Is there a name for a deep neural network, perhaps with stacked autoencoders, that converges to a minimum-size n-dimensional layer, and then expands to output the original size array or matrix?

I know that someone must have done this but I don't know what it is called and don't know if there are libraries in Pytorch or elsewhere for training the network without coding it from scratch. Also, I don't know if there are any tricks for more efficiently training the network, like training the front and back end halves in separate steps with back propagation and then training the entire network as a final step. I'd like to read up …

deep neural network network neural network neuralnetworks