It had previously been shown that generic cortical microcircuit
models can perform complex real-time computations on continuous
input streams, provided that these computations can be carried out
with a rapidly fading memory. We investigate in this article the
computational capability of such circuits in the more realistic case
where not only readout neurons, but in addition a few neurons
within the circuit have been trained for specific tasks. This is
essentially equivalent to the case where the output of trained
readout neurons is fed back into the circuit. We show that this new
model overcomes the limitation of a rapidly fading memory. In fact,
we prove that in the idealized case without noise it can carry out
any conceivable digital or analog computation on time-varying
inputs. But even with noise the resulting computational model can
perform a large class of biologically relevant real-time
computations that require a non-fading memory. We demonstrate these
computational implications of feedback both theoretically, and
through computer simulations of detailed cortical microcircuit
models that are subject to noise and have a complex inherent
dynamics. We show that the application of simple learning
procedures (such as linear regression or perceptron learning) to a
few neurons enables such circuits to represent time over
behaviorally relevant long time spans, to integrate evidence from
incoming spike trains over longer periods of time, and to process
new information contained in such spike trains in diverse ways
according to the current internal state of the circuit. In
particular we show that such generic cortical microcircuits with
feedback provide a new model for working memory that is consistent
with a large set of biological constraints.

Although this article examines primarily the computational role of
feedback in circuits of neurons, the mathematical principles on
which its analysis is based apply to a variety of dynamical
systems. Hence they may also throw new light on the computational
role of feedback in other complex biological dynamical systems, such
as for example genetic regulatory networks.