Solving the XOR and parity N problems using a single universal binary neuron
 Igor Aizenberg
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
A universal binary neuron (UBN) operates with complexvalued weights and a complexvalued activation function, which is the function of the argument of the weighted sum. The activation function of the UBN separates a whole complex plane onto equal sectors, where the activation function is equal to either 1 or −1 depending on the sector parity (even or odd, respectively). Thus, the UBN output is determined by the argument of the weighted sum. This makes it possible the implementation of the nonlinearly separable (nonthreshold) Boolean functions on a single neuron. Hence, the functionality of UBN is incompatibly higher than the functionality of the traditional perceptron. In this paper, we will consider a new modified learning algorithm for the UBN. We will show that classical nonlinearly separable problems XOR and Parity n can be easily solved using a single UBN, without any network. Finally, it will be considered how some other important nonlinearly separable problems may be solved using a single UBN.
 Aizenberg IN (1985) Model of the element with complete functionality. Izvestia Akademii Nauk SSSR, Technicheskaia Kibernetika (J Comput Syst Sci Int) (2):188–191 (in Russian)
 Aizenberg IN (1991) The universal logical element over the field of the complex numbers, Kibernetika (Cybern Syst Anal), (3):116–121 (in Russian)
 Aizenberg I, Moraga C (2007) Multilayer feedforward neural network based on multivalued neurons (MLMVN) and a backpropagation learning algorithm. Soft Comput 11(2):169–183 CrossRef
 Aizenberg I, Aizenberg N, Vandewalle J (2000) Multivalued and universal binary neurons: theory, learning, applications. Kluwer, Boston, Dordrecht, London
 Aizenberg NN, Aizenberg IN (1991) Model of the neural network basic elements (Cells) with universal functionality and various hardware implementations. In: Proceedings of the 2nd international conference “Microelectronics for Neural Networks”, Kyrill & Methody Verlag, Munich, pp 77–83
 Aizenberg NN, Aizenberg IN (1992) CNN based on multivalued neuron as a model of associative memory for grayscale images. In: Proceedings of the 2nd IEEE international workshop on cellular neural networks and their applications, Technical University Munich, Germany, 14–16 October 1992, pp 36–41
 Aizenberg NN, Aizenberg IN (1993) Quickly converging learning algorithms for multilevel and universal binary neurons and solving of the some image processing problems. In: Mira J, Cabestany J, Prieto A (eds). Lecture notes in computer science, vol 686. Springer, Berlin, pp 230–236
 Aizenberg NN, Ivaskiv Yu L (1977) Multiplevalued threshold logic. Naukova Dumka Publisher House, Kiev (in Russian)
 Aizenberg NN, Ivaskiv Yu L, Pospelov DA (1971) About one generalization of the threshold function Doklady Akademii Nauk SSSR (The Reports of the Academy of Sciences of the USSR), 196:1287–1290 (in Russian)
 Dertouzos ML (1965) Threshold logic: a synthesis approach. The MIT Press, Cambridge
 Fung H, Li LK (2001) Minimal feedforward parity networks using threshold gates. Neural Comput 13:319–326 CrossRef
 Haykin S (1999) Neural networks: a comprehensive foundation, 2nd edn. Prentice Hall, Englewood Cliffs
 Hebb DD (1949) The organization of behavior. Wiley, New York
 Minsky LM, Papert AS (1968) Perceptrons: an introduction to computational geometry, expanded edition. MIT Press, Cambridge
 Mizutani E, Dreyfus SE, Jang JSR (2000) On dynamic programminglike recursive gradient formula for alleviating hiddennode saturation in the parity problem. In: Proceedings of the international workshop on intelligent systems resolutions—the 8th Bellman Continuum, Hsinchu, Taiwan, pp 100–104
 Rosenblat F (1962) Principles of neurodynamics: perceptrons and the theory of brain mechanisms. Spartan, New York
 Suzuki K, Horiba I, Sugie N (2003) Neural edge enhancer for supervised edge enhancement from noisy images. IEEE Trans Pattern Anal Mach Intell 25(12):1582–1596 CrossRef
 Wang HM, Zhao JY, Guo SD, Yu DH (2002) A new kind of shadow detector based on CNNUBN. In: Proceedings of the 1st IEEE international conference on machine learning and cybernetics, Beijing, 4–5 November 2002, pp 69–72
 Title
 Solving the XOR and parity N problems using a single universal binary neuron
 Journal

Soft Computing
Volume 12, Issue 3 , pp 215222
 Cover Date
 20080201
 DOI
 10.1007/s0050000702049
 Print ISSN
 14327643
 Online ISSN
 14337479
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 Authors

 Igor Aizenberg ^{(1)}
 Author Affiliations

 1. Department of Computer and Information Sciences, Texas A&M UniversityTexarkana, P.O. Box 5518, 2600 N. Robison Rd., Texarkana, TX, 75505, USA