Functional organization of residual information

Determine the functional organization and role of information retained in the residual subspace after extracting the targeted functional subspaces.

Background

The decomposition framework retains a residual subspace for information not selectively assigned to either of two target functions. Appendix E.10 shows that residual representations can contain or support task-relevant information, but the experiments do not establish how that information is organized or why it is shared or redundant rather than selectively associated with one function.

References

An additional open question concerns the role of the residual subspace. As shown in Appendix Section E.10, the residual is not purely nuisance: it can contain or support task-relevant information, but this information appears to be shared or redundant rather than selectively associated with either task. Understanding the functional organization and role of this residual information remains an open direction for future work.

— Neural networks are more modular than single neurons suggest  (2610.12842 - Saha et al., 9 Oct 2026) in Section 4, Discussion; Appendix E.10

We conjecture that this residual mainly consists of fine pixel detail rather than semantics or layout, consistent with the high-frequency features of pixel models (Figure~\ref{fig:appendix-layer-pca}).

— Learning Representations to Guide Pixel Diffusion Transformers  (2610.12978 - Pan et al., 9 Oct 2026) in Appendix, Section “Relation to Autoguidance and Internal Guidance,” paragraph “Why IG is less effective in pixel space”