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Private computation of nonlinear functions, such as Rectified Linear Units(ReLUs) and max-pooling operations, in deep neural networks (DNNs) posessignificant challenges in terms of storage, bandwidth, and time consumption. Toaddress these challenges, there has been a growing interest in utilizingprivacy-preserving techniques that leverage polynomial activation functions andkernelized convolutions as alternatives to traditional ReLUs. However, thesealternative approaches often suffer from a trade-off between achieving fasterprivate inference (PI) and sacrificing model accuracy. In particular, whenapplied to much deeper networks, these methods encounter traininginstabilities, leading to issues like exploding gradients (resulting in NaNs)or suboptimal approximations. In this study, we focus on PolyKervNets, atechnique known for offering improved dynamic approximations in smallernetworks but still facing instabilities in larger and more complex networks.Our primary objective is to empirically explore optimization-based trainingrecipes to enhance the performance of PolyKervNets in larger networks. By doingso, we aim to potentially eliminate the need for traditional nonlinearactivation functions, thereby advancing the state-of-the-art inprivacy-preserving deep neural network architectures. Code can be found onGitHub at: \url{https://github.com/tolusophy/PolyKervNets/}

Regularized PolyKervNets: Optimizing Expressiveness and Efficiency for Private Inference in Deep Neural Networks