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Recurrent neural networks (RNNs) are complex dynamical systems, capable ofongoing activity without any driving input. The long-term behavior offree-running RNNs, described by periodic, chaotic and fixed point attractors,is controlled by the statistics of the neural connection weights, such as thedensity $d$ of non-zero connections, or the balance $b$ between excitatory andinhibitory connections. However, for information processing purposes, RNNs needto receive external input signals, and it is not clear which of the dynamicalregimes is optimal for this information import. We use both the averagecorrelations $C$ and the mutual information $I$ between the momentary inputvector and the next system state vector as quantitative measures of informationimport and analyze their dependence on the balance and density of the network.Remarkably, both resulting phase diagrams $C(b,d)$ and $I(b,d)$ are highlyconsistent, pointing to a link between the dynamical systems and theinformation-processing approach to complex systems. Information import ismaximal not at the 'edge of chaos', which is optimally suited for computation,but surprisingly in the low-density chaotic regime and at the border betweenthe chaotic and fixed point regime. Moreover, we find a completely new type ofresonance phenomenon, called 'Import Resonance' (IR), where the informationimport shows a maximum, i.e. a peak-like dependence on the coupling strengthbetween the RNN and its input. IR complements Recurrence Resonance (RR), wherecorrelation and mutual information of successive system states peak for acertain amplitude of noise added to the system. Both IR and RR can be exploitedto optimize information processing in artificial neural networks and might alsoplay a crucial role in biological neural systems.

Dynamical Phases and Resonance Phenomena in Information-Processing Recurrent Neural Networks