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

תקציר מקורי באנגליתarXiv:2607.16741v1 Announce Type: new 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 that 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 (one model), 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 is concentrated on a single axis for behaviorally known facts (held-out AUC 0.938) and becomes diffuse as knowledge decreases or material heterogeneity increases; seven falsifi