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<P>
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<H1><A NAME="synopsis">SYNOPSIS</A></H1>
<PRE>
        use AI::NeuralNet::BackProp;

        # Create a new network with 1 layer, 5 inputs, and 5 outputs.
        my $net = new AI::NeuralNet::BackProp(1,5,5);

        # Add a small amount of randomness to the network
        $net-&gt;random(0.001);
        # Demonstrate a simple learn() call
        my @inputs = ( 0,0,1,1,1 );
        my @ouputs = ( 1,0,1,0,1 );

        print $net-&gt;learn(\@inputs, \@outputs),&quot;\n&quot;;

        # Create a data set to learn
        my @set = (
                [ 2,2,3,4,1 ], [ 1,1,1,1,1 ],
                [ 1,1,1,1,1 ], [ 0,0,0,0,0 ],
                [ 1,1,1,0,0 ], [ 0,0,0,1,1 ]    
        );

        # Demo learn_set()
        my $f = $net-&gt;learn_set(\@set);
        print &quot;Forgetfulness: $f unit\n&quot;;

        # Crunch a bunch of strings and return array refs
        my $phrase1 = $net-&gt;crunch(&quot;I love neural networks!&quot;);
        my $phrase2 = $net-&gt;crunch(&quot;Jay Lenno is wierd.&quot;);
        my $phrase3 = $net-&gt;crunch(&quot;The rain in spain...&quot;);
        my $phrase4 = $net-&gt;crunch(&quot;Tired of word crunching yet?&quot;);


        # Make a data set from the array refs
        my @phrases = (
                $phrase1, $phrase2,
                $phrase3, $phrase4
        );

        # Learn the data set    
        $net-&gt;learn_set(\@phrases);


        # Run a test phrase through the network
        my $test_phrase = $net-&gt;crunch(&quot;I love neural networking!&quot;);
        my $result = $net-&gt;run($test_phrase);

        # Get this, it prints &quot;Jay Leno is  networking!&quot; ...  LOL!
        print $net-&gt;uncrunch($result),&quot;\n&quot;
        
</PRE>        
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<H1><A NAME="updates">UPDATES</A></H1>
<P>This is version 0.89. In this version I have included a new feature, output range limits, as
well as automatic crunching of <A HREF="#item_run"><CODE>run()</CODE></A> and learn*() inputs. Included in the examples directory
are seven new practical-use example scripts. Also implemented in this version is a much cleaner 
learning function for individual neurons which is more accurate than previous verions and is 
based on the LMS rule. See <A HREF="#item_range"><CODE>range()</CODE></A> for information on output range limits. I have also updated 
the <A HREF="#item_load"><CODE>load()</CODE></A> and <A HREF="#item_save"><CODE>save()</CODE></A> methods so that they do not depend on Storable anymore. In this version 
you also have the choice between three network topologies, two not as stable, and the third is 
the default which has been in use for the previous four versions.</P>
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<H1><A NAME="description">DESCRIPTION</A></H1>
<P>AI::NeuralNet::BackProp implements a nerual network similar to a feed-foward,
back-propagtion network; learning via a mix of a generalization
of the Delta rule and a disection of Hebbs rule. The actual 
neruons of the network are implemented via the AI::NeuralNet::BackProp::neuron package.
</P>

You constuct a new network via the new constructor:
<PRE>
        my $net = new AI::NeuralNet::BackProp(2,3,1);</PRE>
<P>The <CODE>new()</CODE> constructor accepts two arguments and one optional argument, $layers, $size, 
and $outputs is optional (in this example, $layers is 2, $size is 3, and $outputs is 1).</P>
<P>$layers specifies the number of layers, including the input
and the output layer, to use in each neural grouping. A new
neural grouping is created for each pattern learned. Layers
is typically set to 2. Each layer has $size neurons in it.
Each neuron's output is connected to one input of every neuron
in the layer below it. 
</P>

This diagram illustrates a simple network, created with a call
to &quot;new AI::NeuralNet::BackProp(2,2,2)&quot; (2 layers, 2 neurons/layer, 2 outputs).
<PRE>

     input
     /  \
    O    O
    |\  /|
    | \/ |
    | /\ |
    |/  \|
    O    O
     \  /
    mapper</PRE>
<P>In this diagram, each neuron is connected to one input of every
neuron in the layer below it, but there are not connections
between neurons in the same layer. Weights of the connection
are controlled by the neuron it is connected to, not the connecting
neuron. (E.g. the connecting neuron has no idea how much weight
its output has when it sends it, it just sends its output and the
weighting is taken care of by the receiving neuron.) This is the 
method used to connect cells in every network built by this package.</P>
<P>Input is fed into the network via a call like this:</P>
<PRE>
        use AI;
        my $net = new AI::NeuralNet::BackProp(2,2);

        my @map = (0,1);

        my $result = $net-&gt;run(\@map);</PRE>
<P>Now, this call would probably not give what you want, because
the network hasn't ``learned'' any patterns yet. But this
illustrates the call. Run now allows strings to be used as
input. See <A HREF="#item_run"><CODE>run()</CODE></A> for more information.</P>
<P>Run returns a refrence with $size elements (Remember $size? $size