Today I was in the middle of a particularly boring lecture. During this class I briefly let my mind wander. During this time I wondered:
Given a unique, but possibly similar, set of input data is it possible for the encoder to create overlapping codings for two or more different inputs?.
Suppose that I have an arbitrary set of inputs, $X$. In this input set, there are no duplicate data instances, but the data can be very simular. If you were to feed this data into a sufficiently trained autoencoder is it possible for the encoder to output the same codings for multiple different instances of the input set?