DYNAMICS OF NEURAL NETWORKS WITH NONMONOTONE ACTIVATION FUNCTION

We analyse an artificial neural network which deviates from biological behaviour in two aspects. First, the process of activation of a generic neuron is not described by a monotone increasing output function. This means that, while artificial neurons modelled on biological behaviour are active when the sum of the postsynaptic potentials is larger than a given threshold and quiescient in the opposite case, in our model the state of the neuron depends non-monotonically on its argument, i.e. the activation function is not an increasing function, but has a mom complicated behaviour which reduces to the usual (step or sigmoid) function for some particular values of the parameters describing its shape. Second, we assume as a learning rule of the network a modification of the Hebb rule, namely we choose an iterative algorithm (Edinburgh algorithm) that constructs a synaptic matrix with a given set of stored memories and given retrieval properties, i.e. given domains of attraction of the stored patterns. The non-monotonicity of the output function results, for some values of the parameters, in a larger storage capacity than in conventional models, whereas the choice of the learning rule allows to control the domains of attraction of the memories.