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\begin{titlepage}
\title{\textbf{Evolution of Transfer Functions \\ in Artificial Neural
Networks\\}}
\author{Roland Knall; Elia Husiatynski \\ rknall@cosy.sbg.ac.at ;
etehusia@cosy.sbg.ac.at \\ \\ Version: 23th of march \\ Uhrzeit: 11:00am \\ \\
(LV-Leiter): Univ. Ass. Roland Schwaiger}

\date{}
\end{titlepage}

\clearpage
\begin{document}
\maketitle
\begin{abstract}
The evolution of transfer algorithms in artificial neural networks is not well
 documented yet. This Paper shows up the posibilities and capabilities of
 them, using genetic algorithms for generation and evolution of
transferfunctions in artificial neurons.\end{abstract}

\chapter{Introduction}
\textit{Artificial Neural Networks} are artificial rebuildings or models
of a very complex and highly undocumented structure:our brain. In our 
brain billions of neurons exchange data. This exchange follows a very 
simple scheme. Inputs are recieved by a neuron on one end, and is sent further
 as an output on the other ends. But what is happening in between?

There exist computer algorithms for a process called \textit{cellular
transfer} but we do know just a few facts about how our braincells do this.
 Therefore our algorithms are only simple models of these 
biological structures.\footnote{Imagine a person who installs a new Operating
System. When the computer will boot the first time everybody is hoping it will
do so without problems, but if it does you will not influence the boot process
anymore, normally. But why? This process gains all the information needed for
the system and this process is the key for an efficient \textit{Operating
System}}, or complex mathematical functions such as the sigmoid function:
\ensuremath{ \varphi (s_{j}) = \frac{1}{1 + exp(-s{_j})}}\footnote{This
function is continous and varies from 0 to 1 as \(-s_{j}\) varies from
$-\infty$ to $\infty$.} Taking this example you can see, that you get a
special range of piutput for a special type of input. These is a standard
procedure for \textit{Artificial Neural Networks}. Normally every node of an
\textit{Artificial Neural Networks} uses this function or similair, but you do
not try to use a different function for every node. This has two reasons
\begin{description} \item[Complex Structure] Normally you build
\textit{Artificial Neural Networks}�s with a given topological strtucture. If
you introduce now different functions for every node, network gets even more
complex, and problems can not be trained in an efficient way.
\item[Singularity] Every node, or even you make it a little bit easier, every
subnet should us e diferent nodes which are optimated for their part. But you
can not design a net topological if you have to use such a complex structure
\end{description} So what can you do, to use evolutionary design, but not
getting mad of the topological structure. The answer is quite simple, you use
evolutionary design, and et the net build itself. You do not have to know the
structure of the net, because the net is not your problem. You allow the net
to change the node transfer functions as they are needed. Therefore you gain a
much mor efficient way for solving problems, because the net controls the
structure, and it is not needed to know the structure of the
\textit{Artificial Neural Networks} to solve problem with it.

Evolutionary design is already in use. But many \textit{Artificial Neural Networks} - Designs ignore the fact,
that transfer functions take influence on the net as much as the net
algorithms do. This contains many efficiency problems. In this paper we want
to document this process for gain of information. How they are working now,
and how they can be improved. The goal of this  is not to improve them, but to
understand the processes better, and to understand the part they play in
\textit{Artificial Neural Networks}. We also will show how different types of
\textit{Artificial Neural Networks} use different types of solutions for this,
and how they can be reused in the design of a fully textit{Evolutional Neural
Network}.
\clearpage
\chapter{Different Types of the same thing}
\section{DNNs, LNNs and GNNs}
\subsection{Distributed Neural Networks}
This type of \textit{Artificial Neural Networks} - Design, where the
multilayer perceptron is the most common in use, uses sigmoid functions
\ensuremath{ \varphi (s_{j}) = \frac{1}{1 + exp(-s{_j})}}\footnote{This
function is continous and varies from 0 to 1 as \(-s_{j}\) varies from
$-\infty$ to $\infty$.}
\appendix \chapter{Protokolle}
\section*{1st Meeting}
\begin{description}
  \item[Date:] 10th March 1999
  \item[Place:] Institute for ComputerSciencees Room 2.xx (Room Univ.Ass. Schwaiger)
  \item[Persons:] Elia Husiatynski,  Roland Knall, Roland Schwaiger
  \item[Discussion:] We discussed the structure of this paper, what it
  should contain, which parts should be included, ... Also we defined a
  modus operandi for future project work. We defined the aims and talked
  about \textit{SNNS}\cite{SNNS1}. Our assisting project controller
  explained that \textit{SNNS} is already used by the institute.
  Finally we agreed in creating a protocoll and the first parts of this
  document.
\end{description}
\section*{2nd Meeting}
\begin{description}
  \item[Date:] 17th March 1999
  \item[Place:] Institute for ComputerScience Room 2.xx (Room Univ.Ass. Schwaiger)
  \item[Persons:] Elia Husiatynski,  Roland Knall, Roland Schwaiger
  \item[Discussion:] We did not complete our work for the week before,
  therefore we had almost nothing to discuss. We talked about a paper
  that already has been done on \textit{transfer functions}, but it turned
  out that our aims will be more detailed. Finally we declared a date for
  the next meeting. During the week, we will summarize the paper,
  and learn more about the structure of \textit{Artificial Neural Networks}s and transferfunctions.
\end{description}
\section*{3rd Meeting}
\begin{description}
  \item[Date:] 24th March 1999
  \item[Place:] Institute for ComputerScience Room 2.xx (Room Univ.Ass. Schwaiger)
  \item[Persons:] Elia Husiatynski,  Roland Knall, Roland Schwaiger
  \item[Discussion:]

\end{description}
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