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ICANN ’94 pp 487-492 | Cite as

Outline of a Linear Neural Network and Applications

  • Eduardo R. Caianiello
  • Maria Marinaro
  • Salvatore Rampone
  • Roberto Tagliaferri
Conference paper

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.

Keywords

Linear Code Binary Linear Code Binary Symmetrical Channel Noisy Pattern Codeword Weight 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. • Caianiello, E.R. (1992) Do All Neurons Know Algebra? Art. Neur. Networks II, I. Alexander and J. Taylor ed.s, 1, 221–227, Elsevier.Google Scholar
  2. • Duda, R.O., Hart, P.E. (1973) Pattern Classification and Scene Analysis, New York: J. Wiley and Sons.Google Scholar
  3. • 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. Google Scholar
  4. • Gallager, R.G. (1968) Information Theory and Reliable Communication. New York: J.Wiley and Sons.Google Scholar
  5. • Huseyin, A. (1990) Vector Quantization. New York: IEEE Press.Google Scholar
  6. • MacWilliams, F.J., Sloane, N.J.A. (1981) The Theory of Error Correcting Codes. New York: North Holland.Google Scholar
  7. • McElice, R.J. (1977) The Theory of Information and Coding. In GianCarlo Rota ed., Encyclopedia of Mathematics and its Applications, S. London: Addison Wesley.Google Scholar
  8. • Peterson, W.W., Weldon, W.J. (1972) Error Correcting Code&. Cambridge: The MIT press.Google Scholar
  9. • Rampone, S. (1993) Linear Codes Interpolation from Noisy Patterns by Means of a Vector Quantization Process. IIASS Tech. Rep. I-9303, submitted for pubblication.Google Scholar
  10. • Shannon, C.E. (1959) Coding Theorem for a Discrete Source with a Fidelity Criterion. Ist. of Radio Eng., Int. Conv. Rec., 7, 142–163.Google Scholar

Copyright information

© Springer-Verlag London Limited 1994

Authors and Affiliations

  • Eduardo R. Caianiello
    • 1
    • 2
  • Maria Marinaro
    • 1
    • 2
  • Salvatore Rampone
    • 1
    • 2
  • Roberto Tagliaferri
    • 1
    • 2
  1. 1.I.I.A.S.S.Vietri SM (SA)Italy
  2. 2.Universitá di SalernoBaronissi (SA)Italy

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