  A typical setup in many machine learning scenarios involves a server that
holds a model and a user that possesses data, and the challenge is to perform
inference while safeguarding the privacy of both parties. Private Inference has
been extensively explored in recent years, mainly from a cryptographic
standpoint via techniques like homomorphic encryption and multiparty
computation. These approaches often come with high computational overhead and
may degrade the accuracy of the model. In our work, we take a different
approach inspired by the Private Information Retrieval literature. We view
private inference as the task of retrieving inner products of parameter vectors
with the data, a fundamental operation in many machine learning models. We
introduce schemes that enable such retrieval of inner products for models with
quantized (i.e., restricted to a finite set) weights; such models are
extensively used in practice due to a wide range of benefits. In addition, our
schemes uncover a fundamental tradeoff between user and server privacy. Our
information-theoretic approach is applicable to a wide range of problems and
robust in privacy guarantees for both the user and the server.
