abstract mathematical objects and turn into executable programs generating concrete computations. To differentiate between feedforward artificial neural networks and their functions as abstract mathematical objects and the realizations of these networks and functions on finite memory devices, we introduce the categories of general and actual computabilities and show that there exist correspondences, i.e., bijections, between functions computable by trained feedforward artificial neural networks on finite memory automata and classes of primitive recursive functions.

Suggested Citation

  • Vladimir A. Kulyukin, 2023. "On Correspondences between Feedforward Artificial Neural Networks on Finite Memory Automata and Classes of Primitive Recursive Functions," Mathematics, MDPI, vol. 11(12), pages 1-25, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2620-:d:1166608
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    References listed on IDEAS

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    1. Vladimir Kulyukin, 2022. "On Primitive Recursive Characteristics of Chess," Mathematics, MDPI, vol. 10(7), pages 1-43, March.
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    Cited by:

    1. Vladimir A. Kulyukin, 2024. "On Signifiable Computability: Part I: Signification of Real Numbers, Sequences, and Types," Mathematics, MDPI, vol. 12(18), pages 1-17, September.
    2. Vladimir A. Kulyukin, 2023. "On the Computability of Primitive Recursive Functions by Feedforward Artificial Neural Networks," Mathematics, MDPI, vol. 11(20), pages 1-16, October.

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