# Tabula: Efficiently Computing Nonlinear Activation Functions for Secure Neural Network Inference

arXiv: https://arxiv.org/abs/2203.02833 · HTML: https://mlsanity.com/paper/2203.02833/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 49 references that are in the map.
- First posted on arXiv 5 Mar 2022.

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

- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [Gazelle: A Low Latency Framework for Secure Neural Network Inference](https://mlsanity.com/paper/1801.05507/) (2018)
- [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)
- [DeepSecure: Scalable Provably-Secure Deep Learning](https://mlsanity.com/paper/1705.08963/) (2017)
- [Discovering Low-Precision Networks Close to Full-Precision Networks for Efficient Embedded Inference](https://mlsanity.com/paper/1809.04191/) (2018)
- [SIRNN: A Math Library for Secure RNN Inference](https://mlsanity.com/paper/2105.04236/) (2021)
- [Pareto-Optimal Quantized ResNet Is Mostly 4-bit](https://mlsanity.com/paper/2105.03536/) (2021)
- [Secure Evaluation of Quantized Neural Networks](https://mlsanity.com/paper/1910.12435/) (2019)
- [ARIANN: Low-Interaction Privacy-Preserving Deep Learning via Function Secret Sharing](https://mlsanity.com/paper/2006.04593/) (2020)
- [Circa: Stochastic ReLUs for Private Deep Learning](https://mlsanity.com/paper/2106.08475/) (2021)
- [Sphynx: ReLU-Efficient Network Design for Private Inference](https://mlsanity.com/paper/2106.11755/) (2021)
- [Secure Quantized Training for Deep Learning](https://mlsanity.com/paper/2107.00501/) (2021)
- [Sisyphus: A Cautionary Tale of Using Low-Degree Polynomial Activations in Privacy-Preserving Deep Learning](https://mlsanity.com/paper/2107.12342/) (2021)
- [WrapNet: Neural Net Inference with Ultra-Low-Resolution Arithmetic](https://mlsanity.com/paper/2007.13242/) (2020)
- [Quantization of Deep Neural Networks for Accumulator-constrained Processors](https://mlsanity.com/paper/2004.11783/) (2020)
- [Weightless: Lossy Weight Encoding For Deep Neural Network Compression](https://mlsanity.com/paper/1711.04686/) (2017)
- [Direct Quantization for Training Highly Accurate Low Bit-width Deep Neural Networks](https://mlsanity.com/paper/2012.13762/) (2020)
- [Practical Encrypted Computing for IoT Clients](https://mlsanity.com/paper/2103.06743/) (2021)

## Built on by (most cited first, 2 of 2)

- [Scaling up Trustless DNN Inference with Zero-Knowledge Proofs](https://mlsanity.com/paper/2210.08674/) (2022)
- [PowerQuant: Automorphism Search for Non-Uniform Quantization](https://mlsanity.com/paper/2301.09858/) (2023)

## Abstract (arXiv)

Multiparty computation approaches to secure neural network inference commonly rely on garbled circuits for securely executing nonlinear activation functions. However, garbled circuits require excessive communication between server and client, impose significant storage overheads, and incur large runtime penalties. To reduce these costs, we propose an alternative to garbled circuits: Tabula, an algorithm based on secure lookup tables. Our approach precomputes lookup tables during an offline phase that contains the result of all possible nonlinear function calls. Because these tables incur exponential storage costs in the number of operands and the precision of the input values, we use quantization to reduce these storage costs to make this approach practical. This enables an online phase where securely computing the result of a nonlinear function requires just a single round of communication, with communication cost equal to twice the number of bits of the input to the nonlinear function. In practice our approach costs 2 bytes of communication per nonlinear function call in the online phase. Compared to garbled circuits with 8-bit quantized inputs, when computing individual nonlinear functions during the online phase, experiments show Tabula with 8-bit activations uses between 280-560 × less communication, is over 100× faster, and uses a comparable (within a factor of 2) amount of storage; compared against other state-of-the-art protocols Tabula achieves greater than 40× communication reduction. This leads to significant performance gains over garbled circuits with quantized inputs during the online phase of secure inference of neural networks: Tabula reduces end-to-end inference communication by up to 9 × and achieves an end-to-end inference speedup of up to 50 ×, while imposing comparable storage and offline preprocessing costs.