E3: Layer-wise Geometric Trajectory Analysis

Quantitative study correlating layer-wise anchoring geometry (S_max, AUS_N) with behavioral thresholds θ50

Neighborhood — ranked by edge-count

concept

Meta-Llama-3.1-8B-Instruct
uses
Backbone model used in E3 geometry analysis.
Gemma-3-4B-it
uses
Backbone model used in E3 robustness overlay.
internal threshold θ50
studies
Few-shot midpoint in E3's geometric analysis.
Normalized Area Under Anchoring Trajectory (AUS_N)
studies
Mean of S(ℓ) across layers; weaker geometry correlate with θ50
Peak Layer-wise Anchoring Score (S_max)
studies
Maximum of S(ℓ) across layers; geometry summary used to predict θ50
Phi-4
uses
Backbone model used in E3 robustness overlay.

method

layer-wise trajectory analysis
related_to
Computing per-layer S(ℓ) to summarize geometry.
Dev-Set Whitening and Z-Scoring Protocol
uses
Preprocessing pipeline for standardizing ρd, dr, and S across layers/models using dev-set covariance
Negative Control: Dense Off-Task Anchors
uses
E3 robustness test: dense but off-task anchors yield high ρd AND high dr, confirming mismatch dominates S

dataset

artifact

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.

Three-Stage Layer Trajectoryconcept0.802
Empirically observed pattern in E3: early enrichment (ρd dips), mid-layer alignment (dr falls), late standardization (re-clustering)
Layer-wise anchoring trajectoryconcept0.766
Plot of per-layer anchoring score S(ℓ) across model depth, revealing early dip, mid-layer peak, late standardization.
Trajectory Filteringmethod0.749
Strategic filtering procedure that removes invalid trajectories and maintains optimal positive-to-negative trajectory ratio to stabilize training.
Layer-wise trajectories show early enrichment, mid-layer alignment, and late re-clustering.claim0.748
Qualitative geometry pattern.
Layer-wise geometry shows early dip, mid-layer alignment, and late standardization across tasksclaim0.730
Qualitative pattern from E3.
Gemma-3-4B-it shows three-stage layer trajectory and S(ℓ) peak despite scale differences in dr and ρdfinding0.727
E3 backbone generalization finding for Gemma; validates pattern across diverse architectures
Marr's Three Levels of Analysisframework0.713
Framework for analyzing cognitive systems at computational, algorithmic, and implementation levels; invoked to situate the paper's contributions
Layer-wise geometry summaries (Sbmax, AUSN) predict internal few-shot thresholds θ50claim0.713
Claim that geometry-to-behavior correlates exist