Paper Info
Title
The error surface of the 2-2-1 XOR network: the finite stationary points
Abstract
We investigate the error surface of the XOR problem for a 2-2-1 network with sigmoid transfer functions. It is proved that all stationary points with finite weights are saddle points with positive error or absolute minima with error zero. So, for finite weights no local minima occur. The proof results from a careful analysis of the Taylor series expansion around the stationary points. For some points coefficients of third or even fourth order in the Taylor series expansion are used to complete the proof. The proofs give a deeper insight into the complexity of the error surface in the neighbourhood of saddle points. These results can guide the research in finding learning algorithms that can handle these kinds of saddle paints. (C) 1998 Elsevier Science Ltd. All rights reserved.
Year
DOI
Venue
1998
10.1016/S0893-6080(98)00014-8
Neural Networks
Keywords
DocType
Volume
taylor series expansion,neural network,saddle points,transfer function,saddle point,local minima
Journal
11
Issue
ISSN
Citations 
4
0893-6080
13
PageRank 
References 
Authors
1.88
1
2
Name
Order
Citations
PageRank
Ida G. Sprinkhuizen-kuyper18413.83
Egbert J. W. Boers212220.73