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=== Permutation parity machine ===
The permutation parity machine is a binary variant of the tree parity machine.<ref name="Reyes">{{cite journal |last1=Reyes |first1=O. M. |last2=Kopitzke |first2=I. |last3=Zimmermann |first3=K.-H. |date=April 2009 |title=Permutation Parity Machines for Neural Synchronization |journal=Journal of Physics A: Mathematical and Theoretical |volume=42 |issue=19 |pages=195002 |issn=1751-8113 |doi=10.1088/1751-8113/42/19/195002|bibcode=2009JPhA...42s5002R |s2cid=122126162 }}</ref>
It consists of one input layer, one hidden layer and one output layer. The number of neurons in the output layer depends on the number of hidden units K. Each hidden neuron has N binary input neurons:
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