AI::NeuralNet::Simple - An easy to use backprop neural net.


  use AI::NeuralNet::Simple;
  my $net = AI::NeuralNet::Simple->new(2,1,2);
  # teach it logical 'or'
  for (1 .. 10000) {
  printf "Answer: %d\n",   $net->winner([1,1]);
  printf "Answer: %d\n",   $net->winner([1,0]);
  printf "Answer: %d\n",   $net->winner([0,1]);
  printf "Answer: %d\n\n", $net->winner([0,0]);


  This module is a simple neural net designed for those who have an interest
  in artificial intelligence but need a "gentle" introduction.  This is not
  intended to replace any of the neural net modules currently available on the


The Disclaimer

Please note that the following information is terribly incomplete. That's deliberate. Anyone familiar with neural networks is going to laugh themselves silly at how simplistic the following information is and the astute reader will notice that I've raised far more questions than I've answered.

So why am I doing this? Because I'm giving just enough information for someone new to neural networks to have enough of an idea of what's going on so they can actually use this module and then move on to something more powerful, if interested.

The Biology

A neural network, at its simplest, is merely an attempt to mimic nature's "design" of a brain. Like many successful ventures in the field of artificial intelligence, we find that blatantly ripping off natural designs has allowed us to solve many problems that otherwise might prove intractable. Fortunately, Mother Nature has not chosen to apply for patents.

Our brains are comprised of neurons connected to one another by axons. The axon makes the actual connection to a neuron via a synapse. When neurons receive information, they process it and feed this information to other neurons who in turn process the information and send it further until eventually commands are sent to various parts of the body and muscles twitch, emotions are felt and we start eyeing our neighbor's popcorn in the movie theater, wondering if they'll notice if we snatch some while they're watching the movie.

A simple example of a neuron

Now that you have a solid biology background (uh, no), how does this work when we're trying to simulate a neural network? The simplest part of the network is the neuron (also known as a node or, sometimes, a neurode). A we might think of a neuron as follows (OK, so I won't make a living as an ASCII artist):

Input neurons Synapses Neuron Output

  n1            ---w1----> /    \
  n2            ---w2---->|  n4  |---w4---->
  n3            ---w3----> \    /

(Note that the above doesn't quite match what's in the C code for this module, but it's close enough for you to get the idea. This is one of the many oversimplifications that have been made).

In the above example, we have three input neurons (n1, n2, and n3). These neurons feed whatever output they have through the three synapses (w1, w2, w3) to the neuron in question, n4. The three synapses each have a "weight", which is an amount that the input neurons' output is multiplied by.

The neuron n4 computes its output with something similar to the following:

  output = 0

  foreach (input.neuron)
      output += input.neuron.output * input.neuron.synapse.weight

  ouput = activation_function(output)

The "activation function" is a special function that is applied to the inputs to generate the actual output. There are a variety of activation functions available with three of the most common being the linear, sigmoid, and tahn activation functions. For technical reasons, the linear activation function cannot be used with the type of network that AI::NeuralNet::Simple employs. This module uses the sigmoid activation function. (More information about these can be found by reading the information in the "SEE ALSO" section or by just searching with Google.)

Once the activation function is applied, the output is then sent through the next synapse, where it will be multiplied by w4 and the process will continue.

AI::NeuralNet::Simple architecture

The architecture used by this module has (at present) 3 fixed layers of neurons: an input, hidden, and output layer. In practice, a 3 layer network is applicable to many problems for which a neural network is appropriate, but this is not always the case. In this module, we've settled on a fixed 3 layer network for simplicity.

Here's how a three layer network might learn "logical or". First, we need to determine how many inputs and outputs we'll have. The inputs are simple, we'll choose two inputs as this is the minimum necessary to teach a network this concept. For the outputs, we'll also choose two neurons, with the neuron with the highest output value being the "true" or "false" response that we are looking for. We'll only have one neuron for the hidden layer. Thus, we get a network that resembles the following:

           Input   Hidden   Output

 input1  ----> n1 -+    +----> n4 --->  output1
                    \  /
                    /  \
 input2  ----> n2 -+    +----> n5 --->  output2

Let's say that output 1 will correspond to "false" and output 2 will correspond to true. If we feed 1 (or true) or both input 1 and input 2, we hope that output 2 will be true and output 1 will be false. The following table should illustrate the expected results:

 input   output
 1   2   1    2
 -----   ------
 1   1   0    1
 1   0   0    1
 0   1   0    1
 0   0   1    0

The type of network we use is a forward-feed back error propagation network, referred to as a back-propagation network, for short. The way it works is simple. When we feed in our input, it travels from the input to hidden layers and then to the output layers. This is the "feed forward" part. We then compare the output to the expected results and measure how far off we are. We then adjust the weights on the "output to hidden" synapses, measure the error on the hidden nodes and then adjust the weights on the "hidden to input" synapses. This is what is referred to as "back error propagation".

We continue this process until the amount of error is small enough that we are satisfied. In reality, we will rarely if ever get precise results from the network, but we learn various strategies to interpret the results. In the example above, we use a "winner takes all" strategy. Which ever of the output nodes has the greatest value will be the "winner", and thus the answer.

In the examples directory, you will find a program named "" which demonstrates the above process.

Building a network

In creating a new neural network, there are three basic steps:

1 Designing

This is choosing the number of layers and the number of neurons per layer. In AI::NeuralNet::Simple, the number of layers is fixed.

With more complete neural net packages, you can also pick which activation functions you wish to use and the "learn rate" of the neurons.

2 Training

This involves feeding the neural network enough data until the error rate is low enough to be acceptable. Often we have a large data set and merely keep iterating until the desired error rate is achieved.

3 Measuring results

One frequent mistake made with neural networks is failing to test the network with different data from the training data. It's quite possible for a backpropagation network to hit what is known as a "local minimum" which is not truly where it should be. This will cause false results. To check for this, after training we often feed in other known good data for verification. If the results are not satisfactory, perhaps a different number of neurons per layer should be tried or a different set of training data should be supplied.

Programming AI::NeuralNet::Simple

new($input, $hidden, $output)

new() accepts three integers. These number represent the number of nodes in the input, hidden, and output layers, respectively. To create the "logical or" network described earlier:

  my $net = AI::NeuralNet::Simple->new(2,1,2);

By default, the activation function for the neurons is the sigmoid function S() with delta = 1:

        S(x) = 1 / (1 + exp(-delta * x))

but you can change the delta after creation. You can also use a bipolar activation function T(), using the hyperbolic tangent:

        T(x) = tanh(delta * x)
        tanh(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))

which allows the network to have neurons negatively impacting the weight, since T() is a signed function between (-1,+1) whereas S() only falls within (0,1).


Fetches the current delta used in activation functions to scale the signal, or sets the new delta. The higher the delta, the steeper the activation function will be. The argument must be strictly positive.

You should not change delta during the traning.


Returns whether the network currently uses a bipolar activation function. If an argument is supplied, instruct the network to use a bipolar activation function or not.

You should not change the activation function during the traning.

train(\@input, \@output)

This method trains the network to associate the input data set with the output data set. Representing the "logical or" is as follows:

  $net->train([1,1] => [0,1]);
  $net->train([1,0] => [0,1]);
  $net->train([0,1] => [0,1]);
  $net->train([0,0] => [1,0]);

Note that a one pass through the data is seldom sufficient to train a network. In the example "logical or" program, we actually run this data through the network ten thousand times.

  for (1 .. 10000) {
    $net->train([1,1] => [0,1]);
    $net->train([1,0] => [0,1]);
    $net->train([0,1] => [0,1]);
    $net->train([0,0] => [1,0]);

The routine returns the Mean Squared Error (MSE) representing how far the network answered.

It is far preferable to use train_set() as this lets you control the MSE over the training set and it is more efficient because there are less memory copies back and forth.

train_set(\@dataset, [$iterations, $mse])

Similar to train, this method allows us to train an entire data set at once. It is typically faster than calling individual "train" methods. The first argument is expected to be an array ref of pairs of input and output array refs.

The second argument is the number of iterations to train the set. If this argument is not provided here, you may use the iterations() method to set it (prior to calling train_set(), of course). A default of 10,000 will be provided if not set.

The third argument is the targeted Mean Square Error (MSE). When provided, the traning sequence will compute the maximum MSE seen during an iteration over the training set, and if it is less than the supplied target, the training stops. Computing the MSE at each iteration costs, but you are certain to not over-train your network.

    [1,1] => [0,1],
    [1,0] => [0,1],
    [0,1] => [0,1],
    [0,0] => [1,0],
  ], 10000, 0.01);

The routine returns the MSE of the last iteration, which is the highest MSE seen over the whole training set (and not an average MSE).


If called with a positive integer argument, this method will allow you to set number of iterations that train_set will use and will return the network object. If called without an argument, it will return the number of iterations it was set to.

  $net->iterations;         # returns 100000
  my @training_data = ( 
    [1,1] => [0,1],
    [1,0] => [0,1],
    [0,1] => [0,1],
    [0,0] => [1,0],
  $net->iterations(100000) # let's have lots more iterations!


This method, if called without an argument, will return the current learning rate. .20 is the default learning rate.

If called with an argument, this argument must be greater than zero and less than one. This will set the learning rate and return the object.

  $net->learn_rate; #returns the learning rate

If you choose a lower learning rate, you will train the network slower, but you may get a better accuracy. A higher learning rate will train the network faster, but it can have a tendancy to "overshoot" the answer when learning and not learn as accurately.


This method, if provided with an input array reference, will return an array reference corresponding to the output values that it is guessing. Note that these values will generally be close, but not exact. For example, with the "logical or" program, you might expect results similar to:

  use Data::Dumper;
  print Dumper $net->infer([1,1]);
  $VAR1 = [

That clearly has the second output item being close to 1, so as a helper method for use with a winner take all strategy, we have ...


This method returns the index of the highest value from inferred results:

  print $net->winner([1,1]); # will likely print "1"

For a more comprehensive example of how this is used, see the "examples/" program.


None by default.


This is alpha code. Very alpha. Not even close to ready for production, don't even think about it. I'm putting it on the CPAN lest it languish on my hard-drive forever. Hopefully someone will get some use out of it and think to send me a patch or two.


  • Allow different numbers of layers




AI::FANN - Perl wrapper for the Fast Artificial Neural Network library

AI::NNFlex - A base class for implementing neural networks

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

"AI Application Programming by M. Tim Jones, copyright (c) by Charles River Media, Inc.

The C code in this module is based heavily upon Mr. Jones backpropogation network in the book. The "game ai" example in the examples directory is based upon an example he has graciously allowed me to use. I had to use it because it's more fun than many of the dry examples out there :)

"Naturally Intelligent Systems", by Maureen Caudill and Charles Butler, copyright (c) 1990 by Massachussetts Institute of Technology.

This book is a decent introduction to neural networks in general. The forward feed back error propogation is but one of many types.


Curtis "Ovid" Poe, ovid [at] cpan [dot] org

Multiple network support, persistence, export of MSE (mean squared error), training until MSE below a given threshold and customization of the activation function added by Raphael Manfredi


Copyright (c) 2003-2005 by Curtis "Ovid" Poe

Copyright (c) 2006 by Raphael Manfredi

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself.