multi-hop-drop-as-rank-one-boundary-signature
OUT derived (depth 7)
Created 2026-08-25T03:50:13+00:00 · Reviewed 2026-08-25T04:02:18+00:00
The dramatic 40.5%→7.4% multi-hop accuracy collapse after ROME editing is the operational fingerprint of the rank-one write boundary: multi-hop reasoning requires *composition* of multiple whitened directions, but the covariance-whitened subspace structurally supports only single-direction writes, making multi-hop parametric recall geometrically unreachable.
Justifications
SL — The multi-hop drop is not a "ROME quality" issue but a geometric necessity: partial whitening (O(D²) per edit) defines a single-direction subspace, and composing two such subspaces requires the full covariance inverse, which the rank-one update never constructs. The 7.4% residual is the leakage of the unedited direction.
Antecedents (all must be IN):
- IN rome-gptj-mquake-cf-multi-hop-drop — ROME-edited GPT-J answers only 7.4% of MQuAKE-CF multi-hop questions, down from 40.5% before editing
- OUT parametric-write-subspace-boundary — The operational boundary between parametric recall and contextual retrieval is precisely the geometric boundary of the rank-one addressable subspace: facts whose subject-key projection aligns with the locally-stored key covariance are parametrically editable, while facts outside this subspace must be externally supplied.
- OUT partial-whitening-cost-geometric-necessity — The O(D²) cost of a rank-one ROME edit is the exact geometric price of single-direction partial whitening: modifying one row/column of the inverse covariance while preserving D−1 others is irreducibly O(D²) because C⁻¹ is a full D×D matrix, making the complexity bound a theorem of the geometry rather than an engineering limitation.