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

Do Neural Networks Compress Manifolds Optimally?