Morphological Hopfield Networks

Abstract

This paper reports on the investigation of the effects of neuronal shape, at both individual cell and network level, on the behavior of neuronal systems. More specifically, two-dimensional biologically realistic neuronal networks are obtained that take explicity into account the position and morphology of neuronal cells, with the respective behavior for associative recall being simulated through a diluted version of Hopfield's model. While a specific probability density function is used for the placement of the cell bodies, images of real neuronal cells (namely alpha and beta ganglion cells from the cat retina) are used to obtain biologically realistic models. Several morphological measures – including fractal dimension, the excluded volume, and integral geometry functionals–are estimated for the considered cells, and their values are correlated with the potential of the network for associative recall, which is quantified in terms of the overlap between distorted version of the trained patterns and their original version. Such an approach allows the quantitative and objective characterization of the relationship between neuronal shape and function, an important issue in neuroscience. The obtained results substantiate interesting relationships between the neural morphology and function as determined by the performance of the network.