CNN1 performance.

The widespread adoption of cloud computing necessitates privacy-preserving techniques that allow information to be processed without disclosure. This paper proposes a method to increase the accuracy and performance of privacy-preserving Convolutional Neural Networks with Homomorphic Encryption (CNN-HE) by Self-Learning Activation Functions (SLAF). SLAFs are polynomials with trainable coefficients updated during training, together with synaptic weights, for each polynomial independently to learn task-specific and CNN-specific features. We theoretically prove its feasibility to approximate any continuous activation function to the desired error as a function of the SLAF degree. Two CNN-HE models are proposed: CNN-HE-SLAF and CNN-HE-SLAF-R. In the first model, all activation functions are replaced by SLAFs, and CNN is trained to find weights and coefficients. In the second one, CNN is trained with the original activation, then weights are fixed, activation is substituted by SLAF, and CNN is shortly re-trained to adapt SLAF coefficients. We show that such self-learning can achieve the same accuracy 99.38% as a non-polynomial ReLU over non-homomorphic CNNs and lead to an increase in accuracy (99.21%) and higher performance (6.26 times faster) than the state-of-the-art CNN-HE CryptoNets on the MNIST optical character recognition benchmark dataset.