# Soft Quantization using Entropic Regularization

arXiv: https://arxiv.org/abs/2309.04428 · HTML: https://mlsanity.com/paper/2309.04428/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 34 references that are in the map.
- First posted on arXiv 8 Sep 2023.

## Builds on (most cited first, 10 of 10)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Model compression via distillation and quantization](https://mlsanity.com/paper/1802.05668/) (2018)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [Massively scalable Sinkhorn distances via the Nystr"om method](https://mlsanity.com/paper/1812.05189/) (2018)
- [Training Quantized Neural Networks with a Full-precision Auxiliary Module](https://mlsanity.com/paper/1903.11236/) (2019)
- [From Optimal Transport to Discrepancy](https://mlsanity.com/paper/2002.01189/) (2020)
- [Accelerating the Sinkhorn algorithm for sparse multi-marginal optimal transport by fast Fourier transforms](https://mlsanity.com/paper/2208.03120/) (2022)
- [Nonequispaced Fast Fourier Transform Boost for the Sinkhorn Algorithm](https://mlsanity.com/paper/2201.07524/) (2022)
- [Unbalanced Optimal Transport and Maximum Mean Discrepancies: Interconnections and Rapid Evaluation](https://mlsanity.com/paper/2306.13618/) (2023)

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

- [Robust Clustering on High-Dimensional Data with Stochastic Quantization](https://mlsanity.com/paper/2409.02066/) (2024)

## Abstract (arXiv)

The quantization problem aims to find the best possible approximation of probability measures on ℝd using finite, discrete measures. The Wasserstein distance is a typical choice to measure the quality of the approximation. This contribution investigates the properties and robustness of the entropy-regularized quantization problem, which relaxes the standard quantization problem. The proposed approximation technique naturally adopts the softmin function, which is well known for its robustness in terms of theoretical and practicability standpoints. Moreover, we use the entropy-regularized Wasserstein distance to evaluate the quality of the soft quantization problem's approximation, and we implement a stochastic gradient approach to achieve the optimal solutions. The control parameter in our proposed method allows for the adjustment of the optimization problem's difficulty level, providing significant advantages when dealing with exceptionally challenging problems of interest. As well, this contribution empirically illustrates the performance of the method in various expositions.