|
NeuroCOLT
Technical Report NC-TR-97-001
Multilayer
neural networks: one or two hidden layers?
G.
Brightwell
LSE
UK
C. Kenyon and H. Paugam-Moisy
ENS Lyon
France
Abstract
We study the number of hidden layers required by a multilayer neural
network with threshold units to compute a function $f$ from ${\cal
R}^d$ to $\{ 0,1 \}$. In dimension $d=2$, Gibson characterized the
functions computable with just one hidden layer, under the assumption
that there is no ``multiple intersection point" and that $f$
is only defined on a compact set. We consider the restriction of $f$
to the neighborhood of a multiple intersection point or of infinity,
and give necessary and sufficient conditions for it to be locally
computable with one hidden layer. We show that adding these conditions
to Gibson's assumptions is not sufficient to ensure global computability
with one hidden layer, by exhibiting a new non-local configuration,
the ``critical cycle", which implies that $f$ is not computable
with one hidden layer.
Download Compressed Postscript
|