On the local minima free condition of backpropagation learning

It is shown that if there are P noncoincident input patterns to learn and a two-layered feedforward neural network having P-1 sigmoidal hidden neuron and one dummy hidden neuron is used for the learning, then any suboptimal equilibrium point of the corresponding error surface is unstable in the sense of Lyapunov. This result leads to a sufficient local minima free condition for the backpropagation learning.