# Learning Precise Spike Timings with Eligibility Traces

arXiv: https://arxiv.org/abs/2006.09988 · HTML: https://mlsanity.com/paper/2006.09988/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 May 2020.

## Built on by (most cited first, 2 of 2)

- [Including STDP to eligibility propagation in multi-layer recurrent spiking neural networks](https://mlsanity.com/paper/2201.07602/) (2022)
- [Predictive Spike Timing Enables Distributed Shortest Path Computation in Spiking Neural Networks](https://mlsanity.com/paper/2509.10077/) (2025)

## Abstract (arXiv)

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.