Large Language Model probabilities cannot reliably distinguish between possible and impossible language

A controversial test for Large Language Models concerns the ability to discern possible from impossible language. While some evidence attests to the models sensitivity to what crosses the limits of grammatically impossible language, this evidence has been contested on the grounds of the soundness of the testing material. We use model-internal representations as a direct means of investigating the way Large Language Models represent the grammatical-ungrammatical distinction. In a novel benchmark, we elicit sum log probabilities from 8 models and compute minimal-pair surprisal differences, juxtaposing probabilities assigned to grammatical sentences to probabilities assigned to (i) lower frequency grammatical sentences, (ii) ungrammatical sentences, (iii) semantically odd sentences, and (iv) pragmatically odd sentences. The prediction is that if string-probabilities can function as proxies for the limits of grammar, the ungrammatical condition will stand out among the conditions that involve linguistic violations, showing a spike in the surprisal rates. Our results do not reveal a unique surprisal signature for ungrammatical prompts: across models, we observe comparable surprisal for the pragmatically odd condition, and the semantically odd condition consistently shows even higher surprisal. We thus demonstrate that probabilities do not constitute reliable proxies for grammaticality, showing that probability differences alone cannot be used to infer model-internal representations of syntactic knowledge. Consequently, claims about models being able to distinguish possible from impossible language need verification through a different methodology.