Conformal Language Model Reasoning with Coherent Factuality

Language models are increasingly being used in important decision pipelines, so ensuring the correctness of their outputs is crucial. Recent work has proposed evaluating the “factuality” of claims decomposed from a language model generation and applying conformal prediction techniques to filter out those claims that are not factual. This can be effective for tasks such as information retrieval, where constituent claims may be evaluated in isolation for factuality, but is not appropriate for reasoning tasks, as steps of a logical argument can be evaluated for correctness only within the context of the claims that have preceded them. To capture this, we define “coherent factuality” and develop a conformal-prediction-based method to guarantee coherent factuality of language model outputs. Our approach applies split conformal prediction to subgraphs within a "deducibility" graph that we construct to represent the steps of a reasoning problem. We evaluate our method on mathematical reasoning problems from the MATH and FELM datasets, and find that our algorithm achieves coherent factuality across target coverage levels, consistently producing orderings of correct claims that are substantiated by previous ones. Moreover, we achieve 90% factuality on our stricter definition while retaining 80% or more of the original claims, highlighting the utility of our deducibility-graph-guided approach.