# xMLP: Revolutionizing Private Inference with Exclusive Square Activation

arXiv: https://arxiv.org/abs/2403.08024 · HTML: https://mlsanity.com/paper/2403.08024/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 33 references that are in the map.
- First posted on arXiv 12 Mar 2024.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [AutoAugment: Learning Augmentation Policies from Data](https://mlsanity.com/paper/1805.09501/) (2018)
- [MetaFormer Is Actually What You Need for Vision](https://mlsanity.com/paper/2111.11418/) (2021)
- [ResMLP: Feedforward networks for image classification with data-efficient training](https://mlsanity.com/paper/2105.03404/) (2021)
- [Gazelle: A Low Latency Framework for Secure Neural Network Inference](https://mlsanity.com/paper/1801.05507/) (2018)
- [CrypTen: Secure Multi-Party Computation Meets Machine Learning](https://mlsanity.com/paper/2109.00984/) (2021)
- [Better plain ViT baselines for ImageNet-1k](https://mlsanity.com/paper/2205.01580/) (2022)
- [CrypTFlow2: Practical 2-Party Secure Inference](https://mlsanity.com/paper/2010.06457/) (2020)
- [DeepReDuce: ReLU Reduction for Fast Private Inference](https://mlsanity.com/paper/2103.01396/) (2021)
- [Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEs](https://mlsanity.com/paper/2101.08366/) (2021)
- [CryptoNAS: Private Inference on a ReLU Budget](https://mlsanity.com/paper/2006.08733/) (2020)
- [Selective Network Linearization for Efficient Private Inference](https://mlsanity.com/paper/2202.02340/) (2022)
- [Universal Approximation with Quadratic Deep Networks](https://mlsanity.com/paper/1808.00098/) (2018)
- [Learning to Linearize Deep Neural Networks for Secure and Efficient Private Inference](https://mlsanity.com/paper/2301.09254/) (2023)
- [Sphynx: ReLU-Efficient Network Design for Private Inference](https://mlsanity.com/paper/2106.11755/) (2021)

## Abstract (arXiv)

Private Inference (PI) enables deep neural networks (DNNs) to work on private data without leaking sensitive information by exploiting cryptographic primitives such as multi-party computation (MPC) and homomorphic encryption (HE). However, the use of non-linear activations such as ReLU in DNNs can lead to impractically high PI latency in existing PI systems, as ReLU requires the use of costly MPC computations, such as Garbled Circuits. Since square activations can be processed by Beaver's triples hundreds of times faster compared to ReLU, they are more friendly to PI tasks, but using them leads to a notable drop in model accuracy. This paper starts by exploring the reason for such an accuracy drop after using square activations, and concludes that this is due to an "information compounding" effect. Leveraging this insight, we propose xMLP, a novel DNN architecture that uses square activations exclusively while maintaining parity in both accuracy and efficiency with ReLU-based DNNs. Our experiments on CIFAR-100 and ImageNet show that xMLP models consistently achieve better performance than ResNet models with fewer activation layers and parameters while maintaining consistent performance with its ReLU-based variants. Remarkably, when compared to state-of-the-art PI Models, xMLP demonstrates superior performance, achieving a 0.58% increase in accuracy with 7x faster PI speed. Moreover, it delivers a significant accuracy improvement of 4.96% while maintaining the same PI latency. When offloading PI to the GPU, xMLP is up to 700x faster than the previous state-of-the-art PI model with comparable accuracy.