Origin of Gemma’s better-conditioned covariance

Identify the cause of the better-conditioned per-cluster covariance estimates observed for Gemma-4-26B in the masked SAE feature space.

Background

The paper compares centroid-distance scoring with per-cluster Mahalanobis scoring on masked SAE features. Per-cluster covariance estimates are generally poorly conditioned for the tested models, but Gemma is an exception: Mahalanobis scoring performs better there and appears to benefit from a better-conditioned covariance estimate.

The empirical observation is reported, but its source is not established. Understanding why Gemma has better-conditioned per-cluster covariance could clarify when covariance-based scoring is appropriate for locally sparse anomaly detection.

References

This is consistent with the per-cluster covariance being poorly conditioned on the masked SAE features at the cluster sample sizes available on most models, and substantiates the choice of a magnitude-aware $\ell_1$ scoring in \Cref{alg:freqmask-km} on those models; Gemma is the lone exception, with a better-conditioned per-cluster covariance whose origin we do not fully diagnose.

— Local Sparsity Enables Unsupervised LLM Safety Detection  (2609.20129 - Chen et al., 17 Sep 2026) in Appendix, Section ‘Ablations: Stage-by-Stage Variations on FreqMask-KM’, subsection ‘Scoring Metric: $\ell_1$ vs. $\ell_2$ vs. Mahalanobis’