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 detection%2C where test data may come from classes that are unknown during training (i.e.%2C OOD data). Due to the unavailability and diversity of OOD data%2C good generalization ability is crucial for effective OOD detection algorithms%2C and corresponding learning theory is still an open problem. To study the generalization of OOD detection%2C this paper investigates the probably approximately correct (PAC) learning theory of OOD detection that fits the commonly used evaluation metrics in the literature. First%2C we find a necessary condition for the learnability of OOD detection. Then%2C using this condition%2C we prove several impossibility theorems for the learnability of OOD detection under some scenarios. Although the impossibility theorems are frustrating%2C we find that some conditions of these impossibility theorems may not hold in some practical scenarios. Based on this observation%2C we next give several necessary and sufficient conditions to characterize the learnability of OOD detection in some practical scenarios. Lastly%2C we offer theoretical support for representative OOD detection works based on our OOD theory.?quality=80&w=800)
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