sae-guided-feature-space-editing

OUT derived (depth 5)

Created 2026-08-25T03:11:44+00:00

SAE-identified features provide a semantically-interpretable coordinate system for specifying knowledge edits—enabling edits to be expressed as feature-space operations (e.g., "suppress feature 34M/31164353 and amplify its neighborhood") that the covariance geometry guarantees map to valid rank-one weight-space operations—thereby bridging the interpretability and editing literatures through the shared second-moment structure.

Justifications

SL — The bridge requires both the covariance-editability triangle (providing the mathematical guarantee that feature-space operations are valid) and the empirical feature-neighborhood structure (providing the semantic labels to name the operations); the gate on raw-activation-not-causal-importance acknowledges that if features are not causally meaningful, specifying edits in feature space is unjustified.

Antecedents (all must be IN):

  • OUT superposition-covariance-editability-triangle — Superposition, covariance whitening, and rank-one editability form a closed logical triangle in which each property necessitates the others: over-complete superposition requires covariance separation for feature addressability, covariance separation defines the geometric space in which rank-one updates are well-defined, and the boundedness of rank-one editing confirms the addressable space is finite.
  • OUT feature-neighborhood-as-geometric-theorem-instantiation — SAE feature neighborhood structure (e.g., Golden Gate Bridge → San Francisco → California) is the concrete empirical instantiation of the covariance-geometric semantic space at the interpretable level: decoder-space proximity reflects the same subordination relations predicted by Park's orthogonality theorem, unifying interpretability with geometric theory.

Unless (any of these IN defeats this justification):

  • IN sae-raw-activation-not-causal-importance — Ranking features by raw activation magnitude does not reliably identify causally important features; a feature that fires on the token 'alone' is distinct from one encoding the concept of wanting solitude.