# Do Neural Networks Compress Manifolds Optimally?

arXiv: https://arxiv.org/abs/2205.08518 · HTML: https://mlsanity.com/paper/2205.08518/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 23 references that are in the map.
- First posted on arXiv 17 May 2022.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [High-Fidelity Generative Image Compression](https://mlsanity.com/paper/2006.09965/) (2020)
- [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)
- [The local low-dimensionality of natural images](https://mlsanity.com/paper/1412.6626/) (2014)

## Built on by (most cited first, 2 of 2)

- [Approaching Rate-Distortion Limits in Neural Compression with Lattice Transform Coding](https://mlsanity.com/paper/2403.07320/) (2024)
- [DeCompress: Denoising via Neural Compression](https://mlsanity.com/paper/2503.22015/) (2025)

## Abstract (arXiv)

Artificial Neural-Network-based (ANN-based) lossy compressors have recently obtained striking results on several sources. Their success may be ascribed to an ability to identify the structure of low-dimensional manifolds in high-dimensional ambient spaces. Indeed, prior work has shown that ANN-based compressors can achieve the optimal entropy-distortion curve for some such sources. In contrast, we determine the optimal entropy-distortion tradeoffs for two low-dimensional manifolds with circular structure and show that state-of-the-art ANN-based compressors fail to optimally compress them.