Local homeostatic regulation of the spectral radius of echo-state networks

Criticality is considered an important property for recurrent neural networks. Close to a critical phase transition, RNNs show improved performance in sequential information processing. The theory of reservoir computing provides a basis for the understanding of recurrent neural computation, but it requires adjustments of global network parameters so that the network can operate in a state close to criticality. In the case of echo-state networks, an important quantity is the spectral radius of the recurrent synaptic weight matrix. In terms of biological plausibility, a calculation of the spectral radius is not possible. We show, however, that there exists a local and biologically plausible synaptic scaling mechanism, termed flow control, that can control the spectral radius while the network is operating under the influence of external input. We demonstrate the effectiveness of the new adaption rule by applying it to echo-state networks and testing their task performance under a time-delayed XOR operation on random binary input sequences. A stable network performance over a wide range of input strengths is preserved. This makes our mechanism more flexible to changes in the external driving as compared to scaling mechanisms that use a fixed setpoint of neural activity.