Generating Functionals for Computational Intelligence: The Fisher Information as an Objective Function for Self-Limiting Hebbian Learning Rules
Rodrigo Echeveste, Claudius Gros · Frontiers in Robotics and AI · 2014
Generating functionals may guide the evolution ofa dynamical system and constitute a possible route for handling the complexity of neural networks asrelevant for computational intelligence. We propose and explore a new objective function which allows toobtain plasticity rules for the afferent synaptic weights. The adaption rules are Hebbian and self-limitingand result from the minimization of the the Fisher information with respect to the synaptic flux.We perform a series of simulations examining the behavior of the new learning rules in various circumstances. The vector of synaptic weights aligns with the principal direction of input activities, whenever one is present. A linear discrimination is performed when there are two or more principal directions; directions having bimodal firing-ratedistributions, being characterized by a negative excesskurtosis, are preferred. We find robust performance and full homeostaticadaption of the synaptic weights results as a by-productof the synaptic flux minimization. This self-limiting behaviorallows for stable online learning for arbitrary durations.The neuron acquires new information when the statistics ofinput activities is changed at a certain point of the simulation,showing however a distinct resilience to unlearn previously acquired knowledge. Learning is fast when starting with randomlydrawn synaptic weights and substantially slower when thesynaptic weights are already fully adapted.