Temporal Quotients for Certified Count-Preserving Spike-Retiming Smoothing

Moving spike times can change a spiking neural network's prediction even when event counts remain fixed. We study how to certify robustness to such retiming while preserving event counts and distinct timestamps. We introduce temporal quotient smoothing for discretized event streams under a global budget on total spike displacement. A shared random partition maps each block's events on each line to a common configuration with the same count and distinct timestamps. If retiming crosses no sampled boundary, the transformed inputs coincide, yielding a finite-vote certificate for the smoothed classifier. To control the displacement introduced by smoothing, we minimize expected transport for a fixed event source and placement rule under boundary-hit constraints. A compact dual hierarchy and feasible kernels bound the remaining transport improvement; matching bounds establish periodic-kernel optimality for selected uniform fixed-count families. At global displacement budget $B=2$ on the evaluated fixed checkpoints, Period-5 raises certified accuracy over all-or-none smoothing from $53.8\%$ to $62.8\%$ on DVS-Gesture with VGGSNN and from $25.6\%$ to $76.8\%$ on N-MNIST. A compact DVS classifier gives a small reversal, while source and decoder fitting can lower both transport and certified accuracy. Temporal quotients thus make count-preserving kernel design verifiable, with classification benefits that depend on the source, classifier, and budget.