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Deep learning models can be vulnerable to recovery attacks, raising privacyconcerns to users, and widespread algorithms such as empirical riskminimization (ERM) often do not directly enforce safety guarantees. In thispaper, we study the safety of ERM-trained models against a family of powerfulblack-box attacks. Our analysis quantifies this safety via two separate terms:(i) the model stability with respect to individual training samples, and (ii)the feature alignment between the attacker query and the original data. Whilethe first term is well established in learning theory and it is connected tothe generalization error in classical work, the second one is, to the best ofour knowledge, novel. Our key technical result provides a precisecharacterization of the feature alignment for the two prototypical settings ofrandom features (RF) and neural tangent kernel (NTK) regression. This provesthat privacy strengthens with an increase in the generalization capability,unveiling also the role of the activation function. Numerical experiments showa behavior in agreement with our theory not only for the RF and NTK models, butalso for deep neural networks trained on standard datasets (MNIST, CIFAR-10).

Stability, Generalization and Privacy: Precise Analysis for Random and NTK Features