Propositional truth is mediated by a multi-dimensional concept cone

measured in 1 paper

Yu et al. extend the concept-cone framework from refusal to truth, finding truth judgments in Qwen2.5 and Gemma-2 are causally mediated by a polyhedral cone of up to 5 non-negative-combination directions [yu-etal-2025] Larger models (Qwen-7B, Gemma-9B) sustain near-100% Answer Switching Rate across all 5 tested dimensions while smaller models degrade beyond 2-3 [yu-etal-2025] Only the first cone axis aligns with the classic difference-in-means truth direction (cosine ~0.1-0.2), so difference-in-means captures just one facet of a multi-dimensional truth subspace [yu-etal-2025] Cone-based interventions preserve unrelated behavior (mean KL divergence 0.03-0.05 on Alpaca instructions) [yu-etal-2025]

Structure

Cone

Context

truth, factuality, propositional facts, concept cone, DIM alignment, answer switching rate, truth geometry debate

Confirmed in models

Qwen2.5-3B-Instruct · Qwen, Qwen2.5-7B-Instruct · Qwen, Qwen2.5-14B-Instruct · Qwen, Gemma-2-2B-it · Gemma, Gemma-2-9B-it · Gemma

Method

Difference-in-means direction, Causal interventions (steering), Supervised direction search (gradient-based optimization), Geometric analysis, PCA

Papers

From Directions to Cones: Exploring Multidimensional Representations of Propositional Facts in LLMs — Yu, S., Bulusu, V., Yasunaga, O., Lau, C., Blondin, C., O'Brien, S., Zhu, K., Sharma, V.2025 · arXiv:2505.21800