Matchability-Aware Conformal Prediction for Open-Ended Language Model Generation

Ilia Azizi

Large language models (LLMs) often do not produce calibrated uncertainty estimates for their answers. We propose CAELUM, a framework that builds semantic prediction sets while separating aleatoric from epistemic uncertainty. CAELUM samples answers using an ensemble of clarification prompts, clusters them by semantic equivalence, and estimates the aleatoric and epistemic components via kernel-based von Neumann entropy before calibrating nonconformity scores with split conformal prediction. We use a weight $w_λ(x)=1+U_{\mathrm{ale}}(x)+λ\,U_{\mathrm{epi}}(x)$ to control for the contribution of the epistemic uncertainty of each instance and fit a coefficient $λ^\star$ to minimize prediction set size. When the objective is nonflat and selection is stable across splits, $λ^\star$ could be a diagnostic, where large values may indicate epistemic dominance (retrieve, abstain) and $λ^\star\to 0$ aleatoric dominance (clarify). For individual queries, a log ratio $R(x)$ compares the weighted epistemic component with the aleatoric component. Theoretically, we demonstrate that the coverage is capped by matchability, the fraction of items whose reference answer appears in any sampled cluster.…