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It is well established that training deep neural networks gives usefulrepresentations that capture essential features of the inputs. However, theserepresentations are poorly understood in theory and practice. In the context ofsupervised learning an important question is whether these representationscapture features informative for classification, while filtering outnon-informative noisy ones. We explore a formalization of this question byconsidering a generative process where each class is associated with ahigh-dimensional manifold and different classes define different manifolds.Under this model, each input is produced using two latent vectors: (i) a"manifold identifier" $\gamma$ and; (ii)~a "transformation parameter" $\theta$that shifts examples along the surface of a manifold. E.g., $\gamma$ mightrepresent a canonical image of a dog, and $\theta$ might stand for variationsin pose, background or lighting. We provide theoretical and empirical evidencethat neural representations can be viewed as LSH-like functions that map eachinput to an embedding that is a function of solely the informative $\gamma$ andinvariant to $\theta$, effectively recovering the manifold identifier $\gamma$.An important consequence of this behavior is one-shot learning to unseenclasses.

For Manifold Learning, Deep Neural Networks can be Locality Sensitive Hash Functions