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Generating functionals may guide the evolution of a dynamical system andconstitute a possible route for handling the complexity of neural networks asrelevant for computational intelligence. We propose and explore a new objectivefunction, which allows to obtain plasticity rules for the afferent synapticweights. The adaption rules are Hebbian, self-limiting, and result from theminimization of the Fisher information with respect to the synaptic flux. Weperform a series of simulations examining the behavior of the new learningrules in various circumstances. The vector of synaptic weights aligns with theprincipal direction of input activities, whenever one is present. A lineardiscrimination is performed when there are two or more principal directions;directions having bimodal firing-rate distributions, being characterized by anegative excess kurtosis, are preferred. We find robust performance and fullhomeostatic adaption of the synaptic weights results as a by-product of thesynaptic flux minimization. This self-limiting behavior allows for stableonline learning for arbitrary durations. The neuron acquires new informationwhen the statistics of input activities is changed at a certain point of thesimulation, showing however, a distinct resilience to unlearn previouslyacquired knowledge. Learning is fast when starting with randomly drawn synapticweights and substantially slower when the synaptic weights are already fullyadapted.

Generating functionals for computational intelligence: the Fisher information as an objective function for self-limiting Hebbian learning rules