Tail estimation for dependence-corrected stopping

Develop a tail estimator that uses more of the design set to improve the dependence-corrected stopping rule beyond the independence-based default.

Background

CopRoute includes a dependence-corrected stopping rule that estimates prefix-level dependence using design queries on which the entire prefix of models fails. At deep prefix lengths, such queries are rare, making the corresponding dependence estimates noisy. The paper reports that this correction does not improve on the independence-based stopping rule in its evaluation, motivating the search for an estimator that can exploit more of the available design data when estimating the tail of the joint failure distribution.

References

The dependence-corrected stopping rule is estimated from the design queries that miss an entire prefix, which are few at deep prefixes, and it does not improve on the independence-based default, so the open question is a tail estimator that uses more of the design set.

— CopRoute: Dependence-Aware Conformal Routing for Language Models  (2610.13276 - Kasa et al., 9 Oct 2026) in Section 7, “Limitations and Conclusion,” paragraph beginning “Limitations.”