# Progressive Element-wise Gradient Estimation for Neural Network Quantization

arXiv: https://arxiv.org/abs/2509.00097 · HTML: https://mlsanity.com/paper/2509.00097/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 15 references that are in the map.
- First posted on arXiv 27 Aug 2025.

## Builds on (most cited first, 13 of 13)

- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [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)
- [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)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [Learning to Quantize Deep Networks by Optimizing Quantization Intervals with Task Loss](https://mlsanity.com/paper/1808.05779/) (2018)
- [Additive Powers-of-Two Quantization: An Efficient Non-uniform Discretization for Neural Networks](https://mlsanity.com/paper/1909.13144/) (2019)
- [Network Quantization with Element-wise Gradient Scaling](https://mlsanity.com/paper/2104.00903/) (2021)
- [MQBench: Towards Reproducible and Deployable Model Quantization Benchmark](https://mlsanity.com/paper/2111.03759/) (2021)
- [Automatic Attention Pruning: Improving and Automating Model Pruning using Attentions](https://mlsanity.com/paper/2303.08595/) (2023)

## Built on by (most cited first, 1 of 1)

- [MCAQ-YOLO: Morphological Complexity-Aware Quantization for Efficient Object Detection with Curriculum Learning](https://mlsanity.com/paper/2511.12976/) (2025)

## Abstract (arXiv)

Neural network quantization aims to reduce the bit-widths of weights and activations, making it a critical technique for deploying deep neural networks on resource-constrained hardware. Most Quantization-Aware Training (QAT) methods rely on the Straight-Through Estimator (STE) to address the non-differentiability of discretization functions by replacing their derivatives with that of the identity function. While effective, STE overlooks discretization errors between continuous and quantized values, which can lead to accuracy degradation -- especially at extremely low bit-widths. In this paper, we propose Progressive Element-wise Gradient Estimation (PEGE), a simple yet effective alternative to STE, which can be seamlessly integrated with any forward propagation methods and improves the quantized model accuracy. PEGE progressively replaces full-precision weights and activations with their quantized counterparts via a novel logarithmic curriculum-driven mixed-precision replacement strategy. Then it formulates QAT as a co-optimization problem that simultaneously minimizes the task loss for prediction and the discretization error for quantization, providing a unified and generalizable framework. Extensive experiments on CIFAR-10 and ImageNet across various architectures (e.g., ResNet, VGG) demonstrate that PEGE consistently outperforms existing backpropagation methods and enables low-precision models to match or even outperform the accuracy of their full-precision counterparts.