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.
@article{arxiv.2205.08518,
title = {Do Neural Networks Compress Manifolds Optimally?},
author = {Sourbh Bhadane and Aaron B. Wagner and Johannes Ballé},
journal= {arXiv preprint arXiv:2205.08518},
year = {2022}
}