Title: Enhancing Language Model Reliability Through Posterior Sampling

Large Language Models continue to suffer from significant hallucination issues. While recent research has successfully mitigated these problems using conformal prediction techniques—delivering both theoretical rigor and empirical results—existing approaches are fundamentally limited by their post-hoc nature. These methods treat the generation process as a black box, subsequently editing outputs to excise false claims. This separation between creation and correction often leads to incoherent, contradictory, or statistically improbable text. Furthermore, such reactive editing fails to redirect probability mass toward responses that are genuinely more helpful and accurate.

To overcome these limitations, we introduce a novel approach that samples directly from approximations of the LLM posterior distribution. In this framework, the conditioning event targets a calibrated region characterized by high scores. We have developed a specialized calibration procedure designed for conditional sequential generation, which effectively pinpoints this optimal region while ensuring precise risk control. We validated our method through case studies in open-ended biography generation and mathematical problem solving. Our results demonstrate that this approach maintains the same statistical guarantees as previous methods while significantly improving downstream utility.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC