Topological obstructions to autoencoding

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 erroneously seem anomalous due to global issues. Conversely, neural networks typically have an inductive bias or prior to locally interpolate such that undersampled or rare events may be reconstructed with small error, despite actually being the desired anomalies. Taken together, these facts are in tension with the simple picture of the autoencoder as an anomaly detector. Using a series of illustrative low-dimensional examples, we show explicitly how the intrinsic and extrinsic topology of the dataset affects the behavior of an autoencoder and how this topology is manifested in the latent space representation during training. We ground this analysis in the discussion of a mock bump hunt in which the autoencoder fails to identify an anomalous signal for reasons tied to the intrinsic topology of n-particle phase space.

Automated summary

Autoencoders are proposed as a tool for anomaly detection in high-energy physics, but the connection between large reconstruction errors and anomalies is not always clear. Neural networks' bias for local interpolation may lead to rare or undersampled events being reconstructed with small error, challenging the simple picture of autoencoders as anomaly detectors. The intrinsic and extrinsic topology of the dataset influences the behavior of autoencoders, impacting the representation in the latent space during training.