The Anatomy of a Truth Direction: Knowledge-Dependent Dimensionality, a Relational Law, and a Convergent Category Geometry in Small Language Models

תקציר מקורי באנגליתarXiv:2607.16741v2 Announce Type: replace Abstract: B\"urger et al. (2024) demonstrated that truth representations in large language models are universal across statement polarity but reside within a multidimensional subspace. We extend this framework along three questions: how the dimensionality of the subspace depends on the model's knowledge, which architectural component builds the truth direction, and what the direction is a mixture of. In Part I, a training-free directional probe derived from the SVD of hidden-state minimal pairs shows that the dimensionality of truth is knowledge-dependent: the signal concentrates on a single axis for known facts and diffuses as knowledge decreases. In Part II, a relational law emerges across multiple model families: attention propagates truth frame