directionality-as-universal-geometric-property

IN derived (depth 1)

Created 2026-08-25T04:19:08+00:00 · Reviewed 2026-08-25T04:28:09+00:00

Asymmetry (A→B ≠ B→A) appears independently in ROME's separate-edit constraint, Park's signed binary contrasts (ℓ̄_{w0⇒w1} = ℓ̄_{w1} − ℓ̄_{w0}), and SBERT's tied-weight siamese architecture, establishing directionality as an invariant geometric property of the superposed space rather than a per-implementation artifact.

Summary

Directionality — the fact that the path from A to B is structurally distinct from the path from B to A — appears independently across ROME's editing rules, Park's signed contrast vectors, and SBERT's tied-weight design, making it a fundamental property of the representational geometry rather than a quirk of any one architecture. This means any system working in this space must treat relationships as inherently one-directional: swapping endpoints changes what is encoded, and no architectural choice can engineer that asymmetry away.

Justifications

This belief has 3 justifications — it is IN if any one holds.

SL — Three independent systems (editing, representation theory, training architecture) all encode the same directional structure; convergent evidence across modalities.

Antecedents (all must be IN):

  • IN rome-directional-edits — ROME edits are directional: 'A is B' and 'B is A' are stored as separate associations and require two independent edits to alter both.
SL — Three independent systems (editing, representation theory, training architecture) all encode the same directional structure; convergent evidence across modalities.

Antecedents (all must be IN):

  • IN park-2025-binary-contrast-vector-difference — Corollary 6 establishes that binary contrasts are vector differences of binary features: ℓ̄_{w0⇒w1} = ℓ̄_{w1} − ℓ̄_{w0}, enabled by representations having well-defined magnitudes (not just directions).
SL — Three independent systems (editing, representation theory, training architecture) all encode the same directional structure; convergent evidence across modalities.

Antecedents (all must be IN):

  • IN sbert-siamese-tied-weights — In SBERT's siamese network structure, the two BERT encoders share (are tied to) the same weights rather than being separate models.