Abstract
The aim of this paper is to show that additional perspectives are added to research on linear Neural Nets by utilizing a new definition of product, recently introduced (Caianiello, 92) in the context of Neural Nets defined on semirings rather than number fields. This we do by exhibiting its use for the design “on inspection” of a Neural Net which stores as one-step attractor any number of given patterns, with input basins of exactly specified tolerance. The paper is organized in the following way. In the next section we specify the notation and define the Neural Net model. In section three we describe applications in structured and not structured domains.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
• Caianiello, E.R. (1992) Do All Neurons Know Algebra? Art. Neur. Networks II, I. Alexander and J. Taylor ed.s, 1, 221–227, Elsevier.
• Duda, R.O., Hart, P.E. (1973) Pattern Classification and Scene Analysis, New York: J. Wiley and Sons.
• Esposito, A., Rampone, S., Tagliaferri, R. (1992) A Neural Network for Error Correcting Decoding of Binary Linear Codes. IIASS tech. rep I-9901, in press on Neural Networks.
• Gallager, R.G. (1968) Information Theory and Reliable Communication. New York: J.Wiley and Sons.
• Huseyin, A. (1990) Vector Quantization. New York: IEEE Press.
• MacWilliams, F.J., Sloane, N.J.A. (1981) The Theory of Error Correcting Codes. New York: North Holland.
• McElice, R.J. (1977) The Theory of Information and Coding. In GianCarlo Rota ed., Encyclopedia of Mathematics and its Applications, S. London: Addison Wesley.
• Peterson, W.W., Weldon, W.J. (1972) Error Correcting Code&. Cambridge: The MIT press.
• Rampone, S. (1993) Linear Codes Interpolation from Noisy Patterns by Means of a Vector Quantization Process. IIASS Tech. Rep. I-9303, submitted for pubblication.
• Shannon, C.E. (1959) Coding Theorem for a Discrete Source with a Fidelity Criterion. Ist. of Radio Eng., Int. Conv. Rec., 7, 142–163.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag London Limited
About this paper
Cite this paper
Caianiello, E.R., Marinaro, M., Rampone, S., Tagliaferri, R. (1994). Outline of a Linear Neural Network and Applications. In: Marinaro, M., Morasso, P.G. (eds) ICANN ’94. ICANN 1994. Springer, London. https://doi.org/10.1007/978-1-4471-2097-1_114
Download citation
DOI: https://doi.org/10.1007/978-1-4471-2097-1_114
Published:
Publisher Name: Springer, London
Print ISBN: 978-3-540-19887-1
Online ISBN: 978-1-4471-2097-1
eBook Packages: Springer Book Archive