Spiking neural networks (SNNs) inherently rely on the timing of signals for representing and processing information. Transmission delays play an important role in shaping these temporal characteristics. Recent work has demonstrated the substantial advantages of learning these delays along with synaptic weights, both in terms of accuracy and memory efficiency. However, these approaches suffer from drawbacks in terms of precision and efficiency, as they operate in discrete time and with approximate gradients, while also requiring membrane potential recordings for calculating parameter updates. To alleviate these issues, we propose an analytical approach for calculating exact loss gradients with respect to both synaptic weights and delays in an event-based fashion. The inclusion of delays emerges naturally within our proposed formalism, enriching the model's search space with a temporal dimension. Our algorithm is purely based on the timing of individual spikes and does not require access to other variables such as membrane potentials. We explicitly compare the impact on accuracy and parameter efficiency of different types of delays - axonal, dendritic and synaptic. Furthermore, while previous work on learnable delays in SNNs has been mostly confined to software simulations, we demonstrate the functionality and benefits of our approach on the BrainScaleS-2 neuromorphic platform.

翻译：脉冲神经网络（SNNs）本质上依赖信号时序来表征和处理信息，其中传输延迟在塑造这些时间特性中发挥着关键作用。近期研究已证明，将突触权重与延迟共同学习在准确性和内存效率方面具有显著优势。然而，现有方法因采用离散时间近似梯度且需要记录膜电位来计算参数更新，存在精度与效率方面的缺陷。为解决这些问题，我们提出一种基于事件触发的解析方法，可精确计算关于突触权重和延迟的损失梯度。延迟的引入在我们的理论框架中自然实现，通过时间维度丰富了模型的搜索空间。该算法完全基于单个脉冲的时序，无需获取膜电位等其它变量。我们系统比较了轴突、树突和突触三种延迟类型对精度与参数效率的影响。此外，相较于前人将SNNs可学习延迟研究局限于软件仿真的局限，我们在BrainScaleS-2神经形态平台上验证了本方法的有效性与优势。