Establish the within-model relationship between Fisher distortion and ZFGA benefit

Determine whether Fisher-geometry distortion is reliably associated with ZFGA performance gains within individual model families by using temperature-normalized distortion measures and per-model correlation analyses.

Background

The paper reports a positive pooled correlation between the magnitude of Fisher-geometry distortion and ZFGA gain. However, the comparison is confounded because CLIP uses a temperature parameter of approximately 100, whereas ResNet-50 and DINOv3 use temperature 1, causing CLIP Fisher magnitudes to be roughly 10,000 times larger by construction.

The authors therefore do not know whether the apparent distortion-benefit relationship exists within any individual model family. They identify temperature normalization and per-model correlations as necessary analyses before drawing a causal or reliably descriptive conclusion.

References

We did not compute within-model correlations for this version, so we cannot state whether the distortion--gain relationship holds, is stronger, or is absent within any single model family; a $\tau$-normalized distortion measure and per-model correlations are needed before this diagnostic can support a causal or even a reliably descriptive claim, and we leave this to future work.

— Technical note on: Zero-Training Feature-Space Alignment via Information Geometry  (2609.37302 - Khan et al., 29 Sep 2026) in Appendix, Section “Geometry Diagnostics,” paragraph “Cross-model comparability of Fisher distortion”