# Position-based Scaled Gradient for Model Quantization and Pruning

arXiv: https://arxiv.org/abs/2005.11035 · HTML: https://mlsanity.com/paper/2005.11035/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2020.

## Built on by (most cited first, 4 of 4)

- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Self-Distilled Quantization: Achieving High Compression Rates in Transformer-Based Language Models](https://mlsanity.com/paper/2307.05972/) (2023)
- [Prototype-based Personalized Pruning](https://mlsanity.com/paper/2103.15564/) (2021)
- [Ultra-low Precision Multiplication-free Training for Deep Neural Networks](https://mlsanity.com/paper/2302.14458/) (2023)

## Abstract (arXiv)

We propose the position-based scaled gradient (PSG) that scales the gradient depending on the position of a weight vector to make it more compression-friendly. First, we theoretically show that applying PSG to the standard gradient descent (GD), which is called PSGD, is equivalent to the GD in the warped weight space, a space made by warping the original weight space via an appropriately designed invertible function. Second, we empirically show that PSG acting as a regularizer to a weight vector is favorable for model compression domains such as quantization and pruning. PSG reduces the gap between the weight distributions of a full-precision model and its compressed counterpart. This enables the versatile deployment of a model either as an uncompressed mode or as a compressed mode depending on the availability of resources. The experimental results on CIFAR-10/100 and ImageNet datasets show the effectiveness of the proposed PSG in both domains of pruning and quantization even for extremely low bits. The code is released in Github.