The Topology of Ill-Posed Questions: Persistent Homology for Detection and Steering in LLMs

The article presents a novel approach using persistent homology to address ill-posed questions in large language models (LLMs). By modeling the contextual hidden states of prompt tokens as a point cloud and utilizing three topological descriptors, the study demonstrates significant improvements in ill-posedness classification accuracy across three open-weight LLMs, with accuracy increases from 67.4% to 78.9% on AmbigQA, and from 57.6% to 69.6% on CLAMBER. This topology-conditioned activation steering not only enhances classification performance but also improves response quality, indicating that persistent homology can serve as a valuable tool for practitioners seeking to refine LLM responses to ambiguous queries.