Shared projectors for heterogeneous preservation requirements

Determine how clients with heterogeneous preservation requirements can agree on a shared null-space projector and whether a projector constructed from public statistics adequately covers each client’s private preservation requirements.

Background

The exactness theorem assumes that all clients use one shared projector, constructed in the paper from common Wikipedia statistics. This assumption is plausible when participating institutions maintain similar preservation requirements, but it may be inappropriate when clients protect different private knowledge or domains.

The paper explicitly identifies both the agreement problem and the adequacy of public-statistics projectors for private requirements as unresolved questions.

References

This is natural when clients hold similar preservation requirements, as with several hospitals maintaining one clinical model, but how clients with heterogeneous preservation requirements would agree on a shared projector, and whether a projector built from public statistics covers each client's private requirements, are left open.

— FedAlphaEdit: Null-Space-Aligned Merging for Collaborative Knowledge Editing  (2610.11033 - Sugawara et al., 8 Oct 2026) in Section 6, Limitations, item “Shared projector”