The examples are implemented in standard C. They should compile on a standard unix-like operating system, such as ubuntu etc. The C source code archive sources.tar.gz is ready for download.
Assuming the classic software development environment - a terminal running on a unix-, linux-like operating system, please unpack and compile the source files as follows:
tar -xvf sources.tar.gz cd sources make
There are four example programms which can be executed like
./rnnST ./rnnAST ./rnnLowPass ./rnnPG
Without any arguments the programs run with default parameter values. Each prints a series of numeric values on the standard output. This output can be redirected in a file, like this:
./rnnST >t.txt
Now the data are written into file t.txt and can be plotted by other applications.
You might use gnuplot
gnuplot gnuplot> gnuplot> plot [-0.1:1.1][-0.1:1.1] "t.txt" notitle gnuplot>
When executing the command gnuplot the interpreter
environment is activated where you can execute plot-commands as follows
gnuplot> gnuplot> plot [-0.1:1.1][-0.1:1.1] "t.txt" notitle gnuplot>
When executing the command above the following window should be displayed.
The simple time discrete dynamics is applied for these artifical
neural network implementations. Thus, the neuron activity of a single
neuron presented by variable a_1 is calcuated in each
time step by calling the following function
void updateNeuronActivities(double s){
a_1 = B + R*sigmoide(a_1) + s*W;
}
where function paramter s represents the input signal.
Considering a network with more neurons (e.g. the oscillator without input singnal) then the update function is defined as follows:
void updateNeuronActivities(){
a_1 = a*sigmoide(a_1) + b*sigmoide(a_2) - 0.5*(a+b);
a_2 = a*sigmoide(a_2) - b*sigmoide(a_1) + 0.5*(b-a);
a_3 = W*sigmoide(a_2) + P;
}
where neuron activities of three neurons (a_1, a_2 and
a_3) are calculated accordingly.
For all the examples presented here the same transfer function sigmoide(x)
is applied. It is defined as follows:
double sigmoide(double x){
double y;
y = 1.0 / (1 + exp(-x));
return y;
}
According to this definition return value is always large than zero and smaller than one. For this reason all the values serving as input signals for the networks are also in the range of 0.0 to 1.0.
Example 1 - corresponding command:
> >./rnnST >t.txt >gnuplot -e "plot [-0.1:1.1][-0.1:1.1] 't.txt' using 1:2 notitle " -persist >
Example 1 - execution with network and simulation parameters B, R, W and nmbSteps:
> >./rnnST help Wrong number of command line parameters! Please use in the following to ways: 1.) using default values (B=25, R=12, W=-50.0, nmbSteps=5000): ./rnnST 2.) specifing free numeric parameters B, R, W and nmbSteps: ./rnnST <B> <R> <W> <nmbSteps> > > >./rnnST 25 12 -50 5000 >t.txt >gnuplot -e "plot [-0.1:1.1][-0.1:1.1] 't.txt' using 1:2 notitle " -persist >
Example 2 - corresponding command:
> >./rnnLowPass >t.txt >gnuplot -e "plot [:][-0.1:1.1] 't.txt' using 1 with lines notitle " -persist > >gnuplot -e "plot [:][-0.1:1.1] 't.txt' using 2 with lines notitle " -persist > >
Example 2 - execution with network and simulation parameters B, R, W and nmbSteps:
> >./rnnLowPass help Wrong number of command line parameters! Please use in the following to ways: 1.) using default values (B=-2.67, R=5.0, W=0.35, nmbSteps=30000): ./rnnLowPass 2.) specifing free numeric parameters B, R, W and nmbSteps: ./rnnLowPass <B> <R> <W> <nmbSteps> > >./rnnLowPass -2.67 5.0 0.35 30000 > >gnuplot -e "plot 't.txt' using 1 with lines notitle " -persist > >gnuplot -e "plot 't.txt' using 2 with lines notitle " -persist >
Example 3 - corresponding execution with network and simulation parameters B, R, W and nmbSteps:
> >./rnnLowPass help Wrong number of command line parameters! Please use in the following to ways: 1.) using default values (B=-2.67, R=5.0, W=0.35, nmbSteps=30000): ./rnnLowPass 2.) specifing free numeric parameters B, R, W and nmbSteps: ./rnnLowPass <B> <R> <W> <nmbSteps> > >./rnnLowPass -2.67 5.0 0.35 30000 > >gnuplot -e "plot 't.txt' using 1 with lines notitle " -persist > >gnuplot -e "plot 't.txt' using 3 with lines notitle " -persist >
Example 4 - corresponding command:
> >./rnnAST >t.txt >gnuplot -e "plot [-0.1:1.1][-0.1:1.1] 't.txt' using 1:4 notitle " -persist > >
Example 4 - execution with network and simulation parameters S and nmbSteps:
> > ./rnnAST help Wrong number of command line parameters! Please use in the following to ways: 1.) using default values (S=0.6, nmbSteps=5000): ./rnnAST 2.) specifing free numeric parameters S and nmbSteps: ./rnnAST <S> <nmbSteps> > >./rnnAST 0.1 5000 >t.txt > >gnuplot -e "plot 't.txt' using 1:4 notitle " -persist > > >./rnnAST 0.4 5000 >t.txt > >gnuplot -e "plot 't.txt' using 1:4 notitle " -persist >
Example 5 - corresponding command:
> >./rnnPG >t.txt >gnuplot -e "plot [0:400]'t.txt' using 2 notitle, 't.txt' using 3 notitle " -persist > >
Example 5 - execution with network and simulation parameters E, F, B, W and nmbSteps:
> > ./rnnPG help Wrong number of command line parameters! Please use in the following to ways: 1.) using default values (E=0.08, F=0.1, P=-10.0, W=20.0; nmbSteps=5000): ./rnnPG 2.) specifing free numeric parameters E, F, B, W and nmbSteps: ./rnnPG <E> <F> <P> <W> <nmbSteps> > >./rnnPG 0.08 0.1 -10.0 20 5000 >t.txt > >gnuplot -e "plot [0:400]'t.txt' using 2 notitle, 't.txt' using 3 notitle " -persist > >
> > ./rnnPG help Wrong number of command line parameters! Please use in the following to ways: 1.) using default values (E=0.08, F=0.1, P=-10.0, W=20.0; nmbSteps=5000): ./rnnPG 2.) specifing free numeric parameters E, F, B, W and nmbSteps: ./rnnPG <E> <F> <P> <W> <nmbSteps> > >./rnnPG 0.08 0.1 -10.0 20 5000 >t.txt > >gnuplot -e "plot [0:400]'t.txt' using 3 notitle, 't.txt' using 4 notitle " -persist > >
[1] Presentation (pdf)
[2] M. Hülse, Multifunktionalität rekurrenter neuronaler Netze. DISKI 306, 2007.(pdf)
[3] Hülse, M., Pasemann, F.: Dynamical Neural Schmitt Trigger for Robot Control. J. R. Dorronsoro(ed.):
ICANN 2002, LNCS 2415, Springer, 783-788, 2002.(pdf)
[4] Pasemann, F., Hild, M., und Zahedi, K.: SO(2)-Networks as Neural Oscillators. In Proceedings of International
Work-Conference on Artificial and Natural Neural Networks (IWANN) (2003).
(pdf)
[5] Manoonpong, P., Pasemann, F., Fischer, J., Roth, H. (2005). Neural processing of auditory signals and modular neural control for
sound tropism of walking machines. International Journal of Advanced Robotic Systems (ARS), ISSN: 1729-5506, vol. 2, no. 3, pp. 223-234.
(pdf)
[6] Wischmann, S., Hülse, M., Knabe, J., Pasemann, F.: Synchronization of internal neural
rhythms in multi-robotic systems. Adaptive Behavior 14(2): 117-127, 2006. (pdf)
[7] Hülse, M., Wischmann, S., and Pasemann F.: Structure and function of evolved neuro-
controllers for autonomous robots. Connection Science, 16(4): 249-266, 2004.(pdf)
[8] http://manoonpong.com
[9] http://www.neurorobotik.de
[10] Neurocybernetics
[11] http://wischmann.ws