Learning Precise Spike Timings with Eligibility Traces

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.