arXiv:2603.06616v1 Announce Type: cross Abstract: Efficiently routing queries to the optimal large language model (LLM) is crucial for optimizing the cost-performance trade-off in multi-model systems. However, most existing routers rely on single-model selection, making them susceptible to misrouting. In this work, we formulate LLM routing as the $\alpha$-VOR problem to minimize expected set size while controlling the misrouting risk, and propose a novel method -- RACER, extending base routers to output model sets that can be subsequently aggregated for improved output. In particular, RACER constructs nested model sets via augmented scoring and utilizes finite-sample concentration bounds to calibrate a threshold that allows for both variable set sizes and abstention. We theoretically prove that RACER achieves rigorous distribution-free risk control on unseen test data in a post-hoc and model-agnostic manner. Extensive experiments verify our theoretical guarantees and demonstrate that RACER consistently enhances downstream accuracy across a wide range of benchmarks.

arXiv:2510.14581v3 Announce Type: replace-cross Abstract: Obtaining high-quality labels for large datasets is expensive, requiring massive annotations from human experts. While AI models offer a cost-effective alternative by predicting labels, their label quality is compromised by the unavoidable labeling errors. Existing methods mitigate this issue through selective labeling, where AI labels a subset and human labels the remainder. However, these methods lack theoretical guarantees on the quality of AI-assigned labels, often resulting in unacceptably high labeling error within the AI-labeled subset. To address this, we introduce \textbf{Conformal Labeling}, a novel method to identify instances where AI predictions can be provably trusted. This is achieved by controlling the false discovery rate (FDR), the proportion of incorrect labels within the selected subset. In particular, we construct a conformal $p$-value for each test instance by comparing AI models' predicted confidence to those of calibration instances mislabeled by AI models. Then, we select test instances whose $p$-values are below a data-dependent threshold, certifying AI models' predictions as trustworthy. We provide theoretical guarantees that Conformal Labeling controls the FDR below the nominal level, ensuring that a predefined fraction of AI-assigned labels is correct on average. Extensive experiments demonstrate that our method achieves tight FDR control with high power across various tasks, including image and text labeling, and LLM QA.