Re: The Exclusive-Or (XOR) Problem

From: HARNAD Stevan (
Date: Thu Jun 06 1996 - 22:42:42 BST

> From: "Saegusa, Mitu" <>
> Date: Sun, 26 May 1996 20:19:27 GMT
> 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
> XOR.
> 01/yes
> 00/no
> 10/yes
> 11/no
> 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.

Very good; for an A, integrate with Minsky's Critique or
or categorisation or computation...

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