# Soft Quantization: Model Compression Via Weight Coupling

arXiv: https://arxiv.org/abs/2601.21219 · HTML: https://mlsanity.com/paper/2601.21219/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 18 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Do Better ImageNet Models Transfer Better?](https://mlsanity.com/paper/1805.08974/) (2018)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [8-bit Optimizers via Block-wise Quantization](https://mlsanity.com/paper/2110.02861/) (2021)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [Cross-Entropy Loss Functions: Theoretical Analysis and Applications](https://mlsanity.com/paper/2304.07288/) (2023)
- [What makes ImageNet good for transfer learning?](https://mlsanity.com/paper/1608.08614/) (2016)
- [Soft Weight-Sharing for Neural Network Compression](https://mlsanity.com/paper/1702.04008/) (2017)
- [A Comprehensive Evaluation of Quantization Strategies for Large Language Models](https://mlsanity.com/paper/2402.16775/) (2024)
- [BinaryRelax: A Relaxation Approach For Training Deep Neural Networks With Quantized Weights](https://mlsanity.com/paper/1801.06313/) (2018)
- [Histogram-Equalized Quantization for logic-gated Residual Neural Networks](https://mlsanity.com/paper/2501.04517/) (2025)

## Abstract (arXiv)

We show that introducing short-range attractive couplings between the weights of a neural network during training provides a novel avenue for model quantization. These couplings rapidly induce the discretization of a model's weight distribution, and they do so in a mixed-precision manner despite only relying on two additional hyperparameters. We demonstrate that, within an appropriate range of hyperparameters, our "soft quantization'' scheme outperforms histogram-equalized post-training quantization on ResNet-20/CIFAR-10. Soft quantization provides both a new pipeline for the flexible compression of machine learning models and a new tool for investigating the trade-off between compression and generalization in high-dimensional loss landscapes.