# Rejection-Sampled Universal Quantization for Smaller Quantization Errors

arXiv: https://arxiv.org/abs/2402.03030 · HTML: https://mlsanity.com/paper/2402.03030/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 82 references that are in the map.
- First posted on arXiv 5 Feb 2024.

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

- [Universally Quantized Neural Compression](https://mlsanity.com/paper/2006.09952/) (2020)
- [Minimal Random Code Learning: Getting Bits Back from Compressed Model Parameters](https://mlsanity.com/paper/1810.00440/) (2018)
- [Compressing Images by Encoding Their Latent Representations with Relative Entropy Coding](https://mlsanity.com/paper/2010.01185/) (2020)
- [Joint Privacy Enhancement and Quantization in Federated Learning](https://mlsanity.com/paper/2208.10888/) (2022)
- [Algorithms for the Communication of Samples](https://mlsanity.com/paper/2110.12805/) (2021)
- [Understanding Entropy Coding With Asymmetric Numeral Systems (ANS): a Statistician's Perspective](https://mlsanity.com/paper/2201.01741/) (2022)
- [Compression with Exact Error Distribution for Federated Learning](https://mlsanity.com/paper/2310.20682/) (2023)
- [Communication-Efficient Laplace Mechanism for Differential Privacy via Random Quantization](https://mlsanity.com/paper/2309.06982/) (2023)
- [Communication Efficient Private Federated Learning Using Dithering](https://mlsanity.com/paper/2309.07809/) (2023)
- [Layered Randomized Quantization for Communication-Efficient and Privacy-Preserving Distributed Learning](https://mlsanity.com/paper/2312.07060/) (2023)

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

- [Communication-Efficient and Privacy-Adaptable Mechanism for Federated Learning](https://mlsanity.com/paper/2501.12046/) (2025)
- [Communication-Efficient and Privacy-Adaptable Mechanism -- a Federated Learning Scheme with Convergence Analysis](https://mlsanity.com/paper/2601.10701/) (2026)
- [Deep Randomized Distributed Function Computation (DeepRDFC): Neural Distributed Channel Simulation](https://mlsanity.com/paper/2603.10750/) (2026)
- [Privacy-Aligned Personalized Federated Learning with Compact Adaptation and Variable-Length Gaussian Communication](https://mlsanity.com/paper/2609.15950/) (2026)

## Abstract (arXiv)

We construct a randomized vector quantizer which has a smaller maximum error compared to all known lattice quantizers with the same entropy for dimensions 5, 6, ..., 48, and also has a smaller mean squared error compared to known lattice quantizers with the same entropy for dimensions 35, ..., 47, in the high resolution limit. Moreover, our randomized quantizer has a desirable property that the quantization error is always uniform over the ball and independent of the input. Our construction is based on applying rejection sampling on universal quantization, which allows us to shape the error distribution to be any continuous distribution, not only uniform distributions over basic cells of a lattice as in conventional dithered quantization. We also characterize the high SNR limit of one-shot channel simulation for any additive noise channel under a mild assumption (e.g., the AWGN channel), up to an additive constant of 1.45 bits.