The capabilities of two-layer perceptrons are examined with respect to the geometric properties of the decision regions they are able to form. It is known that two-layer perceptrons can form decision regions which are nonconvex and even disconnected, though the extent of their capabilities in comparison to three-layer structures is not well understood. By relating the geometry of arrangements of hyperplanes to combinatorial properties of subsets hypercube vertices, certain facts concerning the decision regions of two-layer perceptrons are deduced, and examples of decision regions which can be realized by three-layer perceptrons but not by a two-layer form are constructed. The results indicate that the graduation in ability between two- and three-layer architectures is strict. The examples of nonconvex and disconnected decision regions illustrate that the two-layer perceptron is a more capable structure than was once supposed. >
[1]
M. Reza Emamy-Khansary.
On the cuts and cut number of the 4-cube
,
1986,
J. Comb. Theory, Ser. A.
[2]
Richard P. Lippmann,et al.
An introduction to computing with neural nets
,
1987
.
[3]
Richard Lippmann,et al.
Neural Net and Traditional Classifiers
,
1987,
NIPS.
[4]
Bernard Widrow,et al.
Layered neural nets for pattern recognition
,
1988,
IEEE Trans. Acoust. Speech Signal Process..
[5]
A. El-Jaroudi,et al.
Classification capabilities of two-layer neural nets
,
1989,
International Conference on Acoustics, Speech, and Signal Processing,.