Per-edit trade-offs within the projected subspace

Characterize whether a per-edit trade-off exists within the projected subspace that accounts for the residual edit-success gap of FedAlphaEdit relative to centralized AlphaEdit.

Background

FedAlphaEdit preserves the null-space constraint and eliminates the measured out-of-null-space component, yet its edit success remains below that of centralized AlphaEdit in the multi-layer sequential setting. The paper attributes this residual to directional distortion within the projected subspace caused by layer-wise state divergence rather than to uniform shrinkage or preservation leakage.

The authors note that determining whether there is a per-edit trade-off inside the projected subspace would require a finer-grained analysis than the aggregate metrics reported in the paper. This question is therefore left unresolved.

References

Excluding a per-edit trade-off within the projected subspace entirely would require edit-level analysis, which we leave open.

— FedAlphaEdit: Null-Space-Aligned Merging for Collaborative Knowledge Editing  (2610.11033 - Sugawara et al., 8 Oct 2026) in Section 5.4, Diagnostics, subsection “Why the residual costs editing but not preservation”

We attribute this to the layer-wise state divergence that Theorem~\ref{thm:exact} explicitly excludes, and a protocol that evaluates key statistics at a common model state is left to future work.

— FedAlphaEdit: Null-Space-Aligned Merging for Collaborative Knowledge Editing  (2610.11033 - Sugawara et al., 8 Oct 2026) in Section 6, Limitations, item “Edit-success residual on GPT-2 XL”