ANN Activation Function Estimators for Homomorphic Encrypted Inference

The growing use of cloud-based machine learning services has heightened concerns about data privacy, especially in sensitive domains such as healthcare and finance. Homomorphic Encryption (HE) allows computations on encrypted data, making it a key enabler for Privacy-Preserving Machine Learning (PPML). However, the non-linear nature of activation functions like Sigmoid and Tanh poses significant challenges for efficient encrypted inference in Artificial Neural Networks (ANNs). This paper introduces a lightweight, single-layer ANN-based estimator for activation functions, which achieves higher accuracy and improved efficiency compared to polynomial and piecewise linear methods, without resorting to computationally intensive techniques such as bootstrapping or high-degree approximations. The estimators are trained on plaintext data and seamlessly deployed during encrypted inference, demonstrating strong performance against conventional linear and piecewise approaches. Experimental results show that the proposed ANN estimators improve accuracy by approximately 2% (Sigmoid) to 73% (Tanh), enhance F1-scores by about 2% (Sigmoid) to 88% (Tanh), and significantly reduce Mean Square Error (MSE) by 50% (Sigmoid) to 96% (Tanh) compared to polynomial estimators, all while maintaining practical computational times. The ANN estimator achieves 97.70% accuracy and an AUC of 0.9997 within a CNN architecture on the MNIST dataset, and 85.25% accuracy with a 0.9459 AUC on the UCI Heart Disease dataset under ciphertext inference. These results demonstrate the method’s practicality for privacy-sensitive, real-world applications. Our approach provides a flexible and accurate solution for activation function approximation, supporting robust PPML deployment in cloud environments.