Per-operator-class two-dimensional overlap analysis

Conduct a production-scale two-dimensional spectral analysis that breaks down the overlap-law behavior by perturbation-operator class, particularly for anisotropic operators such as motion blur and rotation, to determine whether orientation-specific effects are obscured by radial spectral collapse.

Background

The paper’s primary overlap predictor radially collapses the two-dimensional attention-derived filter and perturbation spectrum into frequency bands, thereby discarding orientation information. A 100-sample pilot on GQA-8B found that the radial predictor and an orientation-preserving two-dimensional variant had similar grouped Pearson correlations, suggesting that radial collapse loses little aggregate predictive power.

However, the pilot was not large enough to isolate anisotropic perturbations, including motion blur and rotation, at production scale. The unresolved task is therefore to determine whether operator-specific orientation structure yields additional predictive information beyond the radial overlap measure.

References

A per-operator-class 2D breakdown isolating anisotropic operators (motion blur, rotation) at production scale is left to future work.

— Cross-Modal Attention Acts as a Frequency Filter: Why Verbose Prompts Improve Robustness in Vision-Language Models  (2609.20139 - Wani et al., 17 Sep 2026) in Appendix, Section “Overlap-law variants,” paragraph “Orientation-preserving 2D variant”