The effect of noise on a class of energy-based learning rules

Authors:
A. Bazzani;D. Remondini;N. Intrator;G. C. Castellani
Affiliations:
Department of Physics and INFN, University of Bologna, 40126, Bologna, Italy;Department of Physics and INFN, University of Bologna, 40126, Bologna, Italy;Instituted for Brain and Neural Systems, Brown University, Providence, RI;Department of Physics and DIMORFIPA, University of Bologna, 40126, Bologna, Italy
Venue:
Neural Computation
Year:
2003

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Abstract

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.