What Lies Beyond Perception: A Partition Theory of the Limits of AI Evaluation and Oversight

Replacing the judge can move a benchmark score, and models can be trained to hide capabilities. It comes from a paper posted to arXiv on 23 October 2026. Both put the evaluator in question: what can it certify? We develop a partition theory of evaluation from one principle: judgement is bounded by perception. An agent's discrimination is the partition of its inputs into classes it cannot tell apart. Discrimination is necessary for capability but not sufficient, so bounds on it bear directly on whether evaluation can show that a model lacks an ability. We prove a one-sided bound. An examinee whose partition refines its evaluator's has the discrimination to pass every test the evaluator can grade, provided each input has an acceptable reply. We define the echo test, which accepts any reply the evaluator perceives as identical to the input, and show that it is complete for the tests the evaluator can grade. Passing therefore certifies at most a floor on discrimination, never a ceiling, and only a sharper evaluator can raise it. Used to detect concealment, echo-test failure points the wrong way: under exhaustive probing it flags every honestly weaker examinee and no concealer that presents as the evaluator's peer. Exact imitation of a weaker model is undetectable by any behavioural evaluator. We extend the bound to ensembles of monitors and to channels a model controls, explain published findings on judge disagreement and sandbagging, and derive testable predictions. A safety case that argues from behavioural evaluation alone that a model lacks an ability must assume the model's cooperation.

Why it counts

Replacing the judge can move a benchmark score, and models can be trained to hide capabilities.

Sources

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What is not known

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