Yoni Kahn, Assistant Professor from the Grainger College of Engineering at the University of Illinois at Urbana-Champaign, will present "Topological Obstructions to Autoencoders" on Monday, October 26 at 11:00 a.m.
Abstract: Autoencoders have found widespread application in recent years as generalized anomaly detectors. Intuitively, an autoencoder is supposed to compress high-dimensional data to a lower-dimensional space in order to capture its essential features. The performance of an autoencoder is measured by how well it can decompress the data back to its original form; data points which do not belong to the space of training data will be reconstructed poorly, thus flagging them as anomalies. However, since a typical neural network autoencoder compresses the data to a latent space which is a subset of Rn, datasets with nontrivial topology may be impossible to compress even when the dimension of the latent space equals the intrinsic dimension of the data. Using a series of illustrative low-dimensional examples, I will show how the topology of the dataset affects the behavior of the autoencoder and how this topology manifests itself in the network architecture during training. I will speculate on how knowledge of the data topology could improve signal-to-noise in anomaly detection. I will conclude with applications of this work to high-energy physics, where all data is originally drawn from the manifold of Lorentz-invariant phase space, which does have nontrivial topology.
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Seminar Zoom link.