Exact Compute Allocation on Acyclic Inference Pipelines

For an acyclic inference pipeline with a fixed error model, the decrease in an error surrogate from one more unit of compute factorizes into two parts. One is local: how much a stage’s residual improves. The other is global: how much that residual matters after propagating through later stages. The global weights follow from one backward pass, and dynamic programming then allocates an integer budget exactly. This reduction requires residual curves and propagation bounds that remain valid across feasible allocations. We characterize when downstream weighting improves on exact allocation using local curves alone. A dispersion bound has an asymptotically sharp constant. A six-stage counterexample shows that every proper truncation can perform worse than every unweighted optimizer, including ties. Rational experiments on four syn- thetic systems verify the optima by exhaustive enumeration and isolate branching, amplification, plateaus, and constant weights.