# Inhibitor Transformers and Gated RNNs for Torus Efficient Fully Homomorphic Encryption

arXiv: https://arxiv.org/abs/2308.05629 · HTML: https://mlsanity.com/paper/2308.05629/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 74 references that are in the map.
- First posted on arXiv 10 Aug 2023.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [Fastformer: Additive Attention Can Be All You Need](https://mlsanity.com/paper/2108.09084/) (2021)
- [A Study on ReLU and Softmax in Transformer](https://mlsanity.com/paper/2302.06461/) (2023)
- [SHE: A Fast and Accurate Deep Neural Network for Encrypted Data](https://mlsanity.com/paper/1906.00148/) (2019)
- [Deep Neural Networks for Encrypted Inference with TFHE](https://mlsanity.com/paper/2302.10906/) (2023)
- [Privacy-Preserving Tree-Based Inference with TFHE](https://mlsanity.com/paper/2303.01254/) (2023)

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

- [The Inhibitor: ReLU and Addition-Based Attention for Efficient Transformers under Fully Homomorphic Encryption on the Torus](https://mlsanity.com/paper/2310.02041/) (2023)
- [Public-Decay Homomorphic State Space Models for Private Sequence Inference](https://mlsanity.com/paper/2605.16647/) (2026)

## Abstract (arXiv)

This paper introduces efficient modifications to neural network-based sequence processing approaches, laying new grounds for scalable privacy-preserving machine learning under Fully Homomorphic Encryption (FHE). Transformers are now ubiquitous in AI applications and have largely supplanted Gated Recurrent Neural Networks (RNNs) as the standard architecture for sequence modeling. Both architectures rely on costly multiplications and complex activations that hinder encrypted inference. We focus on TFHE, which supports deep circuit evaluation and efficient univariate function evaluation but makes variable-to-variable multiplication particularly expensive. To address this, we propose inhibitor designs for Transformers and gated RNNs that replace multiplications and Softmax/Sigmoid activations with additive and ReLU-based operations. These changes enable integer-only computation, reduce circuit depth, and improve the efficiency of encrypted execution while preserving learning capacity. We present complexity analyses and scaling experiments that indicate significant reductions in circuit depth and execution time under TFHE, with 3-6 times speedup for encrypted inference and 30-50% reductions in plaintext inference time. Empirical evaluations on MNIST, IMDB, and IAM handwriting show inhibitor-based models maintain competitive accuracy. Knowledge distillation further demonstrates that an inhibitor-based DistilBERT achieves performance close to that of the conventional attention model on GLUE, positioning these architectures as a viable approach for scalable, privacy-preserving AI.