2 papers: 1. Phase transitions in multilayered nets, 2. Self-averaging and online learning

[Michael Biehl]

FTP-host:       ftp.physik.uni-wuerzburg.de 
FTP-filename:   /pub/preprint/1998/WUE-ITP-98-014.ps.gz
FTP-filename:   /pub/preprint/1998/WUE-ITP-98-002.ps.gz  

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

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Ref.  WUE-ITP-98-014                                     [8 pages]

        Phase transitions in soft--committee machines
            M.Biehl, E. Schl\"osser, and M. Ahr

Equilibrium statistical physics is applied to layered neural networks 
with differentiable activation functions.  A first analysis of off-line 
learning in soft-committee machines with N input and K hidden units 
learning a perfectly matching rule is performed.
Our results are exact in the limit of high training temperatures. For
K=2 we find a second order phase transition from  unspecialized to 
specialized student configurations at a critical size P of the training 
set, whereas for K > 2 the transition is first order. 
The limit K to infinity can be performed analytically, the transition 
occurs after presenting  on the order of  N K  examples. However, an
unspecialized metastable state  persists up to  P= O (N K^2).
Monte Carlo simulations indicate that our results are also valid for
moderately low temperatures qualitatively.

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Ref.  WUE-ITP-98-002                                     [10 pages]

        Self-averaging and On-line Learning
           G. Reents and R. Urbanczik           
         (to appear in Phys. Rev. Letters)

Conditions are given under which one may prove that the stochastic
dynamics of on-line learning can be described by the deterministic
evolution of a finite set of order parameters in the thermodynamic
limit. A global constraint on the average magnitude of the increments 
in the stochastic process is necessary to ensure self-averaging. In the
absence of such a constraint, convergence may only be in probability.
          

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  e-mail :   biehl at physik.uni-wuerzburg.de
            reents at physik.uni-wuerzburg.de