Topological obstructions to autoencoding

@article{Batson2021TopologicalOT,
  title={Topological obstructions to autoencoding},
  author={Joshua D. Batson and C. Grace Haaf and Yonatan Kahn and Daniel A. Roberts},
  journal={Journal of High Energy Physics},
  year={2021},
  volume={2021},
  pages={1-43}
}
Autoencoders have been proposed as a powerful tool for model-independent anomaly detection in high-energy physics. The operating principle is that events which do not belong to the space of training data will be reconstructed poorly, thus flagging them as anomalies. We point out that in a variety of examples of interest, the connection between large reconstruction error and anomalies is not so clear. In particular, for data sets with nontrivial topology, there will always be points that… 
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