Optimal learning with excitatory and inhibitory synapses

Alessandro Ingrosso

Abstract: Author summary A general analysis of learning with biological synaptic constraints in the presence of statistically structured signals is lacking. Here, analytical techniques from statistical mechanics are leveraged to analyze association storage between analog inputs and outputs with excitatory and inhibitory synaptic weights. The linear perceptron performance is characterized and a link is provided between the weight distribution and the correlations of input/output signals. This formalism can be used to predict the typical properties of perceptron solutions for single learning instances in terms of the principal component analysis of input and output data. This study provides a mean-field theory for sign-constrained regression of practical importance in neuroscience as well as in adaptive control applications.