In Qwen-2.5-9B, only v1 has meaningful cosine similarity to DIM direction; all additional basis vectors have cosine similarities ~1e-9

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

• In Gemma-2-9B, only the first cone axis (v1) has non-negligible cosine similarity to the DIM direction; all other axes have near-zero similarity (~1e-9)finding0.850
  Experiment 4 result showing DIM captures only one facet of the multi-dimensional truth subspace
• Experimental condition adjective embeddings show mean cosine similarity 0.657 (n=9,591 pairs), significantly higher than history (0.628, t=15.8, p=1.4×10⁻⁵⁵), conceptual (0.587, t=38.5, p<10⁻³⁰⁰), and zero-shot (0.603, t=35.1, p=4.3×10⁻²⁶²)finding0.805
  Core result of Experiment 3: cross-model semantic convergence under self-referential processing
• Cosine similarity between perturbed and baseline residual streams returns toward 1.0 and projection onto injection direction decays exponentially over subsequent layersfinding0.791
  Mechanistic evidence that network actively attenuates injected perturbations, explaining late-layer introspection failure
• Base and instruct Gemma 2 27B role PCs have cosine similarities of 0.93, 0.87, 0.83 for the top 3 PCs respectively; role vector cosine similarities >0.99 for every role pairfinding0.790
  Shows persona space axes are inherited from pre-training, not solely created by post-training
• Top-5 instructions by µ(1→2) at ℓ=12 achieve average cosine similarity .9893 and average accuracy .5645 on gsm8k_adv for Gemma3-4B-ITfinding0.779
  High cosine similarity for Gemma3 steering vectors suggests strong linear reflection structure.
• Cosine similarity between truth probesmethod0.775
  Geometric evaluation of truth direction alignment across layers and prompt templates.
• Cosine similarity between Assistant Axis and role PC1 is >0.60 at all layers and >0.71 at middle layer across all three modelsfinding0.769
  Validates that the contrast vector method and PCA-based PC1 capture the same direction
• The degree of similarities which exist in a structure must correspond exactly to the degree of similarity of the conditions there, and the degrees of differences which exist in a structure must also correspond to the degrees of difference in the conditions there.claim0.768
  The profound principle that underlies all living structure; symmetry as the mathematical trace of necessity.