Balanced excitation and inhibition are required for high-capacity, noise-robust neuronal selectivity.

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 given statistics of afferent activations. Previous work has shown that balanced networks amplify spatiotemporal variability and account for observed asynchronous irregular states. Here we present a distinct type of balanced network that amplifies small changes in the impinging signals and emerges automatically from learning to perform neuronal and network functions robustly.