# Fine-grained Data Distribution Alignment for Post-Training Quantization

arXiv: https://arxiv.org/abs/2109.04186 · HTML: https://mlsanity.com/paper/2109.04186/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 41 references that are in the map.
- First posted on arXiv 9 Sep 2021.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [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)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [Dreaming to Distill: Data-free Knowledge Transfer via DeepInversion](https://mlsanity.com/paper/1912.08795/) (2019)
- [ZeroQ: A Novel Zero Shot Quantization Framework](https://mlsanity.com/paper/2001.00281/) (2020)
- [Data-Free Learning of Student Networks](https://mlsanity.com/paper/1904.01186/) (2019)
- [Loss Aware Post-training Quantization](https://mlsanity.com/paper/1911.07190/) (2019)
- [Improving Post Training Neural Quantization: Layer-wise Calibration and Integer Programming](https://mlsanity.com/paper/2006.10518/) (2020)
- [Generative Low-bitwidth Data Free Quantization](https://mlsanity.com/paper/2003.03603/) (2020)
- [Post-Training Piecewise Linear Quantization for Deep Neural Networks](https://mlsanity.com/paper/2002.00104/) (2020)
- [Rotated Binary Neural Network](https://mlsanity.com/paper/2009.13055/) (2020)
- [Diversifying Sample Generation for Accurate Data-Free Quantization](https://mlsanity.com/paper/2103.01049/) (2021)
- [The Knowledge Within: Methods for Data-Free Model Compression](https://mlsanity.com/paper/1912.01274/) (2019)
- [Zero-shot Adversarial Quantization](https://mlsanity.com/paper/2103.15263/) (2021)
- [MixMix: All You Need for Data-Free Compression Are Feature and Data Mixing](https://mlsanity.com/paper/2011.09899/) (2020)
- [Permute, Quantize, and Fine-tune: Efficient Compression of Neural Networks](https://mlsanity.com/paper/2010.15703/) (2020)
- [Post-training Quantization with Multiple Points: Mixed Precision without Mixed Precision](https://mlsanity.com/paper/2002.09049/) (2020)

## Built on by (most cited first, 9 of 9)

- [Data-Free Knowledge Transfer: A Survey](https://mlsanity.com/paper/2112.15278/) (2021)
- [I&S-ViT: An Inclusive & Stable Method for Pushing the Limit of Post-Training ViTs Quantization](https://mlsanity.com/paper/2311.10126/) (2023)
- [Bi-ViT: Pushing the Limit of Vision Transformer Quantization](https://mlsanity.com/paper/2305.12354/) (2023)
- [Low-bit Model Quantization for Deep Neural Networks: A Survey](https://mlsanity.com/paper/2505.05530/) (2025)
- [Parameter and Computation Efficient Transfer Learning for Vision-Language Pre-trained Models](https://mlsanity.com/paper/2309.01479/) (2023)
- [Towards Feature Distribution Alignment and Diversity Enhancement for Data-Free Quantization](https://mlsanity.com/paper/2205.00179/) (2022)
- [Data Generation for Hardware-Friendly Post-Training Quantization](https://mlsanity.com/paper/2410.22110/) (2024)
- [Attention Round for Post-Training Quantization](https://mlsanity.com/paper/2207.03088/) (2022)
- [SynQ: Accurate Zero-shot Quantization by Synthesis-aware Fine-tuning](https://mlsanity.com/paper/2603.18423/) (2026)

## Abstract (arXiv)

While post-training quantization receives popularity mostly due to its evasion in accessing the original complete training dataset, its poor performance also stems from scarce images. To alleviate this limitation, in this paper, we leverage the synthetic data introduced by zero-shot quantization with calibration dataset and propose a fine-grained data distribution alignment (FDDA) method to boost the performance of post-training quantization. The method is based on two important properties of batch normalization statistics (BNS) we observed in deep layers of the trained network, (i.e.), inter-class separation and intra-class incohesion. To preserve this fine-grained distribution information: 1) We calculate the per-class BNS of the calibration dataset as the BNS centers of each class and propose a BNS-centralized loss to force the synthetic data distributions of different classes to be close to their own centers. 2) We add Gaussian noise into the centers to imitate the incohesion and propose a BNS-distorted loss to force the synthetic data distribution of the same class to be close to the distorted centers. By utilizing these two fine-grained losses, our method manifests the state-of-the-art performance on ImageNet, especially when both the first and last layers are quantized to the low-bit. Code is at urlhttps://github.com/zysxmu/FDDA.