Gaussian RBF Centered Kernel Alignment (CKA) in the Large Bandwidth Limit

We prove that Centered Kernel Alignment (CKA) based on a Gaussian RBF kernel converges to linear CKA in the large-bandwidth limit. We show that convergence onset is sensitive to the geometry of the feature representations, and that representation eccentricity bounds the range of bandwidths for which Gaussian CKA behaves nonlinearly.