# Nonuniform-to-Uniform Quantization: Towards Accurate Quantization via Generalized Straight-Through Estimation

arXiv: https://arxiv.org/abs/2111.14826 · HTML: https://mlsanity.com/paper/2111.14826/

## Key facts

- Cited by 79 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 58 references that are in the map.
- First posted on arXiv 29 Nov 2021.

## Builds on (most cited first, 30 of 49)

- [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)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [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)
- [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)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [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)
- [Learning Efficient Convolutional Networks through Network Slimming](https://mlsanity.com/paper/1708.06519/) (2017)
- [ProxylessNAS: Direct Neural Architecture Search on Target Task and Hardware](https://mlsanity.com/paper/1812.00332/) (2018)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [FBNet: Hardware-Aware Efficient ConvNet Design via Differentiable Neural Architecture Search](https://mlsanity.com/paper/1812.03443/) (2018)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [LQ-Nets: Learned Quantization for Highly Accurate and Compact Deep Neural Networks](https://mlsanity.com/paper/1807.10029/) (2018)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [Bi-Real Net: Enhancing the Performance of 1-bit CNNs With Improved Representational Capability and Advanced Training Algorithm](https://mlsanity.com/paper/1808.00278/) (2018)
- [MetaPruning: Meta Learning for Automatic Neural Network Channel Pruning](https://mlsanity.com/paper/1903.10258/) (2019)
- [ReActNet: Towards Precise Binary Neural Network with Generalized Activation Functions](https://mlsanity.com/paper/2003.03488/) (2020)

## Built on by (most cited first, 30 of 79)

- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [LLM-QAT: Data-Free Quantization Aware Training for Large Language Models](https://mlsanity.com/paper/2305.17888/) (2023)
- [A Comprehensive Survey on Model Quantization for Deep Neural Networks in Image Classification](https://mlsanity.com/paper/2205.07877/) (2022)
- [QLLM: Accurate and Efficient Low-Bitwidth Quantization for Large Language Models](https://mlsanity.com/paper/2310.08041/) (2023)
- [Oscillation-free Quantization for Low-bit Vision Transformers](https://mlsanity.com/paper/2302.02210/) (2023)
- [BiT: Robustly Binarized Multi-distilled Transformer](https://mlsanity.com/paper/2205.13016/) (2022)
- [MoH: Multi-Head Attention as Mixture-of-Head Attention](https://mlsanity.com/paper/2410.11842/) (2024)
- [COAT: Compressing Optimizer states and Activation for Memory-Efficient FP8 Training](https://mlsanity.com/paper/2410.19313/) (2024)
- [SpikeLLM: Scaling up Spiking Neural Network to Large Language Models via Saliency-based Spiking](https://mlsanity.com/paper/2407.04752/) (2024)
- [ApiQ: Finetuning of 2-Bit Quantized Large Language Model](https://mlsanity.com/paper/2402.05147/) (2024)
- [Q-DETR: An Efficient Low-Bit Quantized Detection Transformer](https://mlsanity.com/paper/2304.00253/) (2023)
- [LeanQuant: Accurate and Scalable Large Language Model Quantization with Loss-error-aware Grid](https://mlsanity.com/paper/2407.10032/) (2024)
- [A Survey on Deep Learning Hardware Accelerators for Heterogeneous HPC Platforms](https://mlsanity.com/paper/2306.15552/) (2023)
- [FIARSE: Model-Heterogeneous Federated Learning via Importance-Aware Submodel Extraction](https://mlsanity.com/paper/2407.19389/) (2024)
- [ELMGS: Enhancing memory and computation scaLability through coMpression for 3D Gaussian Splatting](https://mlsanity.com/paper/2410.23213/) (2024)
- [IRGen: Generative Modeling for Image Retrieval](https://mlsanity.com/paper/2303.10126/) (2023)
- [How Uniform Random Weights Induce Non-uniform Bias: Typical Interpolating Neural Networks Generalize with Narrow Teachers](https://mlsanity.com/paper/2402.06323/) (2024)
- [PMQ-VE: Progressive Multi-Frame Quantization for Video Enhancement](https://mlsanity.com/paper/2505.12266/) (2025)
- [Quantized Feature Distillation for Network Quantization](https://mlsanity.com/paper/2307.10638/) (2023)
- [A Comprehensive Survey of Compression Algorithms for Language Models](https://mlsanity.com/paper/2401.15347/) (2024)
- [L4Q: Parameter Efficient Quantization-Aware Fine-Tuning on Large Language Models](https://mlsanity.com/paper/2402.04902/) (2024)
- [Advancing Multimodal Large Language Models with Quantization-Aware Scale Learning for Efficient Adaptation](https://mlsanity.com/paper/2408.03735/) (2024)
- [Low-bit Model Quantization for Deep Neural Networks: A Survey](https://mlsanity.com/paper/2505.05530/) (2025)
- [Q-LIC: Quantizing Learned Image Compression with Channel Splitting](https://mlsanity.com/paper/2205.14510/) (2022)
- [Stochastic Approximation Beyond Gradient for Signal Processing and Machine Learning](https://mlsanity.com/paper/2302.11147/) (2023)
- [PassionSR: Post-Training Quantization with Adaptive Scale in One-Step Diffusion based Image Super-Resolution](https://mlsanity.com/paper/2411.17106/) (2024)
- [MetaMix: Meta-state Precision Searcher for Mixed-precision Activation Quantization](https://mlsanity.com/paper/2311.06798/) (2023)
- [Neural Network Quantization for Microcontrollers: A Comprehensive Survey of Methods, Platforms, and Applications](https://mlsanity.com/paper/2508.15008/) (2025)
- [SEAM: Searching Transferable Mixed-Precision Quantization Policy through Large Margin Regularization](https://mlsanity.com/paper/2302.06845/) (2023)
- [Reducing the Side-Effects of Oscillations in Training of Quantized YOLO Networks](https://mlsanity.com/paper/2311.05109/) (2023)

## Abstract (arXiv)

The nonuniform quantization strategy for compressing neural networks usually achieves better performance than its counterpart, i.e., uniform strategy, due to its superior representational capacity. However, many nonuniform quantization methods overlook the complicated projection process in implementing the nonuniformly quantized weights/activations, which incurs non-negligible time and space overhead in hardware deployment. In this study, we propose Nonuniform-to-Uniform Quantization (N2UQ), a method that can maintain the strong representation ability of nonuniform methods while being hardware-friendly and efficient as the uniform quantization for model inference. We achieve this through learning the flexible in-equidistant input thresholds to better fit the underlying distribution while quantizing these real-valued inputs into equidistant output levels. To train the quantized network with learnable input thresholds, we introduce a generalized straight-through estimator (G-STE) for intractable backward derivative calculation w.r.t. threshold parameters. Additionally, we consider entropy preserving regularization to further reduce information loss in weight quantization. Even under this adverse constraint of imposing uniformly quantized weights and activations, our N2UQ outperforms state-of-the-art nonuniform quantization methods by 0.5~1.7 on ImageNet, demonstrating the contribution of N2UQ design. Code and models are available at: https://github.com/liuzechun/Nonuniform-to-Uniform-Quantization.