Replicable Composition

ArXi:2604.10423v1 Announce Type: new As part of our results, we provide a boosting theorem for the success probability of replicable algorithms. For a broad class of problems, the failure probability appears as a separate additive term independent of $\rho$, immediately yielding improved sample complexity bounds for several problems. Finally, we prove an $\Omega(nk^2)$ lower bound for adaptive composition, establishing a quadratic separation from the non-adaptive setting. The key technique, which we call the phantom run, yields structural results of independent interest.