  We develop new conformal inference methods for obtaining validity guarantees
on the output of large language models (LLMs). Prior work in conformal language
modeling identifies a subset of the text that satisfies a high-probability
guarantee of correctness. These methods work by filtering claims from the LLM's
original response if a scoring function evaluated on the claim fails to exceed
a threshold calibrated via split conformal prediction. Existing methods in this
area suffer from two deficiencies. First, the guarantee stated is not
conditionally valid. The trustworthiness of the filtering step may vary based
on the topic of the response. Second, because the scoring function is
imperfect, the filtering step can remove many valuable and accurate claims. We
address both of these challenges via two new conformal methods. First, we
generalize the conditional conformal procedure of Gibbs et al. (2023) in order
to adaptively issue weaker guarantees when they are required to preserve the
utility of the output. Second, we show how to systematically improve the
quality of the scoring function via a novel algorithm for differentiating
through the conditional conformal procedure. We demonstrate the efficacy of our
approach on both synthetic and real-world datasets.
