shift invariance

[Peter Foldiak]

>  Shift invariance is the ability  of a neural system to recognize a pattern
> independent of where appears on the retina. It is generally understood that
> this property can not be learned by neural network methods, but I have
> not seen a published proof. 

Minsky & Papert: Perceptons, 1969, MIT Press, p 54 :
"... order-1 predicates invariant under the usual geometric groups
can do nothing more than define simple ">=m"-type inequalities on
the size or "area" of the figures. In particular, taking the
translation group G we see that no first-order perceptron can
distinguish the A's in the figure on p. 46 from some other
translation-invarian set of figures of the same area."

This doesn't say anything about multi-layer nets, i.e. you can combine
feaures in a way that will be invariant.
 Peter Foldiak