Calibrate the intervention rank separately

Determine whether separately calibrating the rank of the vision-unique intervention subspace can yield further accuracy gains beyond the default rank used for GeoPID intervention.

Background

GeoPID estimates a vision-unique subspace using a rank cap and then amplifies representations along that subspace during inference. The main experiments use a default unique-direction rank of r_u = 32, while an ablation found that r_u = 8 improved intervention gain over r_u = 32 by a median of 0.67 percentage points across 40 matched model–benchmark pairs. The authors therefore identify separate calibration of the intervention rank as an unresolved direction for potentially improving the method.

References

This improvement at $r_u = 8$ suggests separately calibrating the intervention rank may yield even further gains for the future work.

— GeoPID: Decomposing and Steering Visual Information in Vision-Language Models  (2610.08401 - Kim et al., 6 Oct 2026) in Appendix E.1, “Determining r_b, r_u, r_s in batch-wise PCA”