level: research
retrieval systems that mix several domains often return relevant but wrong-domain evidence. ranking metrics miss this issue, and conformal risk control bounds only marginally cover it, under-covering the worst domains. this work introduces c3r, a drop-in control layer that uses an inferred domain posterior to certify a per-domain contamination budget. when feasible, it enforces the budget; otherwise, it abstains rather than silently violating constraints. on the hardest domains, it guarantees a reduction, not just a tight bound.
the core method uses a two-split scheme built on risk-controlling prediction sets. a finite-sample transfer bound crosses from the inferred domain to the true domain with fully estimable slack. the approach supports heterogeneous budgets and inverts for deployment. population validity relies on this bound and a controlled simulation. across a thousand resampled calibrations, the certificate never violates, showing stability, while marginal control violates.
the method works without any query-time labels, making it practical for real-world multi-domain search. it provides formal guarantees that the worst-performing domains meet their contamination limits. by abstaining when necessary, it avoids misleading results from wrong-domain evidence. this is useful for applications like legal or medical retrieval where domain accuracy is critical. the approach can be added to existing retrieval pipelines without retraining the underlying models.
why it matters: it gives ai practitioners a way to control domain-specific errors in retrieval systems with formal guarantees, improving trust in multi-domain search applications.