# Cat: Post-Training Quantization Error Reduction via Cluster-based Affine Transformation

arXiv: https://arxiv.org/abs/2509.26277 · HTML: https://mlsanity.com/paper/2509.26277/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 40 of its 55 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Builds on (most cited first, 30 of 40)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [SAM 2: Segment Anything in Images and Videos](https://mlsanity.com/paper/2408.00714/) (2024)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [MnasNet: Platform-Aware Neural Architecture Search for Mobile](https://mlsanity.com/paper/1807.11626/) (2018)
- [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)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Q8BERT: Quantized 8Bit BERT](https://mlsanity.com/paper/1910.06188/) (2019)
- [LQ-Nets: Learned Quantization for Highly Accurate and Compact Deep Neural Networks](https://mlsanity.com/paper/1807.10029/) (2018)
- [ZeroQ: A Novel Zero Shot Quantization Framework](https://mlsanity.com/paper/2001.00281/) (2020)
- [LoftQ: LoRA-Fine-Tuning-Aware Quantization for Large Language Models](https://mlsanity.com/paper/2310.08659/) (2023)
- [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)
- [RepQ-ViT: Scale Reparameterization for Post-Training Quantization of Vision Transformers](https://mlsanity.com/paper/2212.08254/) (2022)
- [EfficientQAT: Efficient Quantization-Aware Training for Large Language Models](https://mlsanity.com/paper/2407.11062/) (2024)
- [Loss Aware Post-training Quantization](https://mlsanity.com/paper/1911.07190/) (2019)
- [Degree-Quant: Quantization-Aware Training for Graph Neural Networks](https://mlsanity.com/paper/2008.05000/) (2020)
- [Q-DiT: Accurate Post-Training Quantization for Diffusion Transformers](https://mlsanity.com/paper/2406.17343/) (2024)
- [EfficientDM: Efficient Quantization-Aware Fine-Tuning of Low-Bit Diffusion Models](https://mlsanity.com/paper/2310.03270/) (2023)
- [PD-Quant: Post-Training Quantization based on Prediction Difference Metric](https://mlsanity.com/paper/2212.07048/) (2022)
- [Towards Accurate Post-Training Quantization for Vision Transformer](https://mlsanity.com/paper/2303.14341/) (2023)
- [AffineQuant: Affine Transformation Quantization for Large Language Models](https://mlsanity.com/paper/2403.12544/) (2024)
- [QKD: Quantization-aware Knowledge Distillation](https://mlsanity.com/paper/1911.12491/) (2019)
- [Boosting Vision-Language Models with Transduction](https://mlsanity.com/paper/2406.01837/) (2024)
- [ResQ: Mixed-Precision Quantization of Large Language Models with Low-Rank Residuals](https://mlsanity.com/paper/2412.14363/) (2024)

## Abstract (arXiv)

Post-Training Quantization (PTQ) reduces the memory footprint and computational overhead of deep neural networks by converting full-precision (FP) values into quantized and compressed data types. While PTQ is more cost-efficient than Quantization-Aware Training (QAT), it is highly susceptible to accuracy degradation under a low-bit quantization (LQ) regime (e.g., 2-bit). Affine transformation is a classical technique used to reduce the discrepancy between the information processed by a quantized model and that processed by its full-precision counterpart; however, we find that using plain affine transformation, which applies a uniform affine parameter set for all outputs, worsens the results in low-bit PTQ. To address this, we propose Cluster-based Affine Transformation (CAT), an error-reduction framework that employs cluster-specific parameters to align LQ outputs with FP counterparts. CAT refines LQ outputs with only a negligible number of additional parameters, without requiring fine-tuning of the model or quantization parameters. We further introduce a novel PTQ framework integrated with CAT. Experiments on ImageNet-1K show that this framework consistently outperforms prior PTQ methods across diverse architectures and LQ settings, achieving up to 53.18% Top-1 accuracy on W2A2 ResNet-18. Moreover, CAT enhances existing PTQ baselines by more than 3% when used as a plug-in. We plan to release our implementation alongside the publication of this paper.