Decoupling Architecture Search Cost from Deployment Multiplicity

Neural architecture search typically ranks candidates by the validation score of a single trained model, while some deployed systems use a multi-instantiation protocol in which an architecture is trained independently $M$ times and predictions are averaged. The risk of the deployed object is then governed jointly by single-model accuracy, predictive variance, and the correlation between replicas, and rebuilding the full $M$-replica protocol for every proposal makes screening cost scale with $M$. Under homogeneous regeneration and squared loss, we prove an exact reduction: deployment risk equals $E(\pi )-\frac{M-1}{M}{\sigma }^2(\pi )(1-\rho (\pi ))$, so deployment-level ranking is determined by three architecture-level statistics that can be estimated from a fixed number of proxy instantiations, independently of the target $M$. We then lift this population identity to finite validation data, deriving screening rules that control harmful acceptance with high probability when the stated validation-noise and proxy-stability bounds hold. We also delimit the result: under heterogeneous augmentation, whether a candidate helps depends on its error alignment with the deployed system and cannot be decided from candidate-only statistics. On Criteo-1M, Avazu-1M, and MovieLens-1M, the reduced objective attains Spearman $0.974$–$0.997$ against measured deployment risk, versus $0.72$–$0.87$ for single-run validation. Confidence-adjusted screening reduces the observed false acceptance rate from $26.4\%$ to $1.8\%$ on Criteo-1M and admits no harmful updates in the reported end-to-end runs, while requiring a fixed number of proxy trainings per candidate rather than full $M$-replica reconstruction.