A Better Metric Will Not Save You: What You Compare Beats How You Compare It

Abstract: Representational similarity measures (RSA, CKA, Procrustes) are chosen for the transformations they treat as irrelevant, and all of them take the set of conditions as given. That set is fixed by two decisions, which inputs are admitted and how they are grouped, both taken before the matrix a measure operates on exists: no invariance property reaches them. We measure what they are worth where the arrangement the conditions ought to have is known independently of the systems compared, the acoustic organisation of vowels, across fifteen languages and twenty-seven representations. Changing which categories are compared, at a fixed number of them, moves the gap between two representations by more than twice the effect being measured, while changing how many moves it not at all. In this setting rankings of models are identified under these choices, and rankings across languages are not.