# DAQ: Channel-Wise Distribution-Aware Quantization for Deep Image Super-Resolution Networks

arXiv: https://arxiv.org/abs/2012.11230 · HTML: https://mlsanity.com/paper/2012.11230/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2020.

## Built on by (most cited first, 30 of 31)

- [CADyQ: Content-Aware Dynamic Quantization for Image Super-Resolution](https://mlsanity.com/paper/2207.10345/) (2022)
- [Dynamic Dual Trainable Bounds for Ultra-low Precision Super-Resolution Networks](https://mlsanity.com/paper/2203.03844/) (2022)
- [PMQ-VE: Progressive Multi-Frame Quantization for Video Enhancement](https://mlsanity.com/paper/2505.12266/) (2025)
- [CABM: Content-Aware Bit Mapping for Single Image Super-Resolution Network with Large Input](https://mlsanity.com/paper/2304.06454/) (2023)
- [2DQuant: Low-bit Post-Training Quantization for Image Super-Resolution](https://mlsanity.com/paper/2406.06649/) (2024)
- [Low-bit Model Quantization for Deep Neural Networks: A Survey](https://mlsanity.com/paper/2505.05530/) (2025)
- [Rate-Distortion Optimized Post-Training Quantization for Learned Image Compression](https://mlsanity.com/paper/2211.02854/) (2022)
- [Exploring Frequency-Inspired Optimization in Transformer for Efficient Single Image Super-Resolution](https://mlsanity.com/paper/2308.05022/) (2023)
- [AdaBM: On-the-Fly Adaptive Bit Mapping for Image Super-Resolution](https://mlsanity.com/paper/2404.03296/) (2024)
- [RefQSR: Reference-based Quantization for Image Super-Resolution Networks](https://mlsanity.com/paper/2404.01690/) (2024)
- [Activations and Gradients Compression for Model-Parallel Training](https://mlsanity.com/paper/2401.07788/) (2024)
- [Coresets for Data Discretization and Sine Wave Fitting](https://mlsanity.com/paper/2203.03009/) (2022)
- [Reciprocal Attention Mixing Transformer for Lightweight Image Restoration](https://mlsanity.com/paper/2305.11474/) (2023)
- [Overcoming Distribution Mismatch in Quantizing Image Super-Resolution Networks](https://mlsanity.com/paper/2307.13337/) (2023)
- [Thinking in Granularity: Dynamic Quantization for Image Super-Resolution by Intriguing Multi-Granularity Clues](https://mlsanity.com/paper/2409.14330/) (2024)
- [Q-MambaIR: Accurate Quantized Mamba for Efficient Image Restoration](https://mlsanity.com/paper/2503.21970/) (2025)
- [SCALES: Boost Binary Neural Network for Image Super-Resolution with Efficient Scalings](https://mlsanity.com/paper/2303.12270/) (2023)
- [Data Upcycling Knowledge Distillation for Image Super-Resolution](https://mlsanity.com/paper/2309.14162/) (2023)
- [Outlier-Aware Post-Training Quantization for Image Super-Resolution](https://mlsanity.com/paper/2511.00682/) (2025)
- [E2FIF: Push the limit of Binarized Deep Imagery Super-resolution using End-to-end Full-precision Information Flow](https://mlsanity.com/paper/2207.06893/) (2022)
- [Exploration of Lightweight Single Image Denoising with Transformers and Truly Fair Training](https://mlsanity.com/paper/2304.01805/) (2023)
- [Distribution-Flexible Subset Quantization for Post-Quantizing Super-Resolution Networks](https://mlsanity.com/paper/2305.05888/) (2023)
- [Onboard Optimization and Learning: A Survey](https://mlsanity.com/paper/2505.08793/) (2025)
- [Deep Learning Empowered Super-Resolution: A Comprehensive Survey and Future Prospects](https://mlsanity.com/paper/2509.22692/) (2025)
- [Decoder-Free Distillation for Quantized Image Restoration](https://mlsanity.com/paper/2603.09624/) (2026)
- [A Scale-Arbitrary Image Super-Resolution Network Using Frequency-domain Information](https://mlsanity.com/paper/2212.04314/) (2022)
- [Data Overfitting for On-Device Super-Resolution with Dynamic Algorithm and Compiler Co-Design](https://mlsanity.com/paper/2407.02813/) (2024)
- [HarmoQ: Harmonized Post-Training Quantization for High-Fidelity Image](https://mlsanity.com/paper/2511.05868/) (2025)
- [Any Orthogonal Transform Will Do: Range Reduction Explains Rotation-Based Quantization for Super-Resolution](https://mlsanity.com/paper/2601.21069/) (2026)
- [QuantSR+: Pushing the Limit of Quantized Image Super-Resolution Networks](https://mlsanity.com/paper/2605.22351/) (2026)

## Abstract (arXiv)

Quantizing deep convolutional neural networks for image super-resolution substantially reduces their computational costs. However, existing works either suffer from a severe performance drop in ultra-low precision of 4 or lower bit-widths, or require a heavy fine-tuning process to recover the performance. To our knowledge, this vulnerability to low precisions relies on two statistical observations of feature map values. First, distribution of feature map values varies significantly per channel and per input image. Second, feature maps have outliers that can dominate the quantization error. Based on these observations, we propose a novel distribution-aware quantization scheme (DAQ) which facilitates accurate training-free quantization in ultra-low precision. A simple function of DAQ determines dynamic range of feature maps and weights with low computational burden. Furthermore, our method enables mixed-precision quantization by calculating the relative sensitivity of each channel, without any training process involved. Nonetheless, quantization-aware training is also applicable for auxiliary performance gain. Our new method outperforms recent training-free and even training-based quantization methods to the state-of-the-art image super-resolution networks in ultra-low precision.