# EQ-Net: Elastic Quantization Neural Networks

arXiv: https://arxiv.org/abs/2308.07650 · HTML: https://mlsanity.com/paper/2308.07650/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 54 references that are in the map.
- First posted on arXiv 15 Aug 2023.

## Builds on (most cited first, 30 of 42)

- [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)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Once-for-All: Train One Network and Specialize it for Efficient Deployment](https://mlsanity.com/paper/1908.09791/) (2019)
- [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)
- [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)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [Equalization Loss for Long-Tailed Object Recognition](https://mlsanity.com/paper/2003.05176/) (2020)
- [HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks](https://mlsanity.com/paper/1911.03852/) (2019)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [Binary Neural Networks: A Survey](https://mlsanity.com/paper/2004.03333/) (2020)
- [LSQ+: Improving low-bit quantization through learnable offsets and better initialization](https://mlsanity.com/paper/2004.09576/) (2020)
- [BigNAS: Scaling Up Neural Architecture Search with Big Single-Stage Models](https://mlsanity.com/paper/2003.11142/) (2020)
- [QDrop: Randomly Dropping Quantization for Extremely Low-bit Post-Training Quantization](https://mlsanity.com/paper/2203.05740/) (2022)
- [Overcoming Oscillations in Quantization-Aware Training](https://mlsanity.com/paper/2203.11086/) (2022)
- [Loss Aware Post-training Quantization](https://mlsanity.com/paper/1911.07190/) (2019)
- [Rethinking Differentiable Search for Mixed-Precision Neural Networks](https://mlsanity.com/paper/2004.05795/) (2020)
- [EagleEye: Fast Sub-net Evaluation for Efficient Neural Network Pruning](https://mlsanity.com/paper/2007.02491/) (2020)

## Built on by (most cited first, 10 of 10)

- [Retraining-free Model Quantization via One-Shot Weight-Coupling Learning](https://mlsanity.com/paper/2401.01543/) (2024)
- [MGD3: Mode-Guided Dataset Distillation using Diffusion Models](https://mlsanity.com/paper/2505.18963/) (2025)
- [Neural Network Quantization for Microcontrollers: A Comprehensive Survey of Methods, Platforms, and Applications](https://mlsanity.com/paper/2508.15008/) (2025)
- [Thinking in Granularity: Dynamic Quantization for Image Super-Resolution by Intriguing Multi-Granularity Clues](https://mlsanity.com/paper/2409.14330/) (2024)
- [NestQuant: Post-Training Integer-Nesting Quantization for On-Device DNN](https://mlsanity.com/paper/2506.17870/) (2025)
- [EVLF: Early Vision-Language Fusion for Generative Dataset Distillation](https://mlsanity.com/paper/2603.07476/) (2026)
- [TruncQuant: Truncation-Ready Quantization for DNNs with Flexible Weight Bit Precision](https://mlsanity.com/paper/2506.11431/) (2025)
- [Efficient Multi-bit Quantization Network Training via Weight Bias Correction and Bit-wise Coreset Sampling](https://mlsanity.com/paper/2510.20673/) (2025)
- [Nearly Lossless Adaptive Bit Switching](https://mlsanity.com/paper/2502.01199/) (2025)
- [Toward Multi-Domain and Long-Tailed Quantization via Feature Alignment and Scaling](https://mlsanity.com/paper/2606.04920/) (2026)

## Abstract (arXiv)

Current model quantization methods have shown their promising capability in reducing storage space and computation complexity. However, due to the diversity of quantization forms supported by different hardware, one limitation of existing solutions is that usually require repeated optimization for different scenarios. How to construct a model with flexible quantization forms has been less studied. In this paper, we explore a one-shot network quantization regime, named Elastic Quantization Neural Networks (EQ-Net), which aims to train a robust weight-sharing quantization supernet. First of all, we propose an elastic quantization space (including elastic bit-width, granularity, and symmetry) to adapt to various mainstream quantitative forms. Secondly, we propose the Weight Distribution Regularization Loss (WDR-Loss) and Group Progressive Guidance Loss (GPG-Loss) to bridge the inconsistency of the distribution for weights and output logits in the elastic quantization space gap. Lastly, we incorporate genetic algorithms and the proposed Conditional Quantization-Aware Accuracy Predictor (CQAP) as an estimator to quickly search mixed-precision quantized neural networks in supernet. Extensive experiments demonstrate that our EQ-Net is close to or even better than its static counterparts as well as state-of-the-art robust bit-width methods. Code can be available at hrefhttps://github.com/xuke225/EQ-Net.githttps://github.com/xuke225/EQ-Net.