# Highly Accurate CNN Inference Using Approximate Activation Functions over Homomorphic Encryption

arXiv: https://arxiv.org/abs/2009.03727 · HTML: https://mlsanity.com/paper/2009.03727/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2020.

## Built on by (most cited first, 13 of 13)

- [AESPA: Accuracy Preserving Low-degree Polynomial Activation for Fast Private Inference](https://mlsanity.com/paper/2201.06699/) (2022)
- [SLIP: Securing LLMs IP Using Weights Decomposition](https://mlsanity.com/paper/2407.10886/) (2024)
- [HyPHEN: A Hybrid Packing Method and Optimizations for Homomorphic Encryption-Based Neural Networks](https://mlsanity.com/paper/2302.02407/) (2023)
- [Private and Reliable Neural Network Inference](https://mlsanity.com/paper/2210.15614/) (2022)
- [NeuJeans: Private Neural Network Inference with Joint Optimization of Convolution and FHE Bootstrapping](https://mlsanity.com/paper/2312.04356/) (2023)
- [A Training Framework for Optimal and Stable Training of Polynomial Neural Networks](https://mlsanity.com/paper/2505.11589/) (2025)
- [Peregrine: One-Shot Fine-Tuning for FHE Inference of General Deep CNNs](https://mlsanity.com/paper/2511.18976/) (2025)
- [Privacy-Preserving Medical Image Classification through Deep Learning and Matrix Decomposition](https://mlsanity.com/paper/2308.16530/) (2023)
- [Homomorphic WiSARDs: Efficient Weightless Neural Network training over encrypted data](https://mlsanity.com/paper/2403.20190/) (2024)
- [Practical and Private Hybrid ML Inference with Fully Homomorphic Encryption](https://mlsanity.com/paper/2509.01253/) (2025)
- [PRISM: Privacy-preserving Inference System with Homomorphic Encryption and Modular Activation](https://mlsanity.com/paper/2511.07807/) (2025)
- [FastFHE: Packing-Scalable and Depthwise-Separable CNN Inference Over FHE](https://mlsanity.com/paper/2511.22434/) (2025)
- [PRISM: Sensitivity-Aware PolynoMial PRuning for EffIcient Neural Network Encryption](https://mlsanity.com/paper/2607.18342/) (2026)

## Abstract (arXiv)

In the big data era, cloud-based machine learning as a service (MLaaS) has attracted considerable attention. However, when handling sensitive data, such as financial and medical data, a privacy issue emerges, because the cloud server can access clients' raw data. A common method of handling sensitive data in the cloud uses homomorphic encryption, which allows computation over encrypted data without decryption. Previous research usually adopted a low-degree polynomial mapping function, such as the square function, for data classification. However, this technique results in low classification accuracy. In this study, we seek to improve the classification accuracy for inference processing in a convolutional neural network (CNN) while using homomorphic encryption. We adopt an activation function that approximates Google's Swish activation function while using a fourth-order polynomial. We also adopt batch normalization to normalize the inputs for the Swish function to fit the input range to minimize the error. We implemented CNN inference labeling over homomorphic encryption using the Microsoft's Simple Encrypted Arithmetic Library for the Cheon-Kim-Kim-Song (CKKS) scheme. The experimental evaluations confirmed classification accuracies of 99.22% and 80.48% for MNIST and CIFAR-10, respectively, which entails 0.04% and 4.11% improvements, respectively, over previous methods.