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

Understand

It is well established that training deep neural networks gives useful representations that capture essential features of the inputs.

• However, these representations are poorly understood in theory and practice.
• In the context of supervised learning an important question is whether these representations capture features informative for classification, while filtering out non-informative noisy ones.
• We explore a formalization of this question by considering a generative process where each class is associated with a high-dimensional manifold and different classes define different manifolds.