Abstract
Spiking Neural Networks compute using sparse communication and are attracting increased attention as a more energy-efficient alternative to traditional Artificial Neural Networks. While standard Artificial Neural Networks are stateless, spiking neurons are stateful and hence intrinsically recurrent, making them well-suited for spatio-temporal tasks. However, the duration of this intrinsic memory is limited by synaptic and membrane time constants. Delays are a powerful additional mechanism and, in this paper, we propose an event-based training method for Spiking Neural Networks with delays, grounded in the EventProp formalism, which enables the calculation of exact gradients with respect to weights and delays. Our method supports multiple spikes per neuron and introduces a delay learning algorithm that can, in contrast to previous methods, also be applied to recurrent Spiking Neural Networks. We evaluate our method on a simple sequence detection task, as well as the Yin-Yang, Spiking Heidelberg Digits, Spiking Speech Commands and Braille letter reading datasets, demonstrating that our algorithm can optimise delays from suboptimal initial conditions and enhance classification accuracy compared to architectures without delays. We also find that recurrent delays are particularly beneficial in small networks. Finally, we show that our approach uses less than half the memory of the current state-of-the-art delay-learning method and is up to 26 × faster.