Abstract
This paper deals with a significant extension of the neural Threshold Logic pioneered by McCulloch and Pitts. The output of their formal neuron is given by the Heaviside function with an argument depending on a linear weighted sum of the inputs and a threshold parameter. All Boolean Tables cannot be represented by such a formal neuron. For example the exclusive OR and the Parity Problem need hidden neurons to be resolved. A few years ago, Dubois proposed a non-linear fractal neuron to resolve the exclusive OR problem with only one single neuron. Then Dubois and Resconi introduce the Non-linear Threshold Logic, that is to say a Heaviside Function with a non-linear sum of the inputs which can represent any Boolean Tables with only one neuron where the Dubois' non-linear neuron model is a Heaviside Fixed Function. In this framework the Supervised Learning is Direct, that is to say without recursive algorithms for computing the weights and threshold, related to the new foundation of the Threshold Logic by Resconi and Raymondi. This paper will review the main aspects of the linear and non-linear threshold logic with direct learning and applications in pattern recognition with the software TurboBrain. This constitutes a new tool in the framework of neural CAST, Computer Aided Systems Theory and Technology, proposed by F. Pichler.
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References
J. A. Anderson, Ed. Rosenfeld (eds): NEUROCOMPUTING. Foundations of Research, The MIT Press Cambridge, Massachusetts, London, 1988, 729 p.
M. L. Dertouzos: Threshold Logic: A Synthesis Approach. Res. Monogr. no. 32, The MIT Press, Massachusetts 1965
D. M. Dubois: Self-organisation of Fractal Objects in XOR rule-based Multilayer Networks. In: EC2 (ed.): Neural Networks & their Applications, Neuro-Nîmes, Proceedings of the 3rd International Workshop 1990, pp. 555–557
D. M. Dubois: Le Labyrinthe de l'Intelligence. InterEditions/Paris-Academia/Louvain-la-Neuve, 2nd edition, 1990, 331 p.
D. M. Dubois: Mathematical Fundamentals of the Fractal Theory of Artificial Intelligence. Communication & Cognition — Artificial Intelligence, 8, 1, 5–48 (1991)
D. M. Dubois, G. Resconi: Mathematical Foundation of a Non-linear Threshold Logic: a New Paradigm for the Technology of Neural Machines. ACADEMIE ROYALE DE BELGIQUE, Bulletin de la Classe des Sciences, 6ème série, Tome IV, 1–6, 91–122 (1993)
D. M Dubois, G. Resconi: Advanced Research in Non-linear Threshold Logic Applied to Pattern Recognition. COMETT European Lecture Notes in Threshold Logic. Edited by AILg, Association des Ingénieurs sortis de l'Université de Liège, D/1995/3603/02, 1995, 182 p.
D. M. Dubois, G. Resconi, A. Raymondi: TurboBrain 1.0: User's manual, D/1993/Dubois, Resconi, Raymondi: Editeurs, registered the 29th October 1993, 75 p.
K. Fukushima, M. Sei, I. Takayuki. IEEE, Transactions on Systems, Man and Cybernetics SMC-13:826–834(1983)
W. S. McCulloch, W. Pitts. Bulletin of Mathematical Biophysics 5:115–133 (1943)
M. L. Minsky, S. Papert. Perceptrons. MIT, Cambridge, 1969
W. Pitts, W. S. McCulloch. Bulletin of Mathematical Biophysics 9:127–147 (1947)
G. Resconi, A. Raymondi: A New Foundation for the Threshold Logic. Quaderno n∘3/93 del Seminario Matematico di Brescia, 1993, 46 p.
F. Rosenblatt: Principles Neurodynamics. Spartan, Washington DC, 1961
D. E. Rumelhart, G. E. Hinton, R. J. Williams. Nature 323:533–536 (1986)
D. E. Rumelhart, G. E. Hinton, R. J. Williams: Learning internal representations by error propagation. In: D. E. Rumelhart, J. L. McClelland (eds.): Parallel Distributed Processing Explorations in the Microstructures of Cognition, Vol. 1, Cambridge MA: MIT Press 1986, pp. 318–362
K. Zuse: The Computer — My Life. Springer-Verlag 1993
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Dubois, D.M., Resconi, G., Raymondi, A. (1996). TurboBrain: A neural network with direct learning based on linear or Non-Linear Threshold Logics. In: Klir, G.J., Ören, T.I. (eds) Computer Aided Systems Theory — CAST '94. Lecture Notes in Computer Science, vol 1105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61478-8_83
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DOI: https://doi.org/10.1007/3-540-61478-8_83
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