A technique for analyzing neural networks in terms of ternary logic
Suleimenov I.E. Bakirov A.S. Matrassulova D.K.
2021Little Lion Scientific
Journal of Theoretical and Applied Information Technology
2021#99Issue 112537 - 2553 pp.
There is an extensive class of neural networks, the functioning of which can be described in terms of binary logic: A set of logical variables describing the state of the inputs is associated with a set of logical variables characterizing the state of the outputs. Such networks can be described in terms of logical functions, in particular, through the Zhegalkin polynomial. This imposes significant restrictions on the variability of the neuron weights. This fact is of significant interest from the point of view of overcoming the thesis about the logical opacity of neural networks, which is associated with the most common approaches to training neural networks, which are actually the results of computer experiments. Therefore, it can be considered that neuroscience is predominantly an empirical science, with the only difference that its foundations are not laboratory, but computer experiments. An important step towards overcoming the thesis about the logical opacity of neural networks is to establish restrictions on the variability of the weight coefficients, i.e. proof of the fact that in reality neurons can perform only a limited set of operations that can be reduced to logical ones. At the same time, there is no reason to assert that artificial neural networks must necessarily be built on the basis of the apparatus of binary logic. This paper shows that appliance of ternary logic in combination with a geometric interpretation of the operation of neural networks allows us to reveal the existence of more than strict restrictions on the variability of the weight coefficients of a neural network. An exhaustive description of a neuron with four inputs, which shows how the proposed approach can be extended to the analysis of neurons with an arbitrary number of inputs.
Artificial Intelligence , Artificial Neural Networks , Ternary Logic
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Crimean Federal University Named by V.I. Vernadsky, Simferopol, Russian Federation
Almaty University of Power Engineering and Telecommunications, Almaty, Kazakhstan
Crimean Federal University Named by V.I. Vernadsky
Almaty University of Power Engineering and Telecommunications
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