It seems to me that Seq2Seq models and Bidirectional RNNs try to do the same thing. Is that true?
Also, when would you recommend one setup over another?
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Seq2Seq and Bidirectional RNNs are not doing the same thing, at least in their classic form.
Seq2Seq models are used to generate a sequence from another sequence. Consider, for example, the translation task from one language to another. In that sense, Seq2Seq is more a family of models, not an architecture.
On the other hand, the Bidirectional RNN is a neural network architecture and can be used to build several models including Seq2Seq, for example, the encoding part of the Seq2Seq can be a Bi-RNN, but they also can be used for other tasks, for example, sentence classification or sentiment analysis.