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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:

enter image description here "...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?

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    $\begingroup$ I don't think there is any difference, in your interpretation. Usually when we say "error" it can be anything represented by our loss function or success metric, but residual implies the raw difference between prediction and ground truth. $\endgroup$ Jul 4, 2018 at 12:11

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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.

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