# Symmetry Regularization and Saturating Nonlinearity for Robust Quantization

arXiv: https://arxiv.org/abs/2208.00338 · HTML: https://mlsanity.com/paper/2208.00338/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 46 references that are in the map.
- First posted on arXiv 31 Jul 2022.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [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)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [Data-Free Quantization Through Weight Equalization and Bias Correction](https://mlsanity.com/paper/1906.04721/) (2019)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [ZeroQ: A Novel Zero Shot Quantization Framework](https://mlsanity.com/paper/2001.00281/) (2020)
- [HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks](https://mlsanity.com/paper/1911.03852/) (2019)
- [Integer Quantization for Deep Learning Inference: Principles and Empirical Evaluation](https://mlsanity.com/paper/2004.09602/) (2020)
- [QDrop: Randomly Dropping Quantization for Extremely Low-bit Post-Training Quantization](https://mlsanity.com/paper/2203.05740/) (2022)
- [Learning to Quantize Deep Networks by Optimizing Quantization Intervals with Task Loss](https://mlsanity.com/paper/1808.05779/) (2018)
- [Improving Neural Network Quantization without Retraining using Outlier Channel Splitting](https://mlsanity.com/paper/1901.09504/) (2019)
- [Robust Learning with Jacobian Regularization](https://mlsanity.com/paper/1908.02729/) (2019)
- [Bit Fusion: Bit-Level Dynamically Composable Architecture for Accelerating Deep Neural Networks](https://mlsanity.com/paper/1712.01507/) (2017)
- [Loss Aware Post-training Quantization](https://mlsanity.com/paper/1911.07190/) (2019)
- [Defensive Quantization: When Efficiency Meets Robustness](https://mlsanity.com/paper/1904.08444/) (2019)
- [Characterizing signal propagation to close the performance gap in unnormalized ResNets](https://mlsanity.com/paper/2101.08692/) (2021)
- [Robust Quantization: One Model to Rule Them All](https://mlsanity.com/paper/2002.07686/) (2020)
- [HAWQV3: Dyadic Neural Network Quantization](https://mlsanity.com/paper/2011.10680/) (2020)
- [Value-aware Quantization for Training and Inference of Neural Networks](https://mlsanity.com/paper/1804.07802/) (2018)
- [PROFIT: A Novel Training Method for sub-4-bit MobileNet Models](https://mlsanity.com/paper/2008.04693/) (2020)
- [Post-training 4-bit quantization of convolution networks for rapid-deployment](https://mlsanity.com/paper/1810.05723/) (2018)

## Built on by (most cited first, 3 of 3)

- [Can Large Language Models Still Explain Themselves? Investigating the Impact of Quantization on Self-Explanations](https://mlsanity.com/paper/2601.00282/) (2026)
- [Through a Compressed Lens: Investigating The Impact of Quantization on Factual Knowledge Recall](https://mlsanity.com/paper/2505.13963/) (2025)
- [Assessing the Potential for Catastrophic Failure in Dynamic Post-Training Quantization](https://mlsanity.com/paper/2510.02457/) (2025)

## Abstract (arXiv)

Robust quantization improves the tolerance of networks for various implementations, allowing reliable output in different bit-widths or fragmented low-precision arithmetic. In this work, we perform extensive analyses to identify the sources of quantization error and present three insights to robustify a network against quantization: reduction of error propagation, range clamping for error minimization, and inherited robustness against quantization. Based on these insights, we propose two novel methods called symmetry regularization (SymReg) and saturating nonlinearity (SatNL). Applying the proposed methods during training can enhance the robustness of arbitrary neural networks against quantization on existing post-training quantization (PTQ) and quantization-aware training (QAT) algorithms and enables us to obtain a single weight flexible enough to maintain the output quality under various conditions. We conduct extensive studies on CIFAR and ImageNet datasets and validate the effectiveness of the proposed methods.