# GDNSQ: Gradual Differentiable Noise Scale Quantization for Low-bit Neural Networks

arXiv: https://arxiv.org/abs/2508.14004 · HTML: https://mlsanity.com/paper/2508.14004/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 37 references that are in the map.
- First posted on arXiv 19 Aug 2025.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [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)
- [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)
- [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)
- [ReActNet: Towards Precise Binary Neural Network with Generalized Activation Functions](https://mlsanity.com/paper/2003.03488/) (2020)
- [Rotated Binary Neural Network](https://mlsanity.com/paper/2009.13055/) (2020)
- [Searching for Low-Bit Weights in Quantized Neural Networks](https://mlsanity.com/paper/2009.08695/) (2020)
- [Learnable Companding Quantization for Accurate Low-bit Neural Networks](https://mlsanity.com/paper/2103.07156/) (2021)
- [Estimator Meets Equilibrium Perspective: A Rectified Straight Through Estimator for Binary Neural Networks Training](https://mlsanity.com/paper/2308.06689/) (2023)
- [Improving Quantization-aware Training of Low-Precision Network via Block Replacement on Full-Precision Counterpart](https://mlsanity.com/paper/2412.15846/) (2024)

## Built on by (most cited first, 2 of 2)

- [StableQAT: Stable Quantization-Aware Training at Ultra-Low Bitwidths](https://mlsanity.com/paper/2601.19320/) (2026)
- [Local Stability and Gaussian Smoothing of Quantized Neural Networks](https://mlsanity.com/paper/2607.20153/) (2026)

## Abstract (arXiv)

Quantized neural networks can be viewed as a chain of noisy channels, where rounding in each layer reduces capacity as bit-width shrinks; the floating-point (FP) checkpoint sets the maximum input rate. We track capacity dynamics as the average bit-width decreases and identify resulting quantization bottlenecks by casting fine-tuning as a smooth, constrained optimization problem. Our approach employs a fully differentiable Straight-Through Estimator (STE) with learnable bit-width, noise scale and clamp bounds, and enforces a target bit-width via an exterior-point penalty; mild metric smoothing (via distillation) stabilizes training. Despite its simplicity, the method attains competitive accuracy down to the extreme W1A1 setting while retaining the efficiency of STE.