Peak Layer-wise Anchoring Score (S_max)

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

• layer-wise anchoring score S(ℓ) computationmethod0.832
  Compute per-layer S(ℓ) = ρ̃d(ℓ) - d̃r(ℓ) - log k after whitening and standardization.
• peak anchoring Sbmaxconcept0.802
  Maximum layer-wise anchoring score across layers.
• Meta-LLaMA-3.1-8B-Instruct shows optimal anchoring at layer 9 (S ≈ −1.90, median peak layer ℓ* = 10 [IQR 0.384])finding0.798
  E3 result establishing the Goldilocks zone at mid-layers for LLaMA architecture
• Peak layer ℓ* median 10, IQR 0.384finding0.782
  Median layer where S(ℓ) peaks, across seeds.
• Mid-layers (6-15) achieve peak anchoring because semantic structure differentiates while maintaining coherence, forming a Goldilocks zoneclaim0.781
  Interpretation of E3 layer-wise results; motivates targeted UCCT interventions at layers 8-12
• Math and code tasks show strongest mid-layer anchoring on LLaMA (S ≈ −1.65 at layers 8-12)finding0.777
  Task-specific E3 finding showing compositional reasoning requires deeper processing
• Layer-wise anchoring peaks in a 'Goldilocks zone' between early and late layers.claim0.768
  Qualitative characterization of optimal anchoring depth.
• The anchoring score S is a predictive correlate of when anchoring succeeds and why small prompt changes yield threshold-like shifts.claim0.763
  A central claim about the operational value of S.