# AESPA: Accuracy Preserving Low-degree Polynomial Activation for Fast Private Inference

arXiv: https://arxiv.org/abs/2201.06699 · HTML: https://mlsanity.com/paper/2201.06699/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 54 references that are in the map.
- First posted on arXiv 18 Jan 2022.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Towards Federated Learning at Scale: System Design](https://mlsanity.com/paper/1902.01046/) (2019)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Population Based Training of Neural Networks](https://mlsanity.com/paper/1711.09846/) (2017)
- [Gazelle: A Low Latency Framework for Secure Neural Network Inference](https://mlsanity.com/paper/1801.05507/) (2018)
- [Mish: A Self Regularized Non-Monotonic Activation Function](https://mlsanity.com/paper/1908.08681/) (2019)
- [Learning One-hidden-layer Neural Networks with Landscape Design](https://mlsanity.com/paper/1711.00501/) (2017)
- [XONN: XNOR-based Oblivious Deep Neural Network Inference](https://mlsanity.com/paper/1902.07342/) (2019)
- [DeepReDuce: ReLU Reduction for Fast Private Inference](https://mlsanity.com/paper/2103.01396/) (2021)
- [QUOTIENT: Two-Party Secure Neural Network Training and Prediction](https://mlsanity.com/paper/1907.03372/) (2019)
- [CryptoNAS: Private Inference on a ReLU Budget](https://mlsanity.com/paper/2006.08733/) (2020)
- [Precise Approximation of Convolutional Neural Networks for Homomorphically Encrypted Data](https://mlsanity.com/paper/2105.10879/) (2021)
- [HEMET: A Homomorphic-Encryption-Friendly Privacy-Preserving Mobile Neural Network Architecture](https://mlsanity.com/paper/2106.00038/) (2021)
- [Circa: Stochastic ReLUs for Private Deep Learning](https://mlsanity.com/paper/2106.08475/) (2021)
- [A Deep Conditioning Treatment of Neural Networks](https://mlsanity.com/paper/2002.01523/) (2020)
- [Sphynx: ReLU-Efficient Network Design for Private Inference](https://mlsanity.com/paper/2106.11755/) (2021)
- [Effect of Activation Functions on the Training of Overparametrized Neural Nets](https://mlsanity.com/paper/1908.05660/) (2019)
- [Sisyphus: A Cautionary Tale of Using Low-Degree Polynomial Activations in Privacy-Preserving Deep Learning](https://mlsanity.com/paper/2107.12342/) (2021)
- [Generating Accurate Pseudo-labels in Semi-Supervised Learning and Avoiding Overconfident Predictions via Hermite Polynomial Activations](https://mlsanity.com/paper/1909.05479/) (2019)
- [Highly Accurate CNN Inference Using Approximate Activation Functions over Homomorphic Encryption](https://mlsanity.com/paper/2009.03727/) (2020)

## Built on by (most cited first, 14 of 14)

- [AutoFHE: Automated Adaption of CNNs for Efficient Evaluation over FHE](https://mlsanity.com/paper/2310.08012/) (2023)
- [HyPHEN: A Hybrid Packing Method and Optimizations for Homomorphic Encryption-Based Neural Networks](https://mlsanity.com/paper/2302.02407/) (2023)
- [NeuJeans: Private Neural Network Inference with Joint Optimization of Convolution and FHE Bootstrapping](https://mlsanity.com/paper/2312.04356/) (2023)
- [Optimized Layerwise Approximation for Efficient Private Inference on Fully Homomorphic Encryption](https://mlsanity.com/paper/2310.10349/) (2023)
- [A Training Framework for Optimal and Stable Training of Polynomial Neural Networks](https://mlsanity.com/paper/2505.11589/) (2025)
- [Approximating ReLU on a Reduced Ring for Efficient MPC-based Private Inference](https://mlsanity.com/paper/2309.04875/) (2023)
- [CryptoFace: End-to-End Encrypted Face Recognition](https://mlsanity.com/paper/2509.00332/) (2025)
- [Towards Fast and Scalable Private Inference](https://mlsanity.com/paper/2307.04077/) (2023)
- [Peregrine: One-Shot Fine-Tuning for FHE Inference of General Deep CNNs](https://mlsanity.com/paper/2511.18976/) (2025)
- [CrypTorch: PyTorch-based Auto-tuning Compiler for Machine Learning with Multi-party Computation](https://mlsanity.com/paper/2511.19711/) (2025)
- [Regularized PolyKervNets: Optimizing Expressiveness and Efficiency for Private Inference in Deep Neural Networks](https://mlsanity.com/paper/2312.15229/) (2023)
- [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)
- [OptiPrime: Optimizing Private Inference through Protocol-Hardware Co-design](https://mlsanity.com/paper/2609.16898/) (2026)

## Abstract (arXiv)

Hybrid private inference (PI) protocol, which synergistically utilizes both multi-party computation (MPC) and homomorphic encryption, is one of the most prominent techniques for PI. However, even the state-of-the-art PI protocols are bottlenecked by the non-linear layers, especially the activation functions. Although a standard non-linear activation function can generate higher model accuracy, it must be processed via a costly garbled-circuit MPC primitive. A polynomial activation can be processed via Beaver's multiplication triples MPC primitive but has been incurring severe accuracy drops so far. In this paper, we propose an accuracy preserving low-degree polynomial activation function (AESPA) that exploits the Hermite expansion of the ReLU and basis-wise normalization. We apply AESPA to popular ML models, such as VGGNet, ResNet, and pre-activation ResNet, to show an inference accuracy comparable to those of the standard models with ReLU activation, achieving superior accuracy over prior low-degree polynomial studies. When applied to the all-RELU baseline on the state-of-the-art Delphi PI protocol, AESPA shows up to 42.1x and 28.3x lower online latency and communication cost.