# Computational aspects of feedback in neural circuits

**W. Maass, P. Joshi, and E. D. Sontag**

### Abstract:

It has 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 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 nonfading 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 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.

**Reference:** W. Maass, P. Joshi, and E. D. Sontag.
Computational aspects of feedback in neural circuits.
*PLoS Computational Biology*, 3(1):e165, 2007.