# FQ-ViT: Post-Training Quantization for Fully Quantized Vision Transformer

arXiv: https://arxiv.org/abs/2111.13824 · HTML: https://mlsanity.com/paper/2111.13824/

## Key facts

- Cited by 151 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 28 references that are in the map.
- First posted on arXiv 27 Nov 2021.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Rethinking Semantic Segmentation from a Sequence-to-Sequence Perspective with Transformers](https://mlsanity.com/paper/2012.15840/) (2020)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (2019)
- [DynamicViT: Efficient Vision Transformers with Dynamic Token Sparsification](https://mlsanity.com/paper/2106.02034/) (2021)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [LeViT: a Vision Transformer in ConvNet's Clothing for Faster Inference](https://mlsanity.com/paper/2104.01136/) (2021)
- [Q-BERT: Hessian Based Ultra Low Precision Quantization of BERT](https://mlsanity.com/paper/1909.05840/) (2019)
- [Post-Training Quantization for Vision Transformer](https://mlsanity.com/paper/2106.14156/) (2021)
- [I-BERT: Integer-only BERT Quantization](https://mlsanity.com/paper/2101.01321/) (2021)
- [Low-bit Quantization of Neural Networks for Efficient Inference](https://mlsanity.com/paper/1902.06822/) (2019)
- [Evo-ViT: Slow-Fast Token Evolution for Dynamic Vision Transformer](https://mlsanity.com/paper/2108.01390/) (2021)

## Built on by (most cited first, 30 of 151)

- [PTQD: Accurate Post-Training Quantization for Diffusion Models](https://mlsanity.com/paper/2305.10657/) (2023)
- [RepQ-ViT: Scale Reparameterization for Post-Training Quantization of Vision Transformers](https://mlsanity.com/paper/2212.08254/) (2022)
- [ViDiT-Q: Efficient and Accurate Quantization of Diffusion Transformers for Image and Video Generation](https://mlsanity.com/paper/2406.02540/) (2024)
- [I-ViT: Integer-only Quantization for Efficient Vision Transformer Inference](https://mlsanity.com/paper/2207.01405/) (2022)
- [EfficientDM: Efficient Quantization-Aware Fine-Tuning of Low-Bit Diffusion Models](https://mlsanity.com/paper/2310.03270/) (2023)
- [A Theoretical Understanding of Shallow Vision Transformers: Learning, Generalization, and Sample Complexity](https://mlsanity.com/paper/2302.06015/) (2023)
- [TFMQ-DM: Temporal Feature Maintenance Quantization for Diffusion Models](https://mlsanity.com/paper/2311.16503/) (2023)
- [NoisyQuant: Noisy Bias-Enhanced Post-Training Activation Quantization for Vision Transformers](https://mlsanity.com/paper/2211.16056/) (2022)
- [Which Tokens to Use? Investigating Token Reduction in Vision Transformers](https://mlsanity.com/paper/2308.04657/) (2023)
- [A Survey on Transformer Compression](https://mlsanity.com/paper/2402.05964/) (2024)
- [PSAQ-ViT V2: Towards Accurate and General Data-Free Quantization for Vision Transformers](https://mlsanity.com/paper/2209.05687/) (2022)
- [A Survey of Techniques for Optimizing Transformer Inference](https://mlsanity.com/paper/2307.07982/) (2023)
- [Agile-Quant: Activation-Guided Quantization for Faster Inference of LLMs on the Edge](https://mlsanity.com/paper/2312.05693/) (2023)
- [PTQ4SAM: Post-Training Quantization for Segment Anything](https://mlsanity.com/paper/2405.03144/) (2024)
- [AdaLog: Post-Training Quantization for Vision Transformers with Adaptive Logarithm Quantizer](https://mlsanity.com/paper/2407.12951/) (2024)
- [MambaQuant: Quantizing the Mamba Family with Variance Aligned Rotation Methods](https://mlsanity.com/paper/2501.13484/) (2025)
- [BiViT: Extremely Compressed Binary Vision Transformer](https://mlsanity.com/paper/2211.07091/) (2022)
- [Stitchable Neural Networks](https://mlsanity.com/paper/2302.06586/) (2023)
- [Quantization without Tears](https://mlsanity.com/paper/2411.13918/) (2024)
- [Q-DETR: An Efficient Low-Bit Quantized Detection Transformer](https://mlsanity.com/paper/2304.00253/) (2023)
- [Vision Transformers on the Edge: A Comprehensive Survey of Model Compression and Acceleration Strategies](https://mlsanity.com/paper/2503.02891/) (2025)
- [I-LLM: Efficient Integer-Only Inference for Fully-Quantized Low-Bit Large Language Models](https://mlsanity.com/paper/2405.17849/) (2024)
- [Towards Accurate Post-Training Quantization of Vision Transformers via Error Reduction](https://mlsanity.com/paper/2407.06794/) (2024)
- [Boost Vision Transformer with GPU-Friendly Sparsity and Quantization](https://mlsanity.com/paper/2305.10727/) (2023)
- [I&S-ViT: An Inclusive & Stable Method for Pushing the Limit of Post-Training ViTs Quantization](https://mlsanity.com/paper/2311.10126/) (2023)
- [DopQ-ViT: Towards Distribution-Friendly and Outlier-Aware Post-Training Quantization for Vision Transformers](https://mlsanity.com/paper/2408.03291/) (2024)
- [APHQ-ViT: Post-Training Quantization with Average Perturbation Hessian Based Reconstruction for Vision Transformers](https://mlsanity.com/paper/2504.02508/) (2025)
- [A Survey on Efficient Vision-Language Models](https://mlsanity.com/paper/2504.09724/) (2025)
- [FIMA-Q: Post-Training Quantization for Vision Transformers by Fisher Information Matrix Approximation](https://mlsanity.com/paper/2506.11543/) (2025)
- [Jumping through Local Minima: Quantization in the Loss Landscape of Vision Transformers](https://mlsanity.com/paper/2308.10814/) (2023)

## Abstract (arXiv)

Network quantization significantly reduces model inference complexity and has been widely used in real-world deployments. However, most existing quantization methods have been developed mainly on Convolutional Neural Networks (CNNs), and suffer severe degradation when applied to fully quantized vision transformers. In this work, we demonstrate that many of these difficulties arise because of serious inter-channel variation in LayerNorm inputs, and present, Power-of-Two Factor (PTF), a systematic method to reduce the performance degradation and inference complexity of fully quantized vision transformers. In addition, observing an extreme non-uniform distribution in attention maps, we propose Log-Int-Softmax (LIS) to sustain that and simplify inference by using 4-bit quantization and the BitShift operator. Comprehensive experiments on various transformer-based architectures and benchmarks show that our Fully Quantized Vision Transformer (FQ-ViT) outperforms previous works while even using lower bit-width on attention maps. For instance, we reach 84.89% top-1 accuracy with ViT-L on ImageNet and 50.8 mAP with Cascade Mask R-CNN (Swin-S) on COCO. To our knowledge, we are the first to achieve lossless accuracy degradation (~1%) on fully quantized vision transformers. The code is available at https://github.com/megvii-research/FQ-ViT.