SNNs can have both implicit and explicit recurrence. Schematic of the computational graph of a single SNN layer composed of leaky integrate-and-fire (LIF) neurons (see section 4). Input spike trains $S(0)$ enter at the bottom and affect the synaptic current variable $I(1)$ through the feedforward weights $W(1)$⁠. Time flows from left to right. Any link that connects temporally adjacent nodes in the graph constitutes a form of recurrence in the computation whereby the synaptic connections $V(1)$ contribute explicit recurrence to the graph. Implicit recurrence is contributed, for instance, by the decay of synaptic current variables and the membrane potentials $U(1)$⁠. Additionally, the spike reset contributes another form of implicit recurrence by coupling the future states to the output spike train $S(1)$⁠. Recurrences involving the surrogate derivative (e.g. the reset) depend on both the shape and the scale of the surrogate chosen and can substantially alter the surrogate gradient.