title: The effect of noise on a class of energy-based learning rules.
abstract: Westudy the selectivity properties of neurons based on BCM and kurtosis energy functions in a general case of noisy high-dimensional input space. The proposed approach, which is used for characterization of the stable states, can be generalized to a whole class of energy functions. We characterize the critical noise levels beyond which the selectivity is destroyed. We also perform a quantitative analysis of such transitions, which shows interesting dependency on data set size. We observe that the robustness to noise of the BCM neuron (Bienenstock, Cooper, & Munro, 1982; Intrator & Cooper, 1992) increases as a function of dimensionality. We explicitly compute the separability limit of BCM and kurtosis learning rules in the case of a bimodal input distribution. Numerical simulations show a stronger robustness of the BCM rule for practical data set size when compared with kurtosis.
authors.affiliation: Department of Physics, University of Bologna, 40126, Bologna, Italy. bazzani@bologna.infn.it
authors.forename: A
authors.initials: A
authors.lastname: Bazzani
authors.forename: D
authors.initials: D
authors.lastname: Remondini
authors.forename: N
authors.initials: N
authors.lastname: Intrator
authors.forename: G C
authors.initials: GC
authors.lastname: Castellani
mesh_terms: D004560:Electricity; D004734:Energy Metabolism / Q000502:physiology*; D007858:Learning / Q000502:physiology*; D008959:Models, Neurological; D016011:Normal Distribution