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question:do-layer-wise-geometric-signatures-peak-aus-n-correlate-with-behavioral-thresholds-k50

Do layer-wise geometric signatures (τ_peak, AUS_N) correlate with behavioral thresholds (k50)?

E3 research question testing whether internal representations provide a geometry-to-behavior bridge

Source paper

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The Guanyin Protocol: A Framework for Immediately Establishing an Understanding of Both Causality and Compassion in LLM Systems Using Semantic Anchoring

(2025) · Edward Yi Chang · Kaya, Zeyneb N. · Ethan Chang

Neighborhood — ranked by edge-count

Findings (1)

finding

Larger S_max correlates with smaller θ50 across backbones in E3 (negative association consistent across pooling and metric choices)
answered_by
Key geometry-to-behavior bridge finding in E3; robust to pooling choice, cosine vs. L2, and frozen external encoder

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

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

Layer-wise geometry summaries (Sbmax, AUSN) predict internal few-shot thresholds θ50claim0.831
Claim that geometry-to-behavior correlates exist
Peak anchoring Sbmax and normalized area AUSN correlate with per-item success and internal shot midpoints θ50, providing a geometry-to-behavior bridge.claim0.768
Main interpretation of E3.
Gemma-3-4B-it shows three-stage layer trajectory and S(ℓ) peak despite scale differences in dr and ρdfinding0.762
E3 backbone generalization finding for Gemma; validates pattern across diverse architectures
Layer-wise anchoring peaks in a 'Goldilocks zone' between early and late layers.claim0.760
Qualitative characterization of optimal anchoring depth.
Layer-wise geometry shows early dip, mid-layer alignment, and late standardization across tasksclaim0.760
Qualitative pattern from E3.
Mid-layers (6-15) achieve peak anchoring because semantic structure differentiates while maintaining coherence, forming a Goldilocks zoneclaim0.750
Interpretation of E3 layer-wise results; motivates targeted UCCT interventions at layers 8-12
Under ask-correct, arithmetic tasks A1-A2 show gradual AUROC increase peaking only in final layers, unlike the sharp transition under no-prompt.finding0.750
Shows that explicit instructions delay the emergence of truth directions in arithmetic tasks.
AUS_N is a weaker correlate of θ50 than S_max across E3 backbonesfinding0.749
E3 finding distinguishing the two geometry summaries; breadth less predictive than peak height