Stability of completely connected recursive neural networks (Q2705691)

The linear stability of completely connected recursive neural networks is discussed. Conditions are found for the weights in the case when small disturbances of inputs are allowed such that the outputs change also very little. This is done for discrete-time dynamic neural networks with the sigmoidal transfer function. The same is performed when the inputs are kept fixed but the weights can be disturbed. The linear stability is handled for, so to speak, frozen neural networks by means of a Taylor series expansion technique. The authors also require the corresponding conditions for stability to be conditions of structural stability of such neural networks. This seems not to be a precise statement as for structural stability one would need rather the stability against small disturbances of the neural network transfer function as well as of the coefficients in the equations.