Top-K-active baseline control
Sparse Autoencoders Find Highly Interpretable Features in Language Models — introduced
A control experiment (Appendix G) restricting the PCA and ICA baselines to a fixed number K of simultaneously 'active' directions per datapoint, matched to the SAE's average active-feature count, to test whether SAE's interpretability advantage merely reflects its lower per-datapoint activation density rather than genuinely better features. Finds this adjustment explains only a small fraction of the interpretability gap.
A newer method can be made to look better than an older one simply by comparing them on unequal terms, and one specific asymmetry threatens exactly that here: a couple of classical baseline techniques are structurally 'active' across half of all possible data, while the features they're being compared against fire far more sparingly by design. If sparser activation alone makes a feature look more interpretable, the headline comparison might be measuring the wrong thing entirely.
This page explains why the baselines start out less sparse for a structural, geometric reason, how the comparison gets redone with each baseline's activity artificially capped to match, and what survives — and what doesn't — once that adjustment is made.
Checking whether the advantage is real or just geometric
Appendix G exists to close off one specific objection to the paper's headline result that sparse dictionary features score better on the Autointerpretability score than Principal Component Analysis (PCA) or Independent Component Analysis (ICA): maybe the comparison isn't even, because the baselines are structurally "active" on more of the data than a dictionary feature is, at every datapoint, regardless of content. If that were the whole story, the interpretability gap would say more about how activity is defined than about which decomposition finds better features (sparse-autoencoders, §"G TOP K COMPARISONS", p. 18).
Why the baselines start out less sparse by construction
A PCA or ICA direction is "active" across an entire half-space -- everything on one side of a hyperplane through the origin -- since its projection is simply positive or negative. A dictionary feature's activation, by contrast, is $\mathrm{ReLU}(w\cdot x + b)$ with a bias $b$ that is in practice always negative, so it only fires past a hyperplane offset away from the origin, covering a strictly smaller region of activation space. That asymmetry alone would make dictionary features look sparser -- and, if sparsity itself correlates with score the way Interpretability-vs-kurtosis/skew correlation analysis suggests, more interpretable -- even with no difference in the quality of what each direction detects (sparse-autoencoders, §"G TOP K COMPARISONS", p. 18).
Matching activity levels, and what survives
The control forces PCA and ICA into the same regime: only a fixed number $K$ of their directions are allowed to count as active per datapoint, with $K$ set to the average number of simultaneously active features in a sparse dictionary trained with expansion ratio $R=1$ and sparsity coefficient $\alpha = 8.6\times10^{-4}$ on the layer in question, matching PCA and ICA's per-datapoint activity to the SAE's own (sparse-autoencoders, §"G TOP K COMPARISONS", p. 18). Even with density equalized this way, the adjustment "does not explain more than a small fraction of the improvement in scores," which the paper takes as evidence the sparse dictionary's advantage reflects genuinely better features rather than an artifact of how liberally the baselines get to fire. It answers a different worry than Top-and-random vs. random-only interpretability scoring's random-only rerun does: that check targets which text fragments the simulator sees, this one targets how "active" a direction is defined in the first place, and clearing one says nothing about the other.