Using Parity-N Problems as a Way to Compare Abilities of Shallow, Very Shallow and Very Deep Architectures

  • Paweł RóżyckiEmail author
  • Janusz Kolbusz
  • Tomasz Bartczak
  • Bogdan M. Wilamowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9119)


This paper presents a new concept of a dual neural network which is hybrid of linear and nonlinear network. This approach allows for solving the problem of Parity-3 with only one sigmoid neuron or Parity-7 with 2 sigmoid neurons that is shown in the analytical and experimental manner. The paper describes the architecture of ANN, presents an analytical way of choosing the weights and the number of neurons, and provides the results of network training for different ANN architectures solving the Parity-N problem.


Parity-N problem ANN architecture Summator in output layer 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Paweł Różycki
    • 1
    Email author
  • Janusz Kolbusz
    • 1
  • Tomasz Bartczak
    • 2
  • Bogdan M. Wilamowski
    • 2
  1. 1.University of Information Technology and Management in RzeszowRzeszowPoland
  2. 2.Auburn UniversityAuburnUSA

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