This is a very basic question about the functionality of RNN / LSTM. My question is about the RNN outputs. Is there a single output for only the last element in the sequence, or is there an output for every element of the sequence?
There is an output for every node, referred as hidden state in vanilla RNN (LSTM nodes has 2 outputs). In certain cases you only care about the output of the last node so you just avoid previous ones. But each hidden state is still used: Hidden states of the nodes transfered to subsequent nodes thus they are used to construct hidden state (output) of the last node in the sequence.