arXiv:2610.41700v1 Announce Type: new Abstract: AI workloads on supercomputers make interconnect performance a primary design constraint. Hardware specifications and microbenchmarks alone do not show how real workloads respond to latency, bandwidth, and jitter. We present a trace-driven study of network sensitivity for training and inference workloads at scales up to 4,096 GPUs. Our methodology combines signature-based trace decomposition with linear programming to make broad network-parameter sweeps feasible. It preserves the recorded NCCL schedules and program dependencies, and estimates a lower bound on runtime under the LogGP model. We validate the compositional analysis against monolithic linear programs, LogGOPSim, and hardware measurements at feasible scales. The resulting latency-bandwidth envelopes identify low-sensitivity regions and performance cliffs that vary substantially across workloads. They also show when bandwidth upgrades provide meaningful returns and when additional network performance has little effect. These results translate execution traces into practical guidance for evaluating network configurations while making the model assumptions explicit.