On the properties of input-to-output transformations in networks of perceptrons

Information processing in certain neuronal networks in the brain can be considered as a map of binary vectors, where ones (spikes) and zeros (no spikes) of input neurons are transformed into spikes and no spikes of output neurons. A simple but fundamental characteristic of such a map is how it transforms distances between input vectors. In particular what is the mean distance between output vectors given certain distance between input vectors? Using combinatorial approach we found an exact solution to this problem for networks of perceptrons with binary weights. he resulting formulas allow for precise analysis how network connectivity and neuronal excitability affect the transformation of distances between the vectors of neuronal spiking. As an application, we considered a simple network model of information processing in the hippocampus, a brain area critically implicated in learning and memory, and found a combination of parameters for which the output neurons discriminated similar and distinct inputs most effectively. A decrease of threshold values of the output neurons, which in biological networks may be associated with decreased inhibition, impaired optimality of discrimination.