Comparing Linear Probes with Mahalanobis Cosine Similarity
Linear probes are widely used in interpretability research and often compared by cosine similarity. The Mahalanobis cosine similarity (MCS) between two directions, which reweights the inner product by test data covariance, is a natural task-aware refinement. Ying et al. (2026) report that a probe's MCS to a reference probe trained on the out-of-distribution (OOD) data near-perfectly linearly predicts the probe's OOD AUROC (R^2 = 0.98). Here, we extend this empirical finding across models, layers, and concept domains, and prove this general phenomenon in closed form: For balanced classes whose projections are Gaussian, OOD AUROC and MCS to the reference probe are linear because both are si...
| Authors | Zhuofan Josh Ying, Peter Hase, Nikolaus Kriegeskorte |
|---|---|
| Primary category | cs.LG |
| Published | 17 June 2026 |
| Last updated at source | 17 June 2026 |
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