NAME

AI::NeuralNet::BackProp - A simple back-prop neural net that uses Delta's and Hebbs' rule.

SYNOPSIS

use AI::NeuralNet::BackProp;

# Create a new neural net with 2 layers and 3 neurons per layer
my $net = new AI::NeuralNet::BackProp(2,3);

# Associate first pattern and print benchmark
print "Associating (1,2,3) with (4,5,6)...\n";
print $net->learn([1,2,3],[4,5,6]);

# Associate second pattern and print benchmark
print "Associating (4,5,6) with (1,2,3)...\n";
print $net->learn([4,5,6],[1,2,3]);

# Run a test pattern
print "\nFirst run output: (".join(',',@{$net->run([1,3,2])}).")\n\n";


# Declare patterns to learn
my @pattern = (	15, 3,  5  );
my @result  = ( 16, 10, 11 );

# Display patterns to associate using sub interpolation into a string.
print "Associating (@{[join(',',@pattern)]}) with (@{[join(',',@result)]})...\n";

# Run learning loop and print benchmarking info.
print $net->learn(\@pattern,\@result);

# Run final test
my @test 	  = ( 14, 9,  3  );
my $array_ref = $net->run(\@test);

# Display test output
print "\nSecond run output: (".join(',',@{$array_ref}).")\n";

DESCRIPTION

AI::NeuralNet::BackProp is the flagship package for this file. It 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.

You constuct a new network via the new constructor:

my $net = new AI::NeuralNet::BackProp(2,3);
	

The new() constructor accepts two arguments, $layers and $size (in this example, $layers is 2 and $size is 3).

$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.

This diagram illustrates a simple network, created with a call to "new AI::NeuralNet::BackProp(2,2)" (2 layers, 2 neurons/layer).

 input
 /  \
O    O
|\  /|
| \/ |
| /\ |
|/  \|
O    O
 \  /
mapper

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.

Input is fed into the network via a call like this:

use AI;
my $net = new AI::NeuralNet::BackProp(2,2);

my @map = (0,1);

my $result = $net->run(\@map);

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 expects an array refrence, and run gets mad if you don't give it what it wants. So be nice.

Run returns a refrence with $size elements (Remember $size? $size is what you passed as the second argument to the network constructor.) This array contains the results of the mapping. If you ran the example exactly as shown above, $result would contain (1,1) as its elements.

To make the network learn a new pattern, you simply call the learn method with a sample input and the desired result, both array refrences of $size length. Example:

use AI;
my $net = new AI::NeuralNet::BackProp(2,2);

my @map = (0,1);
my @res = (1,0);

$net->learn(\@map,\@res [, $inc]);

my $result = $net->run(\@map);

$inc is an optinal learning speed increment. Good values are around 0.20 and 0.30. You can experiement with $inc to achieve faster learning speeds. Some values of $inc work better for different maps. If $inc is ommitted, it will default to 0.30 for $inc internally.

Now $result will conain (1,0), effectivly flipping the input pattern around. Obviously, the larger $size is, the longer it will take to learn a pattern. Learn() returns a string in the form of

Learning took X loops and X wallclock seconds (X.XXX usr + X.XXX sys = X.XXX CPU).

With the X's replaced by time or loop values for that loop call. So, to view the learning stats for every learn call, you can just:

print $net->learn(\@map,\@res);

If you call "$net->debug(4)" with $net being the refrence returned by the new() constructor, you will get benchmarking information for the learn function, as well as plenty of other information output. See notes on debug() , in METHODS, below.

If you do call $net->debug(1), it is a good idea to point STDIO of your script to a file, as a lot of information is output. I often use this command line:

$ perl some_script.pl > .out

Then I can simply go and use emacs or any other text editor and read the output at my leisure, rather than have to wait or use some 'more' as it comes by on the screen.

This system was originally created to be a type of content-addressable-memory system. As such, it implements "groups" for storing patterns and maps. After the network has learned the patterns you want, then you can call run with a pattern it has never seen before, and it will decide which of the stored patterns best fit the new pattern, returning the results the same as the above examples (as an array ref from $net->run()).

METHODS

new AI::NeuralNet::BackProp($layers, $size)

Returns a newly created neural network from an AI::NeuralNet::BackProp object. Each group of this network will have $layers number layers in it and each layer will have $size number of neurons in that layer.

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.

$net->learn($input_map_ref, $desired_result_ref [, $learning_gradient ]);

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.

The first two arguments must be array refs, and must be of the same length.

$learning_gradient is an optional value used to adjust the weights of the internal connections. If $learning_gradient is ommitted, it defaults to 0.30.

$net->run($input_map_ref);

This compares the input map with the learn()ed input map of each group, and the group who's comparission comes out as the lowest percentage difference is then used to run the input map.

It will return undef on an error. An error is caused by one of two events.

The first is the possibility that the argument passed is not an array ref. If it is not an array ref, it returns silently a value of undef.

The other condition that could cause an error is the fact that your map contained an element with an undefined value. We don't allow this because it has been in testing that an undefined value can never be weighted. We all know that 12958710924 times 0 is still 0, right? The network can't handle that, though. It will still try to apply as much weight as it can to a 0 value, but the weighting will always come back 0, and therefore, never be able to match the desired result output, thereby creating an infinite learn() loop cycle. Soooo... to prevent the infinite looping, we simply don't allow 0 values to be run. You can always shift all values of your map up one number to account for this if need be, and then subtract one number from every element of the output to shift it down again. Let me know if anyone comes up with a better way to do this.

run() will store the pattern index of the group as created by learn(), so it can be retrieved with the pattern() method, below.

See notes on comparison between run() and slow_run() in NOTES section, below.

$net->slow_run($input_map_ref);

When called with an array refrence to a pattern, returns a refrence to an array associated with that pattern. See usage in documentatio above.

This slow_run() is different from run(), above, in that, the run() above compares the input map with the learn()ed input map of each group, and the group who's comparission comes out as the lowest percentage difference is then used to run the input map.

This slow_run() runs the input map through every neuron group and then compares the result map() with the learn()ed result map, and the result map that has the lowest comparrison percentage is returned as the output map. Some may argue that this could be more accurate. I don't know. I plan to run some more tests on the two methods, but right now I don't have the time. If anyone does come up with any results, or even a better way to sort the outputs, let me know please (jdb@wcoil.com).

slow_run() will store the pattern index of the group as created by learn(), so it can be retrieved with the pattern() method, below.

See notes on comparison between run() and slow_run() in NOTES section, below.

$net->pattern();

This will return the pattern index of the last map learned, or the pattern index of the last map matched, whichever occured most recently.

This is useful if you don't care about the mapping output, but just what it mapped. For example, in the letters.pl example under the ./examples/ directory in the installation tree that you should have gotten when you downloaded this pacakge, this method is used to determine which letter was matched, rather than what the output is. See letters.pl for example usage.

$net->benchmarked();

This returns a benchmark info string for the last learn() or the last run() call, whichever occured later. It is easily printed as a string, as following:

print $net->benchmarked() . "\n";

$net->debug($level)

Toggles debugging off if called with $level = 0 or no arguments. There are four levels of debugging.

Level 0 ($level = 0) : Default, no debugging information printed, except for the 'Cannot run 0 value.' error message. Other than that one message, all printing is left to calling script.

Level 1 ($level = 1) : This causes ALL debugging information for the network to be dumped as the network runs. In this mode, it is a good idea to pipe your STDIO to a file, especially for large programs.

Level 2 ($level = 2) : A slightly-less verbose form of debugging, not as many internal data dumps.

Level 3 ($level = 3) : JUST prints weight mapping as weights change.

Level 4 ($level = 4) : JUST prints the benchmark info for EACH learn loop iteteration, not just learning as a whole. Also prints the percentage difference for each loop between current network results and desired results, as well as learning gradient ('incremenet').

Level 4 is useful for seeing if you need to give a smaller learning incrememnt to learn() . I used level 4 debugging quite often in creating the letters.pl example script and the small_1.pl example script.

Toggles debuging off when called with no arguments.

$net->join_cols($array_ref,$row_length_in_elements,$high_state_character,$low_state_character);

This is more of a utility function than any real necessary function of the package. Instead of joining all the elements of the array together in one long string, like join() , it prints the elements of $array_ref to STDIO, adding a newline (\n) after every $row_length_in_elements number of elements has passed. Additionally, if you include a $high_state_character and a $low_state_character, it will print the $high_state_character (can be more than one character) for every element that has a true value, and the $low_state_character for every element that has a false value. If you do not supply a $high_state_character, or the $high_state_character is a null or empty or undefined string, it join_cols() will just print the numerical value of each element seperated by a null character (\0). join_cols() defaults to the latter behaviour.

$net->pdiff($array_ref_A, $array_ref_B);

This function is used VERY heavily internally to calculate the difference in percent between elements of the two array refs passed. It returns a %.02f (sprintf-format) percent sting.

$net->intr($float);

Rounds a floating-point number passed to an integer using sprintf() and int() , Provides better rounding than just calling int() on the float. Also used very heavily internally.

OTHER INCLUDED PACKAGES

AI::NeuralNet::BackProp::File

AI::NeuralNet::BackProp::File implements a simple 'relational'-style database system. It is used internally by AI::NeuralNet::BackProp for storage and retrival of network states. It can also be used independently of AI::NeuralNet::BackProp. PODs are not yet included for this package, I hope to include documentation for this package in future releases.

AI::NeuralNet::BackProp::neuron

AI::NeuralNet::BackProp::neuron is the worker package for AI::NeuralNet::BackProp. It implements the actual neurons of the nerual network. AI::NeuralNet::BackProp::neuron is not designed to be created directly, as it is used internally by AI::NeuralNet::BackProp.

AI::NeuralNet::BackProp::_run

AI::NeuralNet::BackProp::_map

These two packages, _run and _map are used to insert data into the network and used to get data from the network. The _run and _map packages are connected to the neurons so that the neurons think that the IO packages are just another neuron, sending data on. But the IO packs. are special packages designed with the same methods as neurons, just meant for specific IO purposes. You will never need to call any of the IO packs. directly. Instead, they are called whenever you use the run() or learn() methods of your network.

NOTES

run() and slow_run() compared

Authors thoughts...

Hmm.. this could be something. I just realized: With slow_run() , it compares the _outputs_ (result of each group running input map) with the desired result (output) map of each group. run() only compares the input map with the learn() ed input map.

With run() , that means that the first group that matches closest with learn() ed maps will be run, even if you have learned the same map with different desired results.

With slow_run() , you could conceivably learn one input map with multiple desired results, and then slow_run() will match the result from the input map against all desired results, and return the one that matches closest.

Intersting idea. For now, I don't see much of a need for multiple desired asociations with same input map.

Please let me know if anyone sees any other pros or cons to this issue, and what you think should be done.

load() and save()

These are two methods I have not documented, as they don't work (correctly) yet. They rely on the Storable package, not included, and the AI::NeuralNet::BackProp::File pacakge, included here.

The AI::NeuralNet::BackProp::File package works fine, the problem lies in the load() and save() routines themselves. It seems the freeze() and thaw() functions aren't handling the refrences very well.

I included these functions in this beta release in case anyone felt dareing enough to try to get them working themselves. If you do, please send me a copy of the code! :-)

BUGS

This is the beta release of AI::NeuralNet::BackProp, and that holding true, I am sure there are probably bugs in here which I just have not found yet. If you find bugs in this module, I would appreciate it greatly if you could report them to me at <jdb@wcoil.com>, or, even better, try to patch them yourself and figure out why the bug is being buggy, and send me the patched code, again at <jdb@wcoil.com>.

AUTHOR

Josiah Bryan <jdb@wcoil.com>

Copyright (c) 2000 Josiah Bryan. All rights reserved. This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.

The AI::NeuralNet::BackProp and related modules are free software. THEY COMES WITHOUT WARRANTY OF ANY KIND.

DOWNLOAD

You can always download the latest copy of AI::NeuralNet::BackProp from http://www.josiah.countystart.com/modules/AI/cgi-bin/rec.pl

cpanm AI::NeuralNet::BackProp

perl -MCPAN -e shell
install AI::NeuralNet::BackProp