Is there a monotonic relationship between SAE sparsity (L0) and feature interpretability in GPT-2 small?

Sparse autoencoders are trained with a sparsity objective on the premise that sparser (lower-$L_0$) decompositions yield more monosemantic, human-interpretable features -- but sparsity is only a proxy, and denser decompositions might in some regimes be more interpretable. Question: on a fixed GPT-2 small residual-stream layer, train (or use released) SAEs across a sweep of sparsity levels (e.g. $L_0\in\{5,10,20,40,80\}$) at matched dictionary size and comparable reconstruction, and measure mean feature interpretability with an automated-interpretability (autointerp) score computed by an open judge model (e.g. a Gemma-2 or Llama-3 open model). Is the relationship between $L_0$ and mean interpretability monotonic, unimodal, or flat? Report mean autointerp score versus $L_0$ with confidence intervals and the shape of the curve.

Acceptance. FULLY RESOLVES: a reproducible script (fixed seeds; GPT-2 small; pinned open judge model) evaluating $\ge 4$ SAEs spanning a stated $L_0$ range at matched dictionary width and comparable loss-recovered, reporting mean autointerp interpretability (with confidence intervals; $\ge 200$ features each) versus $L_0$ and a stated verdict on the curve shape (monotone increasing with sparsity / unimodal / flat), with a significance test. Deliverable: code + SAE IDs/checkpoints + the per-$L_0$ interpretability table.