  Feedback-driven recurrent spiking neural networks (RSNNs) are powerful
computational models that can mimic dynamical systems. However, the presence of
a feedback loop from the readout to the recurrent layer de-stabilizes the
learning mechanism and prevents it from converging. Here, we propose a
supervised training procedure for RSNNs, where a second network is introduced
only during the training, to provide hint for the target dynamics. The proposed
training procedure consists of generating targets for both recurrent and
readout layers (i.e., for a full RSNN system). It uses the recursive least
square-based First-Order and Reduced Control Error (FORCE) algorithm to fit the
activity of each layer to its target. The proposed full-FORCE training
procedure reduces the amount of modifications needed to keep the error between
the output and target close to zero. These modifications control the feedback
loop, which causes the training to converge. We demonstrate the improved
performance and noise robustness of the proposed full-FORCE training procedure
to model 8 dynamical systems using RSNNs with leaky integrate and fire (LIF)
neurons and rate coding. For energy-efficient hardware implementation, an
alternative time-to-first-spike (TTFS) coding is implemented for the full-
FORCE training procedure. Compared to rate coding, full-FORCE with TTFS coding
generates fewer spikes and facilitates faster convergence to the target
dynamics.
