Huginn-0125 all-layer fixed point cosine similarities converge to 1 for all pairs, indicating convergence to the same fixed point rather than distinct cyclic fixed points

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

• 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)finding0.775
  Core result of Experiment 3: cross-model semantic convergence under self-referential processing
• The model converges to a more stable truth direction in middle-to-late layers, as evidenced by increasing cosine similarity between layer-wise probes.claim0.775
  Supported by the geometric transition visible in cosine similarity heatmaps for F0-F3.
• Convergence to cyclic fixed points implies attention patterns stabilize, which implies mixing-based stages of inference become constant across recurrencesclaim0.765
  Core mechanistic claim linking fixed point theory to observable inference stage behavior
• Different models cannot converge to the same representation if they have access to fundamentally different information; convergence is capped by mutual information between input signalsclaim0.763
  Key limitation of the PRH for non-bijective observations
• Ouro 1.4B does not converge to a fixed point even after 128 recurrences, despite showing small successive differencesfinding0.759
  Key negative result showing that not all looped models reach a true fixed point, contrasting with retrofitted models
• Pre-norm without input injection reaches a degenerate fixed point where all layers converge to the same pointfinding0.752
  Pre-norm model reaches a fixed point without input injection but all layers converge to identical representations
• 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)finding0.751
  Experiment 4 result showing DIM captures only one facet of the multi-dimensional truth subspace
• Cosine similarity between perturbed and baseline residual streams returns toward 1.0 and projection onto injection direction decays exponentially over subsequent layersfinding0.746
  Mechanistic evidence that network actively attenuates injected perturbations, explaining late-layer introspection failure