At the Edge of Chaos: Real-time Computations and Self-Organized Criticality in Recurrent Neural Networks

T. Natschlaeger, N. Bertschinger, and R. Legenstein


In this paper we analyze the relationship between the computational capabilities of randomly connected networks of threshold gates in the timeseries domain and their dynamical properties. In particular we propose a complexity measure which we find to assume its highest values near the edge of chaos, i.e. the transition from ordered to chaotic dynamics. Furthermore we show that the proposed complexity measure predicts the computational capabilities very well: only near the edge of chaos are such networks able to perform complex computations on time series. Additionally a simple synaptic scaling rule for self-organized criticality is presented and analyzed.

Reference: T. Natschlaeger, N. Bertschinger, and R. Legenstein. At the edge of chaos: Real-time computations and self-organized criticality in recurrent neural networks. In L. K. Saul, Y. Weiss, and L. Bottou, editors, Advances in Neural Information Processing Systems 17, pages 145-152. MIT Press, Cambridge, MA, 2005.