High Activation Density could mean either that sparsity was not properly learned, or that it is an important feature needed in various situations. In the Feature Browser, SAE features show higher feature interpretability when they have more high activation Quantile, which demonstrates a limitation where SAE features have low interpretability for low activations and exhibit certain skewness.
However, features with the highest Activation Density in the Activation Distribution are less interpretable, mainly because these features typically don't have high activation values in absolute terms (not quantile). A well-classified and highly interpretable SAE feature should not show density that simply decreases with activation value, but rather should show clustering at high activation levels after an initial decrease.
Towards Monosemanticity: Decomposing Language Models With Dictionary Learning
Mechanistic interpretability seeks to understand neural networks by breaking them into components that are more easily understood than the whole. By understanding the function of each component, and how they interact, we hope to be able to reason about the behavior of the entire network. The first step in that program is to identify the correct components to analyze.
https://transformer-circuits.pub/2023/monosemantic-features#global-analysis-interp-caveats

Seonglae Cho