Computation at the Edge of Chaos in Recurrent Neural Networks

Recurrent Neural Networks are powerful, biologically inspired models for computations on time varying input signals. Due to their high-dimensionality it is difficult to utilize their power for information processing. In this talk a new framework will be presented that allows to investigate the computational capabilities inherent in large, randomly connected networks. Using this framework a link between the network dynamics and its computational capabilities is found.

The results illustrate the idea that dynamical systems support computations optimally if they operate at the "Edge of Chaos", a notation which can be formally defined in networks of McCulloch-Pitts neurons. This allows to analyse how the dynamics of such networks depends on the parameters controlling the connectivity distribution. In particular the critical boundary is calculated where the dynamics changes from ordered to chaotic.