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One Perturbation Is Not Enough: Identifiability and Blind Baselines for Behavioral AI Evaluation

arXiv · AI, language, vision and robotics · article · Sep 5, 2026 · UTC

Behavioral evaluations perturb an input and read the induced change in the output in order to certify that a system uses that input. We show that the number of perturbations such a certificate requires is fixed, and that reporting a single perturbation cannot supply it. Where a response ratio is a property of the policy rather than of the test items, the behavioral record is a linear measurement of an exponent vector recording how much the output depends on each input, so perturbations identify input use exactly when their logarithms span the input space. At least $n$ are needed for $n$ inputs

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