A truth direction's dimensionality, layer-wise construction, and cross-family category geometry

Vicidomini uses SVD-based linear decomposition of real hidden states in small Llama, Qwen, and Gemma-2-2B models to show truth-signal dimensionality concentrates onto a single axis for well-known facts and diffuses across more dimensions as knowledge decreases [vicidomini-2026-anatomy-of-a-truth-direction] Causal component-ablation attributes the truth direction's layer-wise construction to attention propagating the truth frame forward while the FFN opposes the current block's frame [vicidomini-2026-anatomy-of-a-truth-direction] Per-category truth axes converge into a semantically-signed arrangement across model families once a sign instability is corrected with a spectral consensus gauge [vicidomini-2026-anatomy-of-a-truth-direction]