Neural networks are typically associated with specialised applications,
developed only by select groups of experts. This misconception has had a
highly negative effect on its popularity. Hopefully, the FANN library
will help fill this gap.
Introduction
For years, the Hollywood science fiction films such as I, Robot
have portrayed artificial intelligence (AI) as a harbinger of
Armageddon. Nothing, however, could be farther from the truth. While
Hollywood regales us with horror stories of our imminent demise, people
with no interest in the extinction of our species have been harnessing
AI to make our lives easier, more productive, longer, and generally
better.
The robots in the I, Robot film have an artificial brain
based on a network of artificial neurons; this artificial neural network
(ANN) is built to model the human brain's own neural network. The Fast
Artificial Neural Network (FANN) library is an ANN library, which can be
used from C, C++, PHP, Python, Delphi, and Mathematica, and although it
cannot create Hollywood magic, it is still a powerful tool for software
developers. ANNs can be used in areas as diverse as creating more
appealing game-play in computer games, identifying objects in images,
and helping the stock brokers predict trends of the ever-changing stock
market.
Artificial Intelligence
When is something or somebody intelligent? Is a dog intelligent? How
about a newborn baby? Normally, we define intelligence as the ability to
acquire and apply knowledge, reason deductively, and exhibit
creativity. If we were to apply the same standards to artificial
intelligence (AI), it would follow that there is currently no such thing
as AI. Normally, however, AI is defined as the ability to perform
functions that are typically associated with human intelligence.
Therefore, AI can be used to describe all computerised efforts dealing
with learning or application of human knowledge. This definition allows
the AI term to describe even the simplest chess computer or a character
in the computer game.
Function approximation
ANNs apply the principle of function approximation by example,
meaning that they learn a function by looking at examples of this
function. One of the simplest examples is an ANN learning the XOR
function, but it could just as easily be learning to determine the
language of a text, or whether there is a tumour visible in an X-ray
image.
If an ANN is to be able to learn a problem, it must be defined as a
function with a set of input and output variables supported by examples
of how this function should work. A problem like the XOR function is
already defined as a function with two binary input variables and a
binary output variable, and with the examples which are defined by the
results of four different input patterns. However, there are more
complicated problems which can be more difficult to define as functions.
The input variables to the problem of finding a tumour in an X-ray
image could be the pixel values of the image, but they could also be
some values extracted from the image. The output could then either be a
binary value or a floating-point value representing the probability of a
tumour in the image. In ANNs, this floating-point value would normally
be between 0 and 1, inclusive.
The human brain
A function approximator like an ANN can be viewed as a black box, and
when it comes to FANN, this is more or less all you will need to know.
However, basic knowledge of how the human brain operates is needed to
understand how ANNs work.
The human brain is a highly complicated system which is capable
of solving very complex problems. The brain consists of many different
elements, but one of its most important building blocks is the neuron,
of which it contains approximately 1011. These neurons are connected by
around 1015 connections, creating a huge neural network. Neurons send
impulses to each other through the connections and these impulses make
the brain work. The neural network also receives impulses from the five
senses, and sends out impulses to muscles to achieve motion or speech.
The individual neuron can be seen as an input-output machine which
waits for impulses from the surrounding neurons and, when it has
received enough impulses, it sends out an impulse to other neurons.
Artificial Neural Networks
Artificial neurons are similar to their biological counterparts. They
have input connections which are summed together to determine the
strength of their output, which is the result of the sum being fed into
an activation function. Though many activation functions exist, the most
common is the sigmoid activation function, which outputs a number
between 0 (for low input values) and 1 (for high input values). The
resultant of this function is then passed as the input to other neurons
through more connections, each of which are weighted. These weights
determine the behaviour of the network.
In the human brain, the neurons are connected in a seemingly random
order and send impulses asynchronously. If we wanted to model a brain,
this might be the way to organise an ANN, but since we primarily want to
create a function approximator, ANNs are usually not organised like
this.
When we create ANNs, the neurons are usually ordered in layers with
connections going between the layers. The first layer contains the input
neurons and the last layer contains the output neurons. These input and
output neurons represent the input and output variables of the function
that we want to approximate. Between the input and the output layer, a
number of hidden layers exist and the connections (and weights) to and
from these hidden layers determine how well the ANN performs. When an
ANN is learning to approximate a function, it is shown examples of how
the function works, and the internal weights in the ANN are slowly
adjusted so as to produce the same output as in the examples. The hope
is that when the ANN is shown a new set of input variables, it will give
a correct output. Therefore, if an ANN is expected to learn to spot a
tumour in an X-ray image, it will be shown many X-ray images containing
tumours, and many X-ray images containing healthy tissues. After a
period of training with these images, the weights in the ANN should
hopefully contain information which will allow it to positively identify
tumours in X-ray images that it has not seen during the training.
A FANN library tutorial
The Internet has made global communication a part of many people's
lives, but it has also given rise to the problem that everyone does not
speak the same language. Translation tools can help bridge this gap, but
in order for such tools to work, they need to know in what language a
passage of text is written. One way to determine this is by examining
the frequency of letters occurring in a text. While this seems like a
very naïve approach to language detection, it has proven to be very
effective. For many European languages, it is enough to look at the
frequencies of the letters A to Z, even though some languages also use
other letters as well. Easily enough, the FANN library can be used to
make a small program that determines the language of a text file. The
ANN used should have an input neuron for each of the 26 letters, and an
output neuron for each of the languages. But first, a small program must
be made for measuring the frequency of the letters in a text file.
Listing 1 will generate letter frequencies for a file and output them
in a format that can be used to generate a training file for the FANN
library. Training files for the FANN library must consist of a line
containing the input values, followed by a line containing the output
values. If we wish to distinguish between three different languages
(English, French and Polish), we could choose to represent this by
allocating one output variable with a value of 0 for English, 0.5 for
French, and 1 for Polish. Neural networks are, however, known to perform
better if an output variable is allocated for each language, and that
it is set to 1 for the correct language and 0 otherwise.
Listing 1. Program that calculates the frequencies of the letters A-Z in a text file.
#include <vector>
#include <fstream>
#include <iostream>
#include <ctype.h>
void error(const char* p, const char* p2 = "")
{
std::cerr << p << ' ' << p2 << std::endl;
std::exit(1);
}
void generate_frequencies(const char *filename, float *frequencies)
{
std::ifstream infile(filename);
if(!infile) error("Cannot open input file", filename);
std::vector<unsigned int> letter_count(26, 0);
unsigned int num_characters = 0;
char c;
while(infile.get(c)){
c = tolower(c);
if(c >= 'a' && c <= 'z'){
letter_count[c - 'a']++;
num_characters++;
}
}
if(!infile.eof()) error("Something strange happened");
for(unsigned int i = 0; i != 26; i++){
frequencies[i] = letter_count[i]/(double)num_characters;
}
}
int main(int argc, char* argv[])
{
if(argc != 2) error("Remember to specify an input file");
float frequencies[26];
generate_frequencies(argv[1], frequencies);
for(unsigned int i = 0; i != 26; i++){
std::cout << frequencies[i] << ' ';
}
std::cout << std::endl;
return 0;
}With this small program at hand, a training file containing letter
frequencies can be generated for texts written in the different
languages. The ANN will, of course, be better at distinguishing the
languages if frequencies for many different texts are available in the
training file, but for this small example, 3-4 texts in each language
should be enough. Listing 2 shows a pre-generated training file using
four text files for each of the three languages, and Figure 2 shows a
graphical representation of the frequencies in the file. A thorough
inspection of this file shows clear trends: English has more H's than
the other two languages, French has almost no K's, and Polish has more
W's and Z's than the other languages. The training file only uses
letters in the A to Z range, but since a language like Polish uses
letters like Ł, Ą, and Ę which are not used in the other two languages, a
more precise ANN could be made by adding input neurons for these
letters as well. When only comparing three languages, there is, however,
no need for these added letters since the remaining letters contain
enough information to classify the languages correctly, but if the ANN
were to classify hundreds of different languages, more letters would be
required.
Listing 2. The first part of the training file
with character frequencies for English, French, and Polish, the first
line is a header telling that there are 12 training patterns consisting
of 26 inputs and 3 outputs.
12 26 3
0.103 0.016 0.054 0.060 0.113 0.010 0.010 0.048 0.056
0.003 0.010 0.035 0.014 0.065 0.075 0.013 0.000 0.051
0.083 0.111 0.030 0.008 0.019 0.000 0.016 0.000
1 0 0
0.076 0.010 0.022 0.039 0.151 0.013 0.009 0.009 0.081
0.001 0.000 0.058 0.024 0.074 0.061 0.030 0.011 0.069
0.100 0.074 0.059 0.015 0.000 0.009 0.003 0.003
0 1 0
0.088 0.016 0.030 0.034 0.089 0.004 0.011 0.023 0.071
0.032 0.030 0.025 0.047 0.058 0.093 0.040 0.000 0.062
0.044 0.035 0.039 0.002 0.044 0.000 0.037 0.046
0 0 1
0.078 0.013 0.043 0.043 0.113 0.024 0.023 0.041 0.068
0.000 0.005 0.045 0.024 0.069 0.095 0.020 0.001 0.061
0.080 0.090 0.029 0.015 0.014 0.000 0.008 0.000
1 0 0
0.061 0.005 0.028 0.040 0.161 0.019 0.010 0.010 0.066
0.016 0.000 0.035 0.028 0.092 0.061 0.031 0.019 0.059
0.101 0.064 0.076 0.016 0.000 0.002 0.002 0.000
0 1 0
0.092 0.016 0.038 0.025 0.083 0.000 0.015 0.009 0.087
0.030 0.040 0.032 0.033 0.063 0.085 0.033 0.000 0.049
0.053 0.033 0.025 0.000 0.053 0.000 0.038 0.067
0 0 1
...
Figure 2. A bar chart of the average frequencies in English, French, and Polish.
With a training file like this, it is very easy to create a program
using FANN which can be used to train an ANN to distinguish between the
three languages. Listing 2 shows just how simply this can be done with
FANN. This program uses four FANN functions fann_create, fann_train_on_file, fann_save, and fann_destroy. The function struct fann* fann_create(float connection_rate, float learning_rate, unsigned int num_layers, ...) is used to create an ANN, where the connection_rate
parameter can be used to create an ANN that is not fully connected,
although fully connected ANNs are normally preferred, and the learning_rate
is used to specify how aggressive the learning algorithm should be
(only relevant for some learning algorithms). The last parameters for
the function are used to define the layout of the layers in the ANN. In
this case, an ANN with three layers (one input, one hidden, and one
output) has been chosen. The input layer has 26 neurons (one for each
letter), the output layer has three neurons (one for each language), and
the hidden layer has 13 neurons. The number of layers and number of
neurons in the hidden layer has been selected experimentally, as there
is really no easy way of determining these values. It helps, however, to
remember that the ANN learns by adjusting the weights, so if an ANN
contains more neurons and thereby also more weights, it can learn more
complicated problems. Having too many weights can also be a problem,
since learning can be more difficult and there is also a chance that the
ANN will learn specific features of the input variables instead of
general patterns which can be extrapolated to other data sets. In order
for an ANN to accurately classify data not in the training set, this
ability to generalise is crucial – without it, the ANN will be unable to
distinguish frequencies that it has not been trained with.
Listing 3. A program that trains an ANN to learn to distinguish between languages.
#include "fann.h"
int main()
{
struct fann *ann = fann_create(1, 0.7, 3, 26, 13, 3);
fann_train_on_file(ann, "frequencies.data", 200, 10, 0.0001);
fann_save(ann, "language_classify.net");
fann_destroy(ann);
return 0;
}The void fann_train_on_file(struct fann *ann, char *filename,
unsigned int max_epochs, unsigned int epochs_between_reports, float
desired_error) function trains the ANN. The training is done by
continually adjusting the weights so that the output of the ANN matches
the output in the training file. One cycle where the weights are
adjusted to match the output in the training file is called an epoch. In
this example, the maximum number of epochs have been set to 200, and a
status report is printed every 10 epochs. When measuring how close an
ANN matches the desired output, the mean square error is usually used.
The mean square error is the mean value of the squared difference
between the actual and the desired output of the ANN, for individual
training patterns. A small mean square error means a close match of the
desired output.
When the program in Listing 2 is run, the ANN will be trained and
some status information (see Listing 4) will be printed to make it
easier to monitor progress during training. After training, the ANN
could be used directly to determine which language a text is written in,
but it is usually desirable to keep training and execution in two
different programs, so that the more time-consuming training needs only
be done only once. For this reason, Listing 2 simply saves the ANN to a
file that can be loaded by another program.
Listing 4. Output from FANN during training.
Max epochs 200. Desired error: 0.0001000000
Epochs 1. Current error: 0.7464869022
Epochs 10. Current error: 0.7226278782
Epochs 20. Current error: 0.6682052612
Epochs 30. Current error: 0.6573708057
Epochs 40. Current error: 0.5314316154
Epochs 50. Current error: 0.0589125119
Epochs 57. Current error: 0.0000702030
The small program in Listing 5 loads the saved ANN and uses it to
classify a text as English, French, or Polish. When tested with texts in
the three languages found on the Internet, it can properly classify
texts as short as only a few sentences. Although this method for
distinguishing between languages is not bullet-proof, I was not able to
find a single text that could be classified incorrectly.
Listing 5. A program classifying a text as written in one of the three languages (The program uses some functions defined in Listing 1).
int main(int argc, char* argv[])
{
if(argc != 2) error("Remember to specify an input file");
struct fann *ann = fann_create_from_file("language_classify.net");
float frequencies[26];
generate_frequencies(argv[1], frequencies);
float *output = fann_run(ann, frequencies);
std::cout << "English: " << output[0] << std::endl
<< "French : " << output[1] << std::endl
<< "Polish : " << output[2] << std::endl;
return 0;
}The FANN library: Details
The language classification example shows just how easily the FANN
library can be applied to solve simple, everyday computer science
problems which would be much more difficult to solve using other
methods. Unfortunately, not all problems can be solved this easily, and
when working with ANNs, one often finds oneself in a situation in which
it is very difficult to train the ANN to give the correct results.
Sometimes, this is because the problem simply cannot be solved by ANNs,
but often, the training can be helped by tweaking the FANN library
settings.
The most important factor when training an ANN is the size of the
ANN. This can only be set experimentally, but knowledge of the problem
will often help giving good guesses. With a reasonably sized ANN, the
training can be done in many different ways. The FANN library supports
several different training algorithms, and the default algorithm (FANN_TRAIN_RPROP) might not always be the best-suited for a specific problem. If this is the case, the fann_set_training_algorithm function can be used to change the training algorithm.
In version 1.2.0 of the FANN library, there are four different
training algorithms available, all of which use some sort of back
propagation. Back-propagation algorithms change the weights by
propagating the error backwards from the output layer to the input layer
while adjusting the weights. The back-propagated error value could
either be an error calculated for a single training pattern
(incremental), or it could be a sum of errors from the entire training
file (batch). FANN_TRAIN_INCREMENTAL implements an
incremental training algorithm which alters the weights after each
training pattern. The advantage of such a training algorithm is that the
weights are being altered many times during each epoch, and since each
training pattern alters the weights in slightly different directions,
the training will not easily get stuck in local minima – states in which
all small changes in the weights only make the mean square error worse,
even though the optimal solution may have not yet been found.
FANN_TRAIN_BATCH, FANN_TRAIN_RPROP, and FANN_TRAIN_QUICKPROP
are all examples of batch-training algorithms which alter the weight
after calculating the errors for an entire training set. The advantage
of these algorithms is that they can make use of global optimisation
information which is not available to incremental training algorithms.
This can, however, mean that some of the finer points of the individual
training patterns are being missed. There is no clear answer to the
question which training algorithm is the best. One of the advanced
batch-training algorithms like rprop or quickprop
training is usually the best solution. Sometimes, however, incremental
training is more optimal – especially if many training patterns are
available. In the language training example, the most optimal training
algorithm is the default rprop one, which reached the desired
mean square error value after just 57 epochs. The incremental training
algorithm needed 8108 epochs to reach the same result, while the batch
training algorithm needed 91985 epochs. The quickprop training
algorithm had more problems, and at first, it failed altogether at
reaching the desired error value, but after tweaking the decay of the quickprop algorithm, it reached the desired error after 662 epochs. The decay of the quickprop algorithm is a parameter which is used to control how aggressive the quickprop training algorithm is, and it can be altered by the fann_set_quickprop_decay function. Other fann_set_...
functions can also be used to set additional parameters for the
individual training algorithms, although some of these parameters can be
a bit difficult to tweak without knowledge of how the individual
algorithms work.
One parameter, which is independent of the training algorithm, can
however be tweaked rather easily – the steepness of the activation
function. Activation function is the function that determines when the
output should be close to 0 and when it should be close to 1, and the
steepness of this function determines how soft or hard the transition
from 0 to 1 should be. If the steepness is set to a high value, the
training algorithm will converge faster to the extreme values of 0 and
1, which will make training faster, for an e.g., the language
classification problem. However, if the steepness is set to a low value,
it is easier to train an ANN that requires fractional output, like
e.g., an ANN that should be trained to find the direction of a line in
an image. For setting the steepness of the activation function, FANN
provides two functions: fann_set_activation_steepness_hidden and fann_set_activation_steepness_output. There are functions because it is often desirable to have different steepness for the hidden layers and for the output layer.
FANN possibilities
The language identification problem belongs to a special kind of
function approximation problems known as classification problems.
Classification problems have one output neuron per classification, and
in each training pattern, precisely one of these outputs must be 1. A
more general function approximation problem is where the outputs are
fractional values. This could, e.g., be approximating the distance to an
object viewed by a camera, or even the energy consumption of a house.
These problems could of course be combined with classification problems,
so there could be a classification problem of identifying the kind of
object in an image and a problem of approximating the distance to the
object. Often, this can be done by a single ANN, but sometimes it might
be a good idea to keep the two problems separate, and e.g., have an ANN
which classifies the object, and an ANN for each of the different
objects which approximates the distance to the object.
Another kind of approximation problems are the time-series problems,
approximating functions which evolve over time. A well known time-series
problem is predicting how many sunspots there will be in a year by
looking at historical data. Normal functions have an x-value as an input
and a y-value as an output, and the sunspot problem could also be
defined like this, with the year as the x-value and the number of sun
spots as the y-value. This has, however, proved not to be the best way
of solving such problems. Time-series problems can be approximated by
using a period of time as input and then using the next time step as
output. If the period is set to 10 years, the ANN could be trained with
all the 10-year periods where historical data exists, and it could then
approximate the number of sunspots in 2005 by using the number of sun
spots in 1995 – 2004 as inputs. This approach means that each set of
historical data is used in several training patterns, e.g., the number
of sunspots for 1980 is used in training patterns with 1981 – 1990 as
outputs. This approach also means that the number of sunspots cannot be
directly approximated for 2010 without first-approximating 2005 – 2009,
which in turn will mean that half of the input for calculating 2010 will
be approximated data and that the approximation for 2010 will not be as
precise as the approximation for 2005. For this reason, time-series
prediction is only well-fitted for predicting things in the near future.
Time-series prediction can also be used to introduce memory in
controllers for robots etc. This could, e.g., be done by giving the
direction and speed from the last two time steps as input to the third
time step, in addition to other inputs from sensors or cameras. The
major problem of this approach is, however, that training data can be
very difficult to produce, since each training pattern must also include
history.
FANN tips & tricks
Lots of tricks can be used to make FANN train and execute faster and
with greater precision. A simple trick which can be used to make
training faster and more precise is to use input and output values in
the range -1 to 1 as opposed to 0 to 1. This can be done by changing the
values in the training file and using fann_set_activation_function_hidden and fann_set_activation_function_output to change the activation function to FANN_SIGMOID_SYMMETRIC,
which has outputs in the range of -1 and 1 instead of 0 and 1. This
trick works because 0 values in ANNs have an unfortunate feature that no
matter which value the weight has, the output will still be 0. There
are, of course, countermeasures in FANN to prevent this from becoming a
big problem; however, this trick has been proved to reduce training
time. The fann_set_activation_function_output can also be used to change the activation function to the FANN_LINEAR activation function which is unbounded and can therefore be used to create ANNs with arbitrary outputs.
When training an ANN, it is often difficult to find out how many
epochs should be used for training. If too few epochs are used during
training, the ANN will not be able to classify the training data. If,
however, too many iterations are used, the ANN will be too specialised
in the exact values of the training data, and the ANN will not be good
at classifying data it has not seen during training. For this reason, it
is often a good idea to have two sets of training data, one applied
during the actual training and one applied to verify the quality of the
ANN by testing it on data which have not been seen during the training.
The fann_test_data function can be used for this purpose, along with other functions which can be used to handle and manipulate training data.
Transforming a problem into a function which can easily be learned by
an ANN can be a difficult task, but some general guidelines can be
followed:
- Use at least one input/output neuron for each informative unit. In
the case of the language classification system, this means to have one
input neuron for each letter and one output neuron for each language.
- Represent all the knowledge that you as a programmer have about
the problem when choosing the input neurons. If you, e.g., know that
the word length is important for the language classification system,
then you should also add an input neuron for the word length (this could
also be done by adding an input neuron for the frequency of spaces).
Also, if you know that some letters are only used in some languages,
then it might be an idea to add an extra input neuron which is 1 if the
letter is present in the text and 0 if the letter is not present. In
this way, even a single Polish letter in a text can help classifying
this text. Perhaps, you know that some languages contain more vowels
than others and you can then represent the frequency of the vowels as an
extra input neuron.
- Simplify the problem. If you, e.g., want to use an ANN for
detection of some features in an image, then it might be a good idea to
simplify the image in order to make the problem easier to solve, since
the raw image will often contain far too much information and it will be
difficult for the ANN to filter out the relevant information. In
images, simplification can be done by applying some filters to do
smoothing, edge-detection, ridge-detection, grey-scaling etc. Other
problems can be simplified by preprocessing data in other ways to remove
unnecessary information. Simplification can also be done by splitting
an ANN into several easier-to-solve problems. In the language
classification problem, one ANN could, e.g., distinguish between
European and Asian languages, while two others could be used to classify
the individual languages in the two areas.
While training the ANN is often the big time consumer, execution can
often be more time-critical – especially in systems where the ANN needs
to be executed hundreds of times per second or if the ANN is very large.
For this reason, several measures can be applied to make the FANN
library execute even faster than it already does. One method is to
change the activation function to use a stepwise linear activation
function, which is faster to execute, but which is also a bit less
precise. It is also a good idea to reduce the number of hidden neurons
if possible, since this will reduce the execution time. Another method,
only effective on embedded systems without a floating point processor,
is to let the FANN library execute by using integers only. The FANN
library has a few auxiliary functions allowing the library to be
executed using only integers, and on systems which does not have a
floating point processor, this can give a performance enhancement of
more than 5000%.
On the Net
A tale from the open source world
When I first released the FANN library version 1.0 in November 2003, I
did not really know what to expect, but I thought that everybody should
have the option to use this new library that I had created. Much to my
surprise, people actually started downloading and using the library. As
months went by, more and more users started using FANN, and the library
evolved from being a Linux-only library to supporting most major
compilers and operating systems (including MSVC++ and Borland C++). The
functionality of the library was also considerably expanded, and many of
the users started contributing to the library. Soon the library had
bindings for PHP, Python, Delphi, and Mathematica, and the library also
became accepted in the Debian Linux distribution. My work with FANN and
the users of the library take up some of my spare time, but it is a time
that I gladly spend. FANN gives me an opportunity to give something
back to the open source community, and it gives me a chance to help
people, while doing stuff I enjoy. I cannot say that developing Open
Source software is something that all software developers should do, but
I will say that it has given me a great deal of satisfaction, so if you
think that it might be something for you, then find an Open Source
project that you would like to contribute to, and start contributing. Or
even better, start your own Open Source project.
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