Determine whether all arm-symmetric shared-position rules agree

Establish whether every arm-symmetric rule for selecting common measurement positions yields the same reduction of the latent-by-arm variance component in ablation-based sparse-autoencoder evaluation.

Background

The paper evaluates two arm-symmetric rules for choosing a common position: ranking candidates by minimum activation across arms and selecting from the union of each arm’s top positions while requiring nonzero activation for all arms. Both reduce the latent-by-arm interaction, but the magnitude of the reduction differs between models.

Because only two rules were tested, the authors explicitly caution that the evidence does not establish whether the observed agreement holds for every arm-symmetric position-selection rule. The generality of the proposed repair therefore remains unresolved.

References

What it does not establish is that every arm-symmetric rule agrees, two rules agreeing is two data points, and neither is derived from a definition of what the estimand should be.

— Where You Measure Decides What You Measure: Position Selection in Ablation-Based SAE Evaluation  (2608.13337 - Noël, 13 Aug 2026) in Appendix, Section “A shared-position rule that does not select on agreement”