  It has been proposed that neural noise in the cortex arises from chaotic
dynamics in the balanced state: in this model of cortical dynamics, the
excitatory and inhibitory inputs to each neuron approximately cancel, and
activity is driven by fluctuations of the synaptic inputs around their mean. It
remains unclear whether neural networks in the balanced state can perform tasks
that are highly sensitive to noise, such as storage of continuous parameters in
working memory, while also accounting for the irregular behavior of single
neurons. Here we show that continuous parameter working memory can be
maintained in the balanced state, in a neural circuit with a simple network
architecture. We show analytically that in the limit of an infinite network,
the dynamics generated by this architecture are characterized by a continuous
set of steady balanced states, allowing for the indefinite storage of a
continuous parameter. In finite networks, we show that the chaotic noise drives
diffusive motion along the approximate attractor, which gradually degrades the
stored memory. We analyze the dynamics and show that the slow diffusive motion
induces slowly decaying temporal cross correlations in the activity, which
differ substantially from those previously described in the balanced state. We
calculate the diffusivity, and show that it is inversely proportional to the
system size. For large enough (but realistic) neural population sizes, and with
suitable tuning of the network connections, the proposed balanced network can
sustain continuous parameter values in memory over time scales larger by
several orders of magnitude than the single neuron time scale.
