  Neurons and networks in the cerebral cortex must operate reliably despite
multiple sources of noise. To evaluate the impact of both input and output
noise, we determine the robustness of single-neuron stimulus selective
responses, as well as the robustness of attractor states of networks of neurons
performing memory tasks. We find that robustness to output noise requires
synaptic connections to be in a balanced regime in which excitation and
inhibition are strong and largely cancel each other. We evaluate the conditions
required for this regime to exist and determine the properties of networks
operating within it. A plausible synaptic plasticity rule for learning that
balances weight configurations is presented. Our theory predicts an optimal
ratio of the number of excitatory and inhibitory synapses for maximizing the
encoding capacity of balanced networks for a given statistics of afferent
activations. Previous work has shown that balanced networks amplify
spatio-temporal variability and account for observed asynchronous irregular
states. Here we present a novel type of balanced network that amplifies small
changes in the impinging signals, and emerges automatically from learning to
perform neuronal and network functions robustly.
