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

Vladimir A. Kulyukin ()
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Vladimir A. Kulyukin: Department of Computer Science, Utah State University, Logan, UT 84322, USA

Mathematics, 2023, vol. 11, issue 12, 1-25

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.

Keywords: computability theory; theory of recursive functions; artificial neural networks; number theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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