superposition-as-single-root-cause-v2
IN premise
Created 2026-08-25T03:28:00+00:00
Superposition is a central unifying node in a tightly interlocked logical structure linking over-complete representation, covariance whitening, and rank-one editability. The read-broad/write-narrow asymmetry is a direct operational consequence of the over-complete basis (simultaneous linear projection for reading, rank-one injection for writing), covariance separation supports the geometric well-definedness in which rank-one updates operate, and the boundedness of rank-one editing is consistent with a finite addressable space. These three properties form a closed triangle of mutual dependence, so that none must be treated as independent of the others, and the structure is accounted for without invoking additional free parameters among them.
Summary
Superposition is not just one feature of how these networks work; it is the single mechanism that simultaneously explains why representations are over-complete, why the activation statistics look whitened, and why behavior edits stay small and targeted. That means the read-broad/write-narrow asymmetry, the geometric structure that makes edits well-defined, and the fact that edits are bounded all come from the same root, so trying to tweak any one of them in isolation will fail because they are locked together.
Dependents
These beliefs depend on this one:
- OUT superposition-as-single-root-cause — Superposition is the unique root cause from which the full read/write/editing logical structure follows: over-complete representation necessitates covariance whitening (making geometry well-defined), which in turn explains both the broad-read/narrow-write asymmetry (projection vs. rank-one injection) and the closed triangle linking all three properties—there is no independent second principle needed.