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标题: "Certify or Refuse: A Cross-Model Map for Selective Risk Control with Coverage Floors under Covariate Shift"
原文链接: "https://arxiv.org/abs/2608.10893"
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---

## Computer Science > Computation and Language

## Title:Certify or Refuse: A Cross-Model Map for Selective Risk Control with Coverage Floors under Covariate Shift

Authors:[Jiamiao Liu](https://arxiv.org/search/cs?searchtype=author&query=Liu,+J), [Dewen Qiao](https://arxiv.org/search/cs?searchtype=author&query=Qiao,+D), [Yu Zhang](https://arxiv.org/search/cs?searchtype=author&query=Zhang,+Y), [Xuetao Chen](https://arxiv.org/search/cs?searchtype=author&query=Chen,+X)

[View PDF](https://arxiv.org/pdf/2608.10893) [HTML (experimental)](https://arxiv.org/html/2608.10893v1)

> Abstract:Certified selective predictors attain whatever coverage they attain; operators impose an automation floor: answer at least a $\beta$ -fraction of shifted target traffic with at most an $\alpha$ -fraction of answers wrong. Under bounded-ratio covariate shift we prove the Floor Certification Map: once that floor must be certified alongside the selection-conditioned risk $\alpha$, certification acquires a feasibility frontier and a two-resource complexity map, additive up to constants: risk in labeled source, the floor in unlabeled target samples. The rates are local, needing a regular frontier margin, slack below the local-regime threshold, and lattice conditions: pre-registered with a lattice margin for the upper bounds, compatible per-slack for the lower. The displayed split is the operational route; oracle weights also allow a labeled-source floor estimate. Three model-tagged results: a lower bound (Model-B), a matching oracle-weight upper bound (Model-A), and an implementable upper bound (Model-B') valid under a pre-registered exact stratified-shift model with nuisance cost priced explicitly. The match is across these models rather than a single-model minimax theorem, and necessarily so: over the full bounded-ratio class no unknown-weight procedure matches at any sample size (Model-B is inconsistent, witnessed at $\alpha=\beta=1/2$). The nuisance's necessity is only partially settled. Complexity tracks a localized accepted-region functional, not global effective sample size (ESS), on both sides, though a fixed-ESS separation theorem is left open; both lower-bound axes vanish as $\beta\to0$, so the floor creates the map. Empirically, the registered bite family diverges with log-log slope $-2.002$ within its pre-registered band; a 1,024-cell audit records 0 violations where the formal certificates fire; and a single-corpus SQuAD-to-NewsQA feasibility audit returns honest refusal.

| Subjects: | Computation and Language (cs.CL) |
| --- | --- |
| Cite as: | [arXiv:2608.10893](https://arxiv.org/abs/2608.10893) \[cs.CL\] |
|  | (or [arXiv:2608.10893v1](https://arxiv.org/abs/2608.10893v1) \[cs.CL\] for this version) |
|  | [https://doi.org/10.48550/arXiv.2608.10893](https://doi.org/10.48550/arXiv.2608.10893) |

## Submission history

From: Jiamiao Liu \[[view email](https://arxiv.org/show-email/5d6131c0/2608.10893)\]  
**\[v1\]** Tue, 11 Aug 2026 13:10:55 UTC (362 KB)

[Which authors of this paper are endorsers?](https://arxiv.org/auth/show-endorsers/2608.10893) | Disable MathJax ([What is MathJax?](https://info.arxiv.org/help/mathjax.html))
