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Output after network has relaxed Input to network This means that the network has been able to store the correct (uncorrupted) pattern – in other words it has a memory. Because of this these networks are sometimes called Associative Memories or Hopfield Memories. 2 Training – one shot method It is possible to create many types of network which use feedback as part of their structure. Such networks may be trained using variations of Back Propagation2 or Genetic Algorithms as described in later chapters.

Training the Hopfield net as shown above also makes it prone to local minima, so sometimes it has difficulty reconstructing one or more of its trained images. The network structure is rigid, it must have only one layer and there must be the same number of neurons as inputs. A two layer version called a Bidirectional Associative Memory3 or BAM does exist (but is not widely used) and it can not only reconstruct a pattern as just discussed, but also construct a completely different pattern from the input (so the input might be the letter A and the network is trained to produce the latter B).

1 2 A 3 1 A 3 b 5 a 4 6 a i 4 2 b 7 B B 5 6 7 39 Out If we were to increase the number of neurons in the first layer we could increase the separators in the system, increasing the number layer two neurons increases the number of separate regions. So, in theory anyway, a network like this can separate any inputs providing it has enough hidden layer neurons – we should never need more than a three layer network. This was also shown mathematically by the Russian mathematician Kolmogorov and is known as Kolmogorov’s theorem1.

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