A SIMPLE-MODEL FOR NEURAL COMPUTATION WITH FIRING RATES AND FIRING CORRELATIONS

A simple extension of standard neural network models is introduced whi ch provides a model for neural computations that involve both firing r ates and firing correlations. Such an extension appears to be useful s ince it has been shown that firing correlations play a significant com putational role in many biological neural systems. Standard neural net work models are only suitable for describing neural computations in te rms of firing rates. The resulting extended neural network models are still relatively simple, so that their computational power can be anal ysed theoretically. We prove rigorous separation results, which show t hat the use of firing correlations in addition to firing rates can dra stically increase the computational power of a neural network. Further more, one of our separation results also throws new light on a questio n that involves just standard neural network models: we prove that the gap between the computational power of high-order and first-order neu ral nets is substantially larger than shown previously.