1992
@article{Son1992,
vgclass = {refpap},
vgproject = {nn},
author = {Eduardo D. Sontag},
title = {Feedback Stabilization Using Two-Hidden-Layer Nets},
journal = {IEEE Transactions on Neural Networks},
volume = {3},
pages = {981--990},
year = {1992},
abstract = {This report compares the representational capabilities of
three-layer (that is, ``one hidden layer'') and four-layer
(``two-hidden-layer'') nets consisting of feedforward interconnections
of linear threshold units.
It is remarked that for certain problems four layers are required,
contrary to what might be in principle expected from the known
approximation theorems. The differences are not based on numerical
accuracy or number of units needed, nor on capabilities for feature
extraction, but rather on a much more basic classification into
``direct'' and ``inverse'' problems. The former correspond to the
approximation of continuous functions, while the latter are concerned
with approximating one-sided inverses of continuous functions -- and
are often encountered in the context of inverse kinematics
determination or in control questions.
A general result is given showing that nonlinear control systems can be
stabilized using four layers, but not in general using three layers.},
}