Certifying Reuse for LLM Components from Local Interventions

Reusable components are often deployed in combinations that were never tested directly, making it necessary to infer whether local intervention evidence is sufficient to support an untested decision. We study this problem for two functional roles whose marginal values determine a fixed calling rule. Without restrictions on unobserved higher order effects, local interventions cannot certify an untested combination even with unlimited repetitions. Under a degree $h$ model for the decision relevant contrasts, local measurements identify a target containing $k$ background elements exactly, but finite sample certification has matching sample complexity of order $L_h(k{)}^2{\Delta }^{-2}\log (1/\delta )$, where $L_h(k)$ is the exact amplification of the local reconstruction. We then show that measuring at most $2^h-1$ suitable proper subsets reduces the amplification to at most $2^{h+1}-1$, independent of $k$, without observing the target itself. Finally, we give a finite sample certifier that can approve the reuse decision, return a negative witness, or report insufficient evidence. Controlled experiments reproduce the predicted amplification and reduce it from 97 to 7 in a quadratic eight background example. These results characterize when local intervention evidence is missing information, statistically insufficient, or collected at the wrong contexts.