hierarchical-orthogonality-genuine-structure

OUT derived (depth 1)

Created 2026-08-25T03:00:40+00:00

The observed parent⊥(child−parent) orthogonality in LLM representation spaces reflects genuine hierarchical semantics rather than a trivial set-inclusion artifact.

Justifications

SL — Theorem 8 provides the structural guarantee, and the shuffle test (collapsing orthogonality when true hierarchy is broken) provides empirical confirmation. The claim is gated by the spurious-orthogonality finding: if mere set inclusion (Y(z)⊆Y(w)) can reproduce the pattern without true semantic hierarchy, the structural interpretation is undermined.

Antecedents (all must be IN):

IN park-2025-hierarchical-orthogonality-theorem-8 — Theorem 8 states that for subordinate concepts z ≺ w, the parent vector is orthogonal to the child-minus-parent residual: ℓ̄_w ⊥ (ℓ̄_z − ℓ̄_w), and sibling contrast vectors are mutually orthogonal.
IN park-2024-shuffled-baseline-collapses-orthogonality — When WordNet parent/child assignments are randomly shuffled in the unembedding, the predicted orthogonality structure collapses (cosine similarity departs from zero).

Unless (any of these IN defeats this justification):

IN park-2025-set-inclusion-spurious-orthogonality — Shuffled unembeddings reproduce orthogonality between child-parent and parent vectors purely from set inclusion (Y(z) ⊆ Y(w)), not semantic meaning, demonstrating that set inclusion alone is insufficient to explain the geometric structure.