When Is a Routing Decision Safe? A Temporal Robustness Criterion for Heterogeneous Spiking Networks

Routing a spiking workload across heterogeneous compute tiers produces different executions of the same computation. The routing decision is made in milliseconds, based on cost and availability, but rarely evaluates whether the resulting execution preserves the intended behavior. This paper formulates the routing safety problem for order-based spiking neural networks and gives a criterion for when a routing decision is safe. We define executions as finite event posets, characterize the divergence between two executions using a scalarized coupling metric, and define the robustness radius of a temporal specification on a discrete poset. The central proposition states that if the divergence between executions is strictly less than the specification's robustness radius, the specification is preserved. To address the NP-hardness of optimal event matching, we propose a time-aligned greedy heuristic that yields a conservative upper bound on divergence. The criterion is sound and tractable, allowing for safe routing decisions without requiring execution on the target tier.