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The Effect of Noise on a Class of Energy-Based Learning Rules

bazzani{at}bologna.infn.it Department of Physics and INFN, University of Bologna, 40126, Bologna, Italy

D. Remondini

remondini{at}df.unibo.it Department of Physics and INFN, University of Bologna, 40126, Bologna, Italy

N. Intrator

Nathan_Intrator{at}brown.edu Institute for Brain and Neural Systems, Brown University, Providence, RI 02912, U.S.A.

G.C. Castellani

gasto{at}kaiser.alma.unibo.it Department of Physics and DIMORFIPA, University of Bologna, 40126, Bologna, Italy

We study 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.