Certified Private Inference on Neural Networks via Lipschitz-Guided Abstraction Refinement
Edoardo Manino, Bernardo Magri, Mustafa Mustafa, Lucas Carvalho Cordeiro · Kalpa publications in computing · 2023
Private inference on neural networks requires running all the computation on encrypted data. Unfortunately, neural networks contain a large number of non-arithmetic operations, such as ReLU activation functions and max pooling layers, which incur a high latency cost in their encrypted form. To address this issue, the majority of private inference methods re- place some or all of the non-arithmetic operations with a polynomial approximation. This step introduces approximation errors that can substantially alter the output of the neural network and decrease its predictive performance. In this paper, we propose a Lipschitz- Guided Abstraction Refinement method (LiGAR), which provides strong guarantees on the global approximation error. Our method is iterative, and leverages state-of-the-art Lipschitz constant estimation techniques to produce increasingly tighter bounds on the worst-case error. At each iteration, LiGAR designs the least expensive polynomial approx- imation by solving the dual of the corresponding optimization problem. Our preliminary experiments show that LiGAR can easily converge to the optimum on medium-sized neural networks.