For neural networks, function determines form
Albertini, F.
Sontag, E.D.
Dept. of Math., Rutgers Univ., New Brunswick, NJ ;
This paper appears in: Decision and Control, 1992., Proceedings of the 31st IEEE Conference on
Publication Date: 1992
On page(s): 26-31 vol.1
Meeting Date: 12/16/1992 - 12/18/1992
Location: Tucson, AZ, USA
ISBN: 0-7803-0872-7
References Cited: 6
INSPEC Accession Number: 4730145
Current Version Published: 2002-08-06
Abstract
It is proved that, generically on nets, the I/O (input-output)
behavior uniquely determines the internal form, up to simple symmetries.
The sets where this conclusion does not hold are thin in the sense that
they are included in sets defined by algebraic equalities. It is shown
that, under very weak genericity assumptions, the following is true:
assume given two nets, whose neurons all have the same nonlinear
activation function σ; if the two sets have equal behaviors as
`black boxes', then necessarily they must have the same number of
neurons and, except at most for sign reversals at each node, the same
weights. The results obtained imply unique identifiability of
parameters, under all possible I/O experiments. It is also possible to
give a result showing that single experiments are (generically)
sufficient for identification, in the analytic case. Some partial
results can be obtained even if the precise nonlinearities are not known
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