PROBABILITY DENSITY METHODS FOR SMOOTH FUNCTION APPROXIMATION AND LEARNING IN POPULATIONS OF TUNED SPIKING NEURONS

This article proposes a new method for interpreting computations perfo rmed by populations of spiking neurons. Neural firing is modeled as a rate-modulated random process for which the behavior of a neuron in re sponse to external input can be completely described by its tuning fun ction. I show that under certain conditions, cells with any desired tu ning functions can be approximated using only spike coincidence detect ors and linear operations on the spike output of existing cells. I sho w examples of adaptive algorithms based on only spike data that cause the underlying cell-tuning curves to converge according to standard su pervised and unsupervised learning algorithms. Unsupervised learning b ased on principal components analysis leads to independent cell spike trains. These results suggest a duality relationship between the rando m discrete behavior of spiking cells and the deterministic smooth beha vior of their tuning functions. Classical neural network approximation methods and learning algorithms based on continuous variables can thu s be implemented within networks of spiking neurons without the need t o make numerical estimates of the intermediate cell firing rates.