Top-K-active baseline control — tests a separate confound from → Top-and-random vs. random-only interpretability scoring

Both controls answer the same worry, that the SAE's apparent interpretability edge over PCA and ICA is a scoring artifact, but they patch two unrelated seams in the pipeline. Random-only scoring (the alternative to top-random-scoring, run in Appendix C.2/Figure 9) tests whether mixing in cherry-picked highly-activating fragments inflates scores; it says nothing about how 'active' a direction is defined in the first place. The top-K control (Appendix G) instead targets a geometric asymmetry: a PCA or ICA direction is active across an entire half-space on one side of a hyperplane through the origin, while an SAE feature, because its pre-activation bias is in practice always negative, only activates past a hyperplane offset from the origin, making it structurally sparser regardless of content. Top-K forces PCA and ICA to match the SAE's average per-datapoint active-feature count (from the R=1, alpha=8.6e-4 dictionary) before scoring, and Appendix G's Figure 18 shows this explains only a small fraction of the gap. So a feature or baseline could in principle pass one check and fail the other: random-only scoring rules out a data-selection artifact, top-K rules out a density artifact, and neither substitutes for the other.