# A simple model for neural computation with firing rates and firing
correlations

### Abstract:

A simple extension of standard neural network models is introduced which
provides a model for neural computations that involve both firing rates and
firing correlations. Such an extension appears to be useful since it has been
shown that firing correlations play a significant computational role in many
biological neural systems. Standard neural network models are only suitable
for describing neural computations in terms of firing rates. The resulting
extended neural network models are still relatively simple, so that their
computational power can be analysed theoretically. We prove rigorous
separation results, which show that the use of firing correlations in
addition to firing rates can drastically increase the computational power of
a neural network. Furthermore, one of our separation results also throws new
light on a question that involves just standard neural network models: we
prove that the gap between the computational power of high-order and
first-order neural nets is substantially larger than shown previously.

**Reference:** W. Maass.
A simple model for neural computation with firing rates and firing
correlations.
*Network: Computation in Neural Systems*, 9(3):381-397, 1998.