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	^   ^   ^


(Sorry about the bad art...I am no ASCII artist! :-)


B<1>
In addition to flag 0, each neuron in layer X is connected to every input of 
the neurons ahead of itself in layer X.

B<2> I<("L-U Style")>
No, its not "Learning-Unit" style. It gets its name from this: In a 2 layer, 3
neuron network, the connections form a L-U pair, or a W, however you want to look
at it.   


	^   ^   ^
	|   |   |
	O-->O-->O
	^   ^   ^
	|   |   |
	|   |   |
	O-->O-->O
	^   ^   ^
	|   |   |



As you can see, each neuron is connected to the next one in its layer, as well
as the neuron directly above itself.
	

Before you can really do anything useful with your new neural network
object, you need to teach it some patterns. See the learn() method, below.

=item $net->learn($input_map_ref, $desired_result_ref [, options ]);

This will 'teach' a network to associate an new input map with a desired resuly.
It will return a string containg benchmarking information. You can retrieve the
pattern index that the network stored the new input map in after learn() is complete
with the pattern() method, below.

UPDATED: You can now specify strings as inputs and ouputs to learn, and they will be crunched
automatically. Example:

	$net->learn('corn', 'cob');
	# Before update, you have had to do this:
	# $net->learn($net->crunch('corn'), $net->crunch('cob'));

Note, the old method of calling crunch on the values still works just as well.	

UPDATED: You can now learn inputs with a 0 value. Beware though, it may not learn() a 0 value 
in the input map if you have randomness disabled. See NOTES on using a 0 value with randomness
disabled.

The first two arguments may be array refs (or now, strings), and they may be of different lengths.

Options should be written on hash form. There are three options:
	 
	 inc	=>	$learning_gradient
	 max	=>	$maximum_iterations
	 error	=>	$maximum_allowable_percentage_of_error
	 

$learning_gradient is an optional value used to adjust the weights of the internal
connections. If $learning_gradient is ommitted, it defaults to 0.20.
 
$maximum_iterations is the maximum numbers of iteration the loop should do.
It defaults to 1024.  Set it to 0 if you never want the loop to quit before
the pattern is perfectly learned.

$maximum_allowable_percentage_of_error is the maximum allowable error to have. If 
this is set, then learn() will return when the perecentage difference between the
actual results and desired results falls below $maximum_allowable_percentage_of_error.
If you do not include 'error', or $maximum_allowable_percentage_of_error is set to -1,
then learn() will not return until it gets an exact match for the desired result OR it
reaches $maximum_iterations.


=item $net->learn_set(\@set, [ options ]);

UPDATE: Inputs and outputs in the dataset can now be strings. See information on auto-crunching
in learn()

This takes the same options as learn() and allows you to specify a set to learn, rather
than individual patterns. A dataset is an array refrence with at least two elements in the
array, each element being another array refrence (or now, a scalar string). For each pattern to
learn, you must specify an input array ref, and an ouput array ref as the next element. Example:
	
	my @set = (
		# inputs        outputs
		[ 1,2,3,4 ],  [ 1,3,5,6 ],
		[ 0,2,5,6 ],  [ 0,2,1,2 ]
	);


See the paragraph on measuring forgetfulness, below. There are 
two learn_set()-specific option tags available:

	flag     =>  $flag
	pattern  =>  $row

If "flag" is set to some TRUE value, as in "flag => 1" in the hash of options, or if the option "flag"
is not set, then it will return a percentage represting the amount of forgetfullness. Otherwise,
learn_set() will return an integer specifying the amount of forgetfulness when all the patterns 
are learned. 

If "pattern" is set, then learn_set() will use that pattern in the data set to measure forgetfulness by.
If "pattern" is omitted, it defaults to the first pattern in the set. Example:

	my @set = (
		[ 0,1,0,1 ],  [ 0 ],
		[ 0,0,1,0 ],  [ 1 ],
		[ 1,1,0,1 ],  [ 2 ],  #  <---
		[ 0,1,1,0 ],  [ 3 ]
	);
	
If you wish to measure forgetfulness as indicated by the line with the arrow, then you would
pass 2 as the "pattern" option, as in "pattern => 2".

Now why the heck would anyone want to measure forgetfulness, you ask? Maybe you wonder how I 
even measure that. Well, it is not a vital value that you have to know. I just put in a 
"forgetfulness measure" one day because I thought it would be neat to know. 

How the module measures forgetfulness is this: First, it learns all the patterns in the set provided,
then it will run the very first pattern (or whatever pattern is specified by the "row" option)
in the set after it has finished learning. It will compare the run() output with the desired output
as specified in the dataset. In a perfect world, the two should match exactly. What we measure is
how much that they don't match, thus the amount of forgetfulness the network has.

NOTE: In version 0.77 percentages were disabled because of a bug. Percentages are now enabled.

Example (from examples/ex_dow.pl):

	# Data from 1989 (as far as I know..this is taken from example data on BrainMaker)
	my @data = ( 
		#	Mo  CPI  CPI-1 CPI-3 	Oil  Oil-1 Oil-3    Dow   Dow-1 Dow-3   Dow Ave (output)