Correlations in Neural Networks. (360G-Wellcome-082914_Z_07_Z)

A computation in a neural network is a transformation from activity on a set of input fibres to activity on a set of output fibres. Computations depend on the properties of individual neurons in a network and on the connectivity between the neurons. Relating a computation to the connectivity and properties of neurons is one of the central problems in neuroscience. A well known property of neurons is that they are noisy. Recorded activity patterns never repeat, even for the same stimulus. Computations involving neurons in which the noise is uncorrelated have been studied extensively [Averbeck et al., 2006]. By assuming that noise is uncorrelated, the mean activity of a network can be studied and related directly to the computation of interest. This assumption simplifies the study of computation. In the brain, however, noise is correlated. Specifically, the fluctuations in the activity of one neuron about its average are correlated with the fluctuations of other neurons. These noise correlations can increase or decrease the amount of information encoded by a population of neurons [Averbeck et al., 2006]. Correlations may also effect computational strategies of neural networks, learning, and the formation of memories [Roudi and Latham, 2007, Ma et al., 2006] . Correlations are also important as a measure of network structure in experiments [Abeles, 1991]. We will study correlations in neural networks, how they affect the amount of information encoded by a network and the computations it performs. We will relate the connectivity of a network to noise correlations. In this way we will attempt to relate computations to the connectivity and properties of neurons.