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Feedback-driven recurrent spiking neural networks (RSNNs) are powerfulcomputational models that can mimic dynamical systems. However, the presence ofa feedback loop from the readout to the recurrent layer de-stabilizes thelearning mechanism and prevents it from converging. Here, we propose asupervised training procedure for RSNNs, where a second network is introducedonly during the training, to provide hint for the target dynamics. The proposedtraining procedure consists of generating targets for both recurrent andreadout layers (i.e., for a full RSNN system). It uses the recursive leastsquare-based First-Order and Reduced Control Error (FORCE) algorithm to fit theactivity of each layer to its target. The proposed full-FORCE trainingprocedure reduces the amount of modifications needed to keep the error betweenthe output and target close to zero. These modifications control the feedbackloop, which causes the training to converge. We demonstrate the improvedperformance and noise robustness of the proposed full-FORCE training procedureto model 8 dynamical systems using RSNNs with leaky integrate and fire (LIF)neurons and rate coding. For energy-efficient hardware implementation, analternative time-to-first-spike (TTFS) coding is implemented for the full-FORCE training procedure. Compared to rate coding, full-FORCE with TTFS codinggenerates fewer spikes and facilitates faster convergence to the targetdynamics.

Learning in Feedback-driven Recurrent Spiking Neural Networks using full-FORCE Training