Deep Learning (DL) is a powerful solution for complex problems in many disciplines such as finance, medical research, or social sciences. Due to the high computational cost of DL algorithms, data scientists often rely upon Machine Learning as a Service (MLaaS) to outsource the computation onto third-party servers. However, outsourcing the computation raises privacy concerns when dealing with sensitive information, e.g., health or financial records. Also, privacy regulations like the European GDPR limit the collection, distribution, and use of such sensitive data. Recent advances in privacy-preserving computation techniques (i.e., Homomorphic Encryption and Secure Multiparty Computation) have enabled DL training and inference over protected data. However, these techniques are still immature and difficult to deploy in practical scenarios. In this work, we review the evolution of the adaptation of privacy-preserving computation techniques onto DL, to understand the gap between research proposals and practical applications. We highlight the relative advantages and disadvantages, considering aspects such as efficiency shortcomings, reproducibility issues due to the lack of standard tools and programming interfaces, or lack of integration with DL frameworks commonly used by the data science community.

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