Large language models (LLMs) can enhance factuality via retrieval-augmented generation (RAG), but applying RAG to every query is unnecessary when the model-only answer is reliable. This motivates cascaded RAG: each query is first handled by an LLM-only branch, escalated to a RAG fallback only if the primary branch is uncertain, and abstained from when neither branch is sufficiently trustworthy. However, calibrating such cascades stage by stage may be conservative, since the final utility depends on joint uncertainty thresholding of LLM-only and RAG. In this work, we develop **BalanceRAG** to certify threshold pairs at a target risk level. Given uncertainty scores from the two branches, BalanceRAG frames each threshold pair as an operating point on a two-dimensional lattice and identifies safe operating points using sequential graphical testing. This enables risk-adaptive threshold calibration, controlling the system-level error rate among accepted points, while retaining more examples. Furthermore, BalanceRAG extends to multi-risk calibration, allowing retrieval usage to be bounded together with the selection-conditioned risk. Experiments on three open-domain question answering (QA) benchmarks across multiple LLM backbones demonstrate that BalanceRAG meets prescribed risk levels, preserves higher coverage and more accepted correct examples, and reduces unnecessary retrieval calls compared with always-on RAG.

Reliable set-valued prediction provides a principled way to mitigate hallucinations in open-ended question answering (QA), yet existing conformal approaches typically rely on a restrictive premise: finite sampling must produce at least one admissible candidate, or calibration examples violating this condition are discarded. In this paper, we introduce MiRD, a two-stage framework that decomposes overall miscoverage into sampling failure and conditional selection failure. In Stage I, MiRD establishes an expectation-level marginal upper bound on the probability that finite sampling produces no admissible answer under a fixed sampling budget. In Stage II, conditioned on sampling success, MiRD calibrates a conformal selection threshold using admission-correlated nonconformity scores constructed from the full calibration set, thereby preserving calibration-set integrity. Across three open-ended QA datasets and eight models, MiRD controls sampling risk, conditional selection risk, and overall miscoverage, while providing tighter first-stage bounds than PAC-style alternatives and more adaptive prediction sets than successful-only calibration.

As large language models are increasingly utilized in real-world applications, guarantees of task-specific metrics are essential for their reliable deployment. Previous studies have introduced various criteria of conformal uncertainty grounded in split conformal prediction, which offer user-specified correctness coverage. However, existing frameworks often fail to identify uncertainty data outliers that violate the exchangeability assumption, leading to unbounded miscoverage rates and unactionable prediction sets. In this paper, we propose a novel approach termed Selective Conformal Uncertainty (SConU), which, for the first time, implements significance tests, by developing two conformal p-values that are instrumental in determining whether a given sample deviates from the uncertainty distribution of the calibration set at a specific manageable risk level. Our approach not only facilitates rigorous management of miscoverage rates across both single-domain and interdisciplinary contexts, but also enhances the efficiency of predictions. Furthermore, we comprehensively analyze the components of the conformal procedures, aiming to approximate conditional coverage, particularly in high-stakes question-answering tasks.

Uncertainty quantification (UQ) in natural language generation (NLG) tasks remains an open challenge, exacerbated by the closed-source nature of the latest large language models (LLMs). This study investigates applying conformal prediction (CP), which can transform any heuristic uncertainty notion into rigorous prediction sets, to black-box LLMs in open-ended NLG tasks. We introduce a novel uncertainty measure based on self-consistency theory, and then develop a conformal uncertainty criterion by integrating the uncertainty condition aligned with correctness into the CP algorithm. Empirical evaluations indicate that our uncertainty measure outperforms prior state-of-the-art methods. Furthermore, we achieve strict control over the correctness coverage rate utilizing 7 popular LLMs on 4 free-form NLG datasets, spanning general-purpose and medical scenarios. Additionally, the calibrated prediction sets with small size further highlights the efficiency of our method in providing trustworthy guarantees for practical open-ended NLG applications.