superposition-necessitates-covariance-whitening-v2
IN premise
Created 2026-08-25T04:10:03+00:00
Over-complete superposition in the residual stream (identified as a locus of interpretable structure across multiple depths) is a primary structural condition that motivates the use of empirical second-moment matrices as a natural inner product for reasoning about individual features and performing targeted interventions; independent lines of work (ROME's key-space projection, Park's unembedding whitening) converge on this covariance-geometry approach as a practical framework for feature manipulation in over-complete representation spaces.
Summary
Because a model's features are crammed into fewer dimensions than there are features, they overlap and interfere with each other, so you cannot treat them as independent axes. This means that to isolate or edit a single feature, you need to account for the statistical relationships between all features (their shared variance), and multiple independent research threads have converged on using this covariance structure as the correct geometric tool for targeted model interventions.
Dependents
These beliefs depend on this one:
- OUT superposition-necessitates-covariance-whitening — Over-complete superposition in the shared residual-stream substrate is the precise structural condition that necessitates covariance/whitening (second-moment projection) as the canonical tool for isolating individual features and performing targeted rank-one edits; without superposition, raw Euclidean geometry would suffice and the entire covariance-geometry framework would be unnecessary.