sae-circular-feature-ambiguity
IN premise — summaries/2026/08/24/engels-2024-not-all-features-linear-sR-references-chunk-1.md
Created 2026-08-25T02:58:02+00:00
An SAE with m=2 dictionary features must activate both on every point of a circular feature (degenerate), while m=10 features spread around the circle with no canonical feature direction, meaning SAE feature directions for irreducible multi-dimensional features are not unique.
Summary
When a concept in model space is inherently multi-dimensional (like a circle), there is no single correct set of sparse directions to describe it. This means the specific feature directions an SAE picks out for such a concept are somewhat arbitrary — rotating or redistributing them still captures the same structure — so we should not treat any particular SAE decomposition of a complex feature as the one true answer.