A Proof of the Upper Bounds of the Number of Hidden Units in Multistory Feedforward Neural Networks

To investigate the upper bound of the number of the hidden units in feedforward nerual networks and how to utilize the property of the patterns set to reduce the needed number. The property of the two unequal limits at infinities of Sigmoid function was used to make one hidden unit to represent one to two patterns. When the patterns set possesses the property of local monotone, the upper bound is BHDG1,K*2W( p -1)/2BHDG1,WK*2. In general, the upper bound ranges from BHDG1,K*2W( p -1)/2BHDG1,WK*2 to ( p -1).