Local PCA Distance

Measures off-manifold distance by computing the orthogonal residual from the local tangent subspace

Neighborhood — ranked by edge-count

paper

method

Algorithm 1: Harmlessness Classification
uses
Proposed algorithm using local PCA to classify a divergence vector as harmless or harmful via behavioral null-space testing

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.

Principal components analysis (PCA)method0.722
Statistical method used to analyze neural activity data.
PCA Visualizationmethod0.695
Used to visually inspect separation of truth-related directions in model activation space across layers
LOCAL SYMMETRYconcept0.673
One of Alexander's fifteen properties; appears in birthday table, handshake, and namaste examples
Local Hamiltonianconcept0.670
Sum of windowed Hamiltonians with same window length; a key construct introduced in the paper to model local interactions on graphs
PCA is the appropriate dimensionality reduction technique for constructing the RN because it preserves global structure and provides deterministic, interpretable projections.claim0.667
Justifies PCA choice over UMAP or t-SNE for the node-structured RN model.
Local learning rulemethod0.666
Learning rule where change in a parameter at point x,t depends only on system state at same or nearby spacetime points, without requiring global cost function computation
Local Linear Reconstruction Errormethod0.663
Measures how well an intervened point can be expressed as a convex combination of nearby natural manifold points
Non-Local Action in Assemblyconcept0.662
Penrose's claim that assembling quasicrystals requires examining the state of the pattern many atoms away, implying that global structure guides local assembly