Topological self-organization and critical dynamics of input-driven neural threshold networks

It has been proposed that computational capabilities and adaptation are optimized by dynamical systems that self-organize into a critical state at the border between chaos and order. Recent work on real-time computation at the 'edge of chaos' in recurrent neural networks strongly supports this conjecture [1]. Here, based on a simple model of network self-organization by a local 'homeostasis rule' coupling rewiring events to a dynamical order parameter (average neural activity) [2,3], we study topological evolution of input-driven neural threshold networks. In addition to the original system, a subset of network nodes is driven by external (stochastic) input signals. Compared to the undriven model, we find a much faster convergence to criticality; if a sufficiently large (but finite) fraction of neurons is driven, networks become critical even for finite system size N. Several dynamical order parameters exhibit pronounced power-law scaling, long-range correlations and 1/f noise, including the average neural activity. Finally, we discuss possibilities to exploit this mechanism for computations (e.g. on time series) in neural systems, e.g. by combining it with dynamical or evolutionary learning rules, and whether similar self-organizing principles might be at work in real neural systems.

[1] Bertschinger, N. and Natschlaeger, T., Neural Computation 16, 1413-1436 (2004)
[2] Bornholdt, S. and Rohlf, T., Phys. Rev. Lett. 84, 6114 (2000)
[3] Rohlf, T. and Bornholdt, S., Physica A 310, 245-259 (2002)