"residual error" of LSTM during backprop vs usual "error" What does the residual error mean when we are talking about LSTM? 

Taken from the middle of section 3 of this paper, where it says:


"...of the residual error $\epsilon$"

Where $s_0$ is the initial state of the RNN network.

Question: how is a residual error different to a usual error? Why to use such a term?
Residual errors are the errors that remain after a model has tried fitting to some data. It is the error which resides.

People use that term, along with just error or residuals interchangeably, but after a model has been tested, it just means how much of the data cannot be explained by the model.

The letter $\epsilon$ is commonly used to explain stochastic noise inherent in (co)-variates of a model, i.e. noise.error that we cannot explain with the given data.