# Principles of real-time computing with feedback applied to cortical
microcircuit models

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

### Abstract:

The network topology of neurons in the brain exhibits an abundance of feedback
connections, but the computational function of these feedback connections is
largely unknown. We present a computational theory that characterizes the
gain in computational power achieved through feedback in dynamical systems
with fading memory. It implies that many such systems acquire through
feedback universal computational capabilities for analog computing with a
non-fading memory. In particular, we show that feedback enables such systems
to process time-varying input streams in diverse ways according to rules that
are implemented through internal states of the dynamical system. In contrast
to previous attractor-based computational models for neural networks, these
flexible internal states are *high-dimensional* attractors of the circuit
dynamics, that still allow the circuit state to absorb new information from
online input streams. In this way one arrives at novel models for working
memory, integration of evidence, and reward expectation in cortical circuits.
We show that they are applicable to circuits of conductance-based
Hodgkin-Huxley (HH) neurons with high levels of noise that reflect
experimental data on in-vivo conditions.

**Reference:** W. Maass, P. Joshi, and E. D. Sontag.
Principles of real-time computing with feedback applied to cortical
microcircuit models.
In Y. Weiss, B. Schoelkopf, and J. Platt, editors, *Advances in Neural
Information Processing Systems*, volume 18, pages 835-842. MIT Press, 2006.