# Is it possible to have the latent vector of an auto-encoder with size 1?

Given e.g. 1M vectors of $$1000$$ floating points each, where every point in vectors is sampled from a uniform distribution between $$-1$$ to $$1$$:

Is it possible to have the bottleneck of the AE network with size 1? In other words, without caring about generalization, is it possible to train a network, where, given only 1 encoded value, it can recreate any of the 1M examples?