  Resonate-and-Fire (RF) neurons are an interesting complementary model for
integrator neurons in spiking neural networks (SNNs). Due to their resonating
membrane dynamics they can extract frequency patterns within the time domain.
While established RF variants suffer from intrinsic shortcomings, the recently
proposed balanced resonate-and-fire (BRF) neuron marked a significant
methodological advance in terms of task performance, spiking and parameter
efficiency, as well as, general stability and robustness, demonstrated for
recurrent SNNs in various sequence learning tasks. One of the most intriguing
result, however, was an immense improvement in training convergence speed and
smoothness, overcoming the typical convergence dilemma in backprop-based SNN
training. This paper aims at providing further intuitions about how and why
these convergence advantages emerge. We show that BRF neurons, in contrast to
well-established ALIF neurons, span a very clean and smooth - almost convex -
error landscape. Furthermore, empirical results reveal that the convergence
benefits are predominantly coupled with a divergence boundary-aware
optimization, a major component of the BRF formulation that addresses the
numerical stability of the time-discrete resonator approximation. These results
are supported by a formal investigation of the membrane dynamics indicating
that the gradient is transferred back through time without loss of magnitude.
