three preprints available

[Michael Biehl]

FTP-host:       ftp.physik.uni-wuerzburg.de 
FTP-filename:   /pub/preprint/1998/WUE-ITP-98-049.ps.gz
FTP-filename:   /pub/preprint/1998/WUE-ITP-98-055.ps.gz
FTP-filename:   /pub/preprint/1998/WUE-ITP-98-057.ps.gz

The following (three) manuscripts are now available via anonymous ftp,
see below for the retrieval procedure.  More conveniently, they can be 
obtained from the  Wuerzburg Theoretical Physics preprint server in
the WWW: 
         http://theorie.physik.uni-wuerzburg.de/~publications.shtml

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1)  Ref.  WUE-ITP-98-049                           

Receiver Operating Characteristics of Perceptrons: 
Influence of Sample Size and Prevalence
A. Freking, M. Biehl, C. Braun, W. Kinzel, and M. Meesmann

                     ABSTRACT
In many practical classification problems it is important to
distinguish false positive from false negative results when evaluating
the performance of the classifier. This is of particular importance
for medical diagnostic tests. In this context, receiver operating
characteristic (ROC) curves have become a standard tool.
Here we apply this concept to characterize the performance of a simple
neural network. Investigating the binary classification of a
perceptron we calculate analytically the shape of the corresponding
ROC curves. The influence of the size of the training set and the
prevalence of the quality considered are studied by means of a
statistical-mechanics analysis.

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2)  Ref.  WUE-ITP-98-055

Optimisation of on-line principal component analysis
E. Schl"osser, D. Saad, and M. Biehl

                    ABSTRACT 
Various techniques, used to optimise on-line principal component
analysis, are investigated by methods of statistical mechanics. These
include local and global optimisation of node-dependent learning-rates
which are shown to be very efficient in speeding up the learning
process. They are investigated further for gaining insight into the
learning rates' time-dependence, which is then employed for devising
simple practical methods to improve training performance.  Simulations
demonstrate the benefit gained from using the new methods.

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3) Ref.  WUE-ITP-98-057

Statistical physics and practical training of soft-committee machines
M. Ahr, M. Biehl, and R. Urbanczik

                       ABSTRACT
Equilibrium states of large layered neural networks with differentiable 
activation function and a single, linear output unit are investigated 
using the replica formalism. The quenched free energy of a student network 
with a very large number of hidden units learning a rule of perfectly 
matching complexity  is  calculated analytically.  
The system undergoes a first order phase transition from unspecialized 
to specialized student configurations at a critical size of the training 
set. Computer simulations of learning by stochastic gradient descent from 
a fixed training set demonstrate that the equilibrium results describe 
quantitatively the plateau states which occur in practical training 
procedures at sufficiently small but finite learning rates. 

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___________________________________________________________________ 
Retrieval procedure via anonymous ftp: 

     unix> ftp  ftp.physik.uni-wuerzburg.de
     Name: anonymous  Password: {your e-mail address}
     ftp>  cd pub/preprint/1998
     ftp>  binary
     ftp>  get WUE-ITP-98.XXX.ps.gz               (*)   
     ftp>  quit
     unix> gunzip WUE-ITP-98-XXX.ps.gz
e.g. unix> lp -odouble WUE-ITP-98-XXX.ps                        

(*) can be replaced by "get WUE-ITP-98-XXX.ps". The file will then
    be uncompressed before transmission (slow!). 
___________________________________________________________________ 


Michael Biehl     
Institut fuer Theoretische Physik              
Julius-Maximilians-Universitaet Wuerzburg
Am Hubland
D-97074 Wuerzburg 

email:     biehl at physik.uni-wuerzburg.de
www:       http://theorie.physik.uni-wuerzburg.de/~biehl 
Tel.:      (+49) (0)931 888 5865   
             "      "    "  5131
Fax :      (+49) (0)931 888 5141