# On One-Bit Quantization

arXiv: https://arxiv.org/abs/2202.05292 · HTML: https://mlsanity.com/paper/2202.05292/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 13 references that are in the map.
- First posted on arXiv 10 Feb 2022.

## Builds on (most cited first, 3 of 3)

- [Nonlinear Transform Coding](https://mlsanity.com/paper/2007.03034/) (2020)
- [Universally Quantized Neural Compression](https://mlsanity.com/paper/2006.09952/) (2020)
- [Neural Networks Optimally Compress the Sawbridge](https://mlsanity.com/paper/2011.05065/) (2020)

## Abstract (arXiv)

We consider the one-bit quantizer that minimizes the mean squared error for a source living in a real Hilbert space. The optimal quantizer is a projection followed by a thresholding operation, and we provide methods for identifying the optimal direction along which to project. As an application of our methods, we characterize the optimal one-bit quantizer for a continuous-time random process that exhibits low-dimensional structure. We numerically show that this optimal quantizer is found by a neural-network-based compressor trained via stochastic gradient descent.