The Exclusive-Or (XOR) Problem

From: Saegusa, Mitu (
Date: Sun May 26 1996 - 21:19:27 BST

What is the Exclusive-or Problem?

The simplest type of building block is the perceptron which
works by being a two-layer network: An input layer of nodes
and an output layer of nodes. Each input node connects to
each output node. Whenever the perceptron gives a correct
output in response to input, the strengh of the connections
that lead to it is increased, whenever the output is wrong,
the strength of the connections is decreased.

There are however some problems the two-layer systems cannot
handle, regardless of the size. One of these problems is
the "exclusive-or" problem (XOR problem). It is how to make
a neural network produce an identical output when the input
conditions don't have anything in common. The inability to
handle this type of problem would be a fatal flaw for neural
networks as the human neural system and so the human
cognitive system can handle the type of situation that the
XOR problem represents.

There is a pattern that the perceptron cannot learn based on


The rule: Say yes if the first one is 0 or the second is 1,
but not both.

The solution requires the addition of a third layer of
neurodes to the neural network. This layer is placed
between the the input and output layers. The operation of
this layer is never observed as directly as are the input
and output layers and the neurodes of the third layer are
referred to as hidden units.

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