# FIMA-Q: Post-Training Quantization for Vision Transformers by Fisher Information Matrix Approximation

arXiv: https://arxiv.org/abs/2506.11543 · HTML: https://mlsanity.com/paper/2506.11543/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 38 references that are in the map.
- First posted on arXiv 13 Jun 2025.

## Builds on (most cited first, 30 of 31)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [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)
- [MMDetection: Open MMLab Detection Toolbox and Benchmark](https://mlsanity.com/paper/1906.07155/) (2019)
- [Cascade R-CNN: Delving into High Quality Object Detection](https://mlsanity.com/paper/1712.00726/) (2017)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [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)
- [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)
- [FQ-ViT: Post-Training Quantization for Fully Quantized Vision Transformer](https://mlsanity.com/paper/2111.13824/) (2021)
- [Understanding and Overcoming the Challenges of Efficient Transformer Quantization](https://mlsanity.com/paper/2109.12948/) (2021)
- [RepQ-ViT: Scale Reparameterization for Post-Training Quantization of Vision Transformers](https://mlsanity.com/paper/2212.08254/) (2022)
- [Q-ViT: Accurate and Fully Quantized Low-bit Vision Transformer](https://mlsanity.com/paper/2210.06707/) (2022)
- [I-ViT: Integer-only Quantization for Efficient Vision Transformer Inference](https://mlsanity.com/paper/2207.01405/) (2022)
- [Towards Accurate Post-Training Quantization for Vision Transformer](https://mlsanity.com/paper/2303.14341/) (2023)
- [NoisyQuant: Noisy Bias-Enhanced Post-Training Activation Quantization for Vision Transformers](https://mlsanity.com/paper/2211.16056/) (2022)
- [OcTr: Octree-based Transformer for 3D Object Detection](https://mlsanity.com/paper/2303.12621/) (2023)
- [AdaLog: Post-Training Quantization for Vision Transformers with Adaptive Logarithm Quantizer](https://mlsanity.com/paper/2407.12951/) (2024)
- [Instance-Aware Group Quantization for Vision Transformers](https://mlsanity.com/paper/2404.00928/) (2024)
- [I&S-ViT: An Inclusive & Stable Method for Pushing the Limit of Post-Training ViTs Quantization](https://mlsanity.com/paper/2311.10126/) (2023)

## Built on by (most cited first, 19 of 19)

- [SGMD: Score Gradient Matching Distillation for Few-Step Video Diffusion Distillation](https://mlsanity.com/paper/2605.30116/) (2026)
- [TreeQ: Pushing the Quantization Boundary of Diffusion Transformer via Tree-Structured Mixed-Precision Search](https://mlsanity.com/paper/2512.06353/) (2025)
- [Activation Quantization of Vision Encoders Needs Prefixing Registers](https://mlsanity.com/paper/2510.04547/) (2025)
- [I-Segmenter: Integer-Only Vision Transformer for Efficient Semantic Segmentation](https://mlsanity.com/paper/2509.10334/) (2025)
- [Joint Post-Training Quantization of Vision Transformers with Learned Prompt-Guided Data Generation](https://mlsanity.com/paper/2602.18861/) (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)
- [Revisiting Adaptive Rounding with Vectorized Reparameterization for LLM Quantization](https://mlsanity.com/paper/2602.02151/) (2026)
- [When W4A4 Breaks Camouflaged Object Detection: Token-Group Dual-Constraint Activation Quantization](https://mlsanity.com/paper/2604.16855/) (2026)
- [MARR: Module-Adaptive Residual Reconstruction for Low-Bit Post-Training Quantization](https://mlsanity.com/paper/2605.17997/) (2026)
- [ScalePredictor: Instance-aware Scale Learning for Accurate Quantization of Vision Transformers](https://mlsanity.com/paper/2606.21947/) (2026)
- [MixFrag: Fragility-Guided Mixed-Precision Post-Training Quantization for Vision Transformers](https://mlsanity.com/paper/2607.28589/) (2026)
- [QuaSAR: Quantization Compensation via Stable Activation-Aware Rank Truncation](https://mlsanity.com/paper/2608.14149/) (2026)
- [SandwichQuant: Which Parameters Matter Before and After Quantization?](https://mlsanity.com/paper/2608.24173/) (2026)
- [Channel-Wise and Token-Aware Post-Training Quantization for Visual State Space Duality](https://mlsanity.com/paper/2609.16656/) (2026)
- [GLF-Q: Global-Local Feature-based Quantization for Vision Transformers](https://mlsanity.com/paper/2609.34564/) (2026)
- [VisionMX: Unlocking Microscaling Post-Training Quantization for Vision Models](https://mlsanity.com/paper/2610.03218/) (2026)
- [RPFQ-ViT: Rotated Phase-Frame Quantization for Extremely Low-Bit Weights in Vision Transformers](https://mlsanity.com/paper/2610.04457/) (2026)
- [Hardware-Friendly Token-Group Activation Quantization for Low-Bit Mamba Super-Resolution](https://mlsanity.com/paper/2610.16261/) (2026)

## Abstract (arXiv)

Post-training quantization (PTQ) has stood out as a cost-effective and promising model compression paradigm in recent years, as it avoids computationally intensive model retraining. Nevertheless, current PTQ methods for Vision Transformers (ViTs) still suffer from significant accuracy degradation, especially under low-bit quantization. To address these shortcomings, we analyze the prevailing Hessian-guided quantization loss, and uncover certain limitations of conventional Hessian approximations. By following the block-wise reconstruction framework, we propose a novel PTQ method for ViTs, dubbed FIMA-Q. Specifically, we firstly establish the connection between KL divergence and FIM, which enables fast computation of the quantization loss during reconstruction. We further propose an efficient FIM approximation method, namely DPLR-FIM, by employing the diagonal plus low-rank principle, and formulate the ultimate quantization loss. Our extensive experiments, conducted across various vision tasks with representative ViT-based architectures on public datasets, demonstrate that our method substantially promotes the accuracy compared to the state-of-the-art approaches, especially in the case of low-bit quantization. The source code is available at https://github.com/ShiheWang/FIMA-Q.