# CondiQuant: Condition Number Based Low-Bit Quantization for Image Super-Resolution

arXiv: https://arxiv.org/abs/2502.15478 · HTML: https://mlsanity.com/paper/2502.15478/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 38 references that are in the map.
- First posted on arXiv 21 Feb 2025.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [Sketch-based Manga Retrieval using Manga109 Dataset](https://mlsanity.com/paper/1510.04389/) (2015)
- [One-Step Effective Diffusion Network for Real-World Image Super-Resolution](https://mlsanity.com/paper/2406.08177/) (2024)
- [Low-bit Quantization of Neural Networks for Efficient Inference](https://mlsanity.com/paper/1902.06822/) (2019)
- [Dynamical Isometry and a Mean Field Theory of CNNs: How to Train 10,000-Layer Vanilla Convolutional Neural Networks](https://mlsanity.com/paper/1806.05393/) (2018)
- [RepQ-ViT: Scale Reparameterization for Post-Training Quantization of Vision Transformers](https://mlsanity.com/paper/2212.08254/) (2022)
- [Dual Aggregation Transformer for Image Super-Resolution](https://mlsanity.com/paper/2308.03364/) (2023)
- [Cross Aggregation Transformer for Image Restoration](https://mlsanity.com/paper/2211.13654/) (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)
- [Simultaneous Super-Resolution and Cross-Modality Synthesis of 3D Medical Images using Weakly-Supervised Joint Convolutional Sparse Coding](https://mlsanity.com/paper/1705.02596/) (2017)
- [MagR: Weight Magnitude Reduction for Enhancing Post-Training Quantization](https://mlsanity.com/paper/2406.00800/) (2024)
- [2DQuant: Low-bit Post-Training Quantization for Image Super-Resolution](https://mlsanity.com/paper/2406.06649/) (2024)
- [Condition Number Analysis of Logistic Regression, and its Implications for Standard First-Order Solution Methods](https://mlsanity.com/paper/1810.08727/) (2018)

## Built on by (most cited first, 4 of 4)

- [PMQ-VE: Progressive Multi-Frame Quantization for Video Enhancement](https://mlsanity.com/paper/2505.12266/) (2025)
- [InfVSR: Toward Consistency-Driven Streaming Generative Video Super-Resolution](https://mlsanity.com/paper/2510.00948/) (2025)
- [AHCQ-SAM: Toward Accurate and Hardware-Compatible Post-Training Segment Anything Model Quantization](https://mlsanity.com/paper/2503.03088/) (2025)
- [Any Orthogonal Transform Will Do: Range Reduction Explains Rotation-Based Quantization for Super-Resolution](https://mlsanity.com/paper/2601.21069/) (2026)

## Abstract (arXiv)

Low-bit model quantization for image super-resolution (SR) is a longstanding task that is renowned for its surprising compression and acceleration ability. However, accuracy degradation is inevitable when compressing the full-precision (FP) model to ultra-low bit widths (2~4 bits). Experimentally, we observe that the degradation of quantization is mainly attributed to the quantization of activation instead of model weights. In numerical analysis, the condition number of weights could measure how much the output value can change for a small change in the input argument, inherently reflecting the quantization error. Therefore, we propose CondiQuant, a condition number based low-bit post-training quantization for image super-resolution. Specifically, we formulate the quantization error as the condition number of weight metrics. By decoupling the representation ability and the quantization sensitivity, we design an efficient proximal gradient descent algorithm to iteratively minimize the condition number and maintain the output still. With comprehensive experiments, we demonstrate that CondiQuant outperforms existing state-of-the-art post-training quantization methods in accuracy without computation overhead and gains the theoretically optimal compression ratio in model parameters. Our code and model are released at https://github.com/Kai-Liu001/CondiQuant.