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The exploitation of publicly accessible data has led to escalating concerns regarding data privacy and intellectual property (IP) breaches in the age of artificial intelligence. As a strategy to safeguard both data privacy and IP-related domain knowledge, efforts have been undertaken to render shared data unlearnable for unauthorized models in the wild. Existing methods apply empirically optimized perturbations to the data in the hope of disrupting the correlation between the inputs and the corresponding labels such that the data samples are converted into Unlearnable Examples (UEs). Nevertheless, the absence of mechanisms that can verify how robust the UEs are against unknown unauthorized models and train-time techniques engenders several problems. First, the empirically optimized perturbations may suffer from the problem of cross-model generalization, which echoes the fact that the unauthorized models are usually unknown to the defender. Second, UEs can be mitigated by train-time techniques such as data augmentation and adversarial training. Furthermore, we find that a simple recovery attack can restore the clean-task performance of the classifiers trained on UEs by slightly perturbing the learned weights. To mitigate the aforementioned problems, in this paper, we propose a mechanism for certifying the so-called -Learnability of an unlearnable dataset via parametric smoothing. A lower certified -Learnability indicates a more robust protection over the dataset. Finally, we try to 1) improve the tightness of certified -Learnability and 2) design Provably Unlearnable Examples (PUEs) which have reduced -Learnability …