Fixed-Input State Dependence of Residual Transmission in Spiking Neural Networks

Residual connections in Spiking Neural Networks (SNNs) merge branch and shortcut signals before a post-add neuron, yet identical merged input need not yield identical transmitted spikes when the receiver retains membrane state. We isolate this dependence by fixing the realized post-add merge and replacing only the state carried from earlier transitions. For additive leaky integrate-and-fire (LIF) and parametric leaky integrate-and-fire (PLIF) dynamics, we derive an exact switching criterion. At a fixed merge, two retained states produce different spikes precisely when their state contributions straddle the firing margin. SpikeDF, a temporal residual SNN for video forgery detection, provides a binary case in which shortcut-only and branch-only origins yield the same unit-valued merged input but different retained states. Nearby cross-video state replacement switches 11.5-15.3 % of deep residual outputs while changing mean output by at most 0.74 pp; propagating only those changed spikes also alters detector scores. The same near-threshold concentration of switches appears in independently trained continuous-merge models on FaceForensics++ and post-add PLIF models on DVS128 Gesture. Across eight PLIF residual sites, pre-replacement boundary occupancy closely tracks the ordering of site-level switch rates, linking switching prevalence to firing-boundary geometry. Together, these results show that a fixed residual merge and nearly unchanged mean activity can coexist with threshold-structured changes in spike identity and downstream computation.