LHDNN: Maintaining High Precision and Low Latency Inference of Deep Neural Networks on Encrypted Data

The advancement of deep neural networks (DNNs) has prompted many cloud service providers to offer deep learning as a service (DLaaS) to users across various application domains. However, in current DLaaS prediction systems, users' data are at risk of leakage. Homomorphic encryption allows operations to be performed on ciphertext without decryption, which can be applied to DLaaS to ensure users' data privacy. However, mainstream homomorphic encryption schemes only support homomorphic addition and multiplication, and do not support the ReLU activation function commonly used in the activation layers of DNNs. Previous work used approximate polynomials to replace the ReLU activation function, but the DNNs they implemented either had low inference accuracy or high inference latency. In order to achieve low inference latency of DNNs on encrypted data while ensuring inference accuracy, we propose a low-degree Hermite deep neural network framework (called LHDNN), which uses a set of low-degree trainable Hermite polynomials (called LotHps) as activation layers of DNNs. Additionally, LHDNN integrates a novel weight initialization and regularization module into the LotHps activation layer, which makes the training process of DNNs more stable and gives a stronger generalization ability. Additionally, to further improve the model accuracy, we propose a variable-weighted difference training (VDT) strategy that uses ReLU-based models to guide the training of LotHps-based models. Extensive experiments on multiple benchmark datasets validate the superiority of LHDNN in terms of inference speed and accuracy on encrypted data.