  Recent research in the field of spiking neural networks (SNNs) has shown that
recurrent variants of SNNs, namely long short-term SNNs (LSNNs), can be trained
via error gradients just as effective as LSTMs. The underlying learning method
(e-prop) is based on a formalization of eligibility traces applied to leaky
integrate and fire (LIF) neurons. Here, we show that the proposed approach
cannot fully unfold spike timing dependent plasticity (STDP). As a consequence,
this limits in principle the inherent advantage of SNNs, that is, the potential
to develop codes that rely on precise relative spike timings. We show that
STDP-aware synaptic gradients naturally emerge within the eligibility equations
of e-prop when derived for a slightly more complex spiking neuron model, here
at the example of the Izhikevich model. We also present a simple extension of
the LIF model that provides similar gradients. In a simple experiment we
demonstrate that the STDP-aware LIF neurons can learn precise spike timings
from an e-prop-based gradient signal.
