Functionally Logical Modeling of the Σπ-Neuron

Abstract

In this paper, we suggest a circuitry method of the realization of a logical ΣΠ-neuron. We present digital and hybrid schemes of the logical ΣΠ-neuron. Each scheme is divided into two layers, which realize the multiplicative and additive operations, respectively. The schemes are constructed on the basis of digital and analogue elements. The layer performing the multiplicative function is identical in both schemes. The additive layer in the digital scheme is realized by the digital summator. In the hybrid scheme, it is realized by digital-to-analogue converters and the analogue summator of voltages. To realize the threshold function, the hybrid scheme uses a comparator and the digital one uses a digital comparator. The results obtained can be used for the construction of ΣΠ-neural networks.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    N. Ch. Babich and I. A. Zhukov, Computer Circuitry. Methods of the Construction and Projecting [in Russian], MK-Press, Kiev (2004).

    Google Scholar 

  2. 2.

    S. Haikin, Neural Networks: A Complete Course, Williams, Moscow (2006).

    Google Scholar 

  3. 3.

    L. D. Harmon, “Studies with artificial neurons, I: Properties and functions of an artificial neuron,” Kybernetik Heft., 3, 89–101 (1961).

    Article  Google Scholar 

  4. 4.

    Z. M. Shibzukhov, “Some questions of theoretical neuroinformatics,” in: XIII All-Russian Scient.-Techn. Conf. ‘Neuroinformatics-2011.’ Lectures on Neuroinformatics, NIYaU MIFI, Moscow (2011), pp. 44–72.

    Google Scholar 

  5. 5.

    Z. M. Shibzukhov, Constructive Methods of Learning Sigma-Pi Neural Networks [in Russian], Nauka, Moscow (2006).

    Google Scholar 

  6. 6.

    Z. M. Shibzukhov, “About ΣΠ-neuron models of aggregating type,” in: Lect. Notes Comput. Sci., 9719, Springer-Verlag, Berlin (2016), pp. 657–664.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to M. A. Kazakov.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 154, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, 2018.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kazakov, M.A. Functionally Logical Modeling of the Σπ-Neuron. J Math Sci 253, 506–510 (2021). https://doi.org/10.1007/s10958-021-05247-z

Download citation

Keywords and phrases

  • artificial neuron
  • logical sigma-pi-neuron
  • neural networks
  • sigma-pi neural networks

AMS Subject Classification

  • 68T05