Differential Privacy has become a widely popular method for data protection in machine learning, especially since it allows formulating strict mathematical privacy guarantees. This survey provides an overview of the state-of-the-art of differentially private centralized deep learning, thorough analyses of recent advances and open problems, as well as a discussion of potential future developments in the field. Based on a systematic literature review, the following topics are addressed: auditing and evaluation methods for private models, improvements of privacy-utility trade-offs, protection against a broad range of threats and attacks, differentially private generative models, and emerging application domains.
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