# Towards Accurate Post-Training Quantization of Vision Transformers via Error Reduction

arXiv: https://arxiv.org/abs/2407.06794 · HTML: https://mlsanity.com/paper/2407.06794/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 75 references that are in the map.
- First posted on arXiv 9 Jul 2024.

## Builds on (most cited first, 30 of 48)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Rethinking Semantic Segmentation from a Sequence-to-Sequence Perspective with Transformers](https://mlsanity.com/paper/2012.15840/) (2020)
- [Cascade R-CNN: Delving into High Quality Object Detection](https://mlsanity.com/paper/1712.00726/) (2017)
- [Pre-Trained Image Processing Transformer](https://mlsanity.com/paper/2012.00364/) (2020)
- [MobileViT: Light-weight, General-purpose, and Mobile-friendly Vision Transformer](https://mlsanity.com/paper/2110.02178/) (2021)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning](https://mlsanity.com/paper/2208.11580/) (2022)
- [Post-Training Quantization for Vision Transformer](https://mlsanity.com/paper/2106.14156/) (2021)
- [Transformers in Medical Imaging: A Survey](https://mlsanity.com/paper/2201.09873/) (2022)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [TinyViT: Fast Pretraining Distillation for Small Vision Transformers](https://mlsanity.com/paper/2207.10666/) (2022)
- [QDrop: Randomly Dropping Quantization for Extremely Low-bit Post-Training Quantization](https://mlsanity.com/paper/2203.05740/) (2022)
- [PTQ4ViT: Post-training quantization for vision transformers with twin uniform quantization](https://mlsanity.com/paper/2111.12293/) (2021)
- [DuQuant: Distributing Outliers via Dual Transformation Makes Stronger Quantized LLMs](https://mlsanity.com/paper/2406.01721/) (2024)
- [FQ-ViT: Post-Training Quantization for Fully Quantized Vision Transformer](https://mlsanity.com/paper/2111.13824/) (2021)
- [Additive Powers-of-Two Quantization: An Efficient Non-uniform Discretization for Neural Networks](https://mlsanity.com/paper/1909.13144/) (2019)
- [RepQ-ViT: Scale Reparameterization for Post-Training Quantization of Vision Transformers](https://mlsanity.com/paper/2212.08254/) (2022)
- [RPTQ: Reorder-based Post-training Quantization for Large Language Models](https://mlsanity.com/paper/2304.01089/) (2023)

## Built on by (most cited first, 23 of 23)

- [Flow caching for autoregressive video generation](https://mlsanity.com/paper/2602.10825/) (2026)
- [DopQ-ViT: Towards Distribution-Friendly and Outlier-Aware Post-Training Quantization for Vision Transformers](https://mlsanity.com/paper/2408.03291/) (2024)
- [Low-Bit Quantization Favors Undertrained LLMs: Scaling Laws for Quantized LLMs with 100T Training Tokens](https://mlsanity.com/paper/2411.17691/) (2024)
- [Motion-Aware Caching for Efficient Autoregressive Video Generation](https://mlsanity.com/paper/2605.01725/) (2026)
- [Mixed Non-linear Quantization for Vision Transformers](https://mlsanity.com/paper/2407.18437/) (2024)
- [AHCQ-SAM: Toward Accurate and Hardware-Compatible Post-Training Segment Anything Model Quantization](https://mlsanity.com/paper/2503.03088/) (2025)
- [MixA-Q: Revisiting Activation Sparsity for Vision Transformers from a Mixed-Precision Quantization Perspective](https://mlsanity.com/paper/2507.19131/) (2025)
- [Activation Quantization of Vision Encoders Needs Prefixing Registers](https://mlsanity.com/paper/2510.04547/) (2025)
- [MLoRQ: Bridging Low-Rank and Quantization for Transformer Compression](https://mlsanity.com/paper/2507.09616/) (2025)
- [I-Segmenter: Integer-Only Vision Transformer for Efficient Semantic Segmentation](https://mlsanity.com/paper/2509.10334/) (2025)
- [S2D: Selective Spectral Decay for Quantization-Friendly Conditioning of Neural Activations](https://mlsanity.com/paper/2602.14432/) (2026)
- [Colinearity Decay: Training Quantization-Friendly ViTs with Outlier Decay](https://mlsanity.com/paper/2605.01330/) (2026)
- [Nonlinear Bipolar Compensation: Handling Outliers in Post-Training Quantization](https://mlsanity.com/paper/2605.16423/) (2026)
- [Shift-and-Sum Quantization for Visual Autoregressive Models](https://mlsanity.com/paper/2606.16131/) (2026)
- [NuWa: Deriving Lightweight Class-Specific Vision Transformers for Edge Devices](https://mlsanity.com/paper/2504.03118/) (2025)
- [Cat: Post-Training Quantization Error Reduction via Cluster-based Affine Transformation](https://mlsanity.com/paper/2509.26277/) (2025)
- [Binary Quadratic Quantization: Beyond First-Order Quantization for Real-Valued Matrix Compression](https://mlsanity.com/paper/2510.18650/) (2025)
- [D4C: Data-Free Quantization for Contrastive Language-Image Pre-training Models](https://mlsanity.com/paper/2511.15411/) (2025)
- [Amortized-Precision Quantization for Early-Exit Vision Transformers](https://mlsanity.com/paper/2605.07317/) (2026)
- [ALGOGEN: Tool-Generated Verifiable Traces for Reliable Algorithm Visualization](https://mlsanity.com/paper/2605.12159/) (2026)
- [MARR: Module-Adaptive Residual Reconstruction for Low-Bit Post-Training Quantization](https://mlsanity.com/paper/2605.17997/) (2026)
- [Jacobian-guided Noise Injection for Quantization Robustness in Large Language Models](https://mlsanity.com/paper/2608.20988/) (2026)
- [STEPQuant: When and Where Errors Matter in Delta-Rule Recurrent State Quantization](https://mlsanity.com/paper/2609.38169/) (2026)

## Abstract (arXiv)

Post-training quantization (PTQ) for vision transformers (ViTs) has received increasing attention from both academic and industrial communities due to its minimal data needs and high time efficiency. However, many current methods fail to account for the complex interactions between quantized weights and activations, resulting in significant quantization errors and suboptimal performance. This paper presents ERQ, an innovative two-step PTQ method specifically crafted to reduce quantization errors arising from activation and weight quantization sequentially. The first step, Activation quantization error reduction (Aqer), first applies Reparameterization Initialization aimed at mitigating initial quantization errors in high-variance activations. Then, it further mitigates the errors by formulating a Ridge Regression problem, which updates the weights maintained at full-precision using a closed-form solution. The second step, Weight quantization error reduction (Wqer), first applies Dual Uniform Quantization to handle weights with numerous outliers, which arise from adjustments made during Reparameterization Initialization, thereby reducing initial weight quantization errors. Then, it employs an iterative approach to further tackle the errors. In each iteration, it adopts Rounding Refinement that uses an empirically derived, efficient proxy to refine the rounding directions of quantized weights, complemented by a Ridge Regression solver to reduce the errors. Comprehensive experimental results demonstrate ERQ's superior performance across various ViTs variants and tasks. For example, ERQ surpasses the state-of-the-art GPTQ by a notable 36.81% in accuracy for W3A4 ViT-S. Our codes are available at https://github.com/zysxmu/ERQ.