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I was trying to read RNN Encoder Decoder paper.

RNN (plain RNN i.e. non encoder-decoder RNN)

It starts with giving equation for RNN:

  • hidden state in RNN is given as:

    List item ... equation (1)

    where f is a non linear activation function.

  • The output is a softmax:
    enter image description here ... equation(2)
    for all possible symbols j = 1, ..., K.

RNN encoder-decoder

Then it explains RNN encoder-decoder:

  • The RNN encoder decoder architecture is given as follows:
    enter image description here
  • There are two equations for encoder:
    • The encoder hidden state equation is same as that for plain RNN, i.e. equation (1)
    • The summary of the whole input sequence, which is indicated by letter c is nothing but the hidden state produced after reading last input word. (c for "context" as that forms input context for decoder):
      enter image description here
  • The decoder hidden state is calculated as follows:
    enter image description here
    This is indicated by circles in decoder in above image each of which takes y_(t-1), c and h_(t-1) as input.

What I am not able to get is how y_t is calculated in decoder? Is it by using softmax as in equation(2). If yes exactly how? Note that diagram shows three inputs for calculating y_t: h_t, c and y_(t-1). How these inputs are incorporated for calculating y. The paper does not seem to discuss this, or am I misreading?

Update

I just found that paper says:

enter image description here

for an activation function g which must produce valid probabilities, e.g. a softmax. But still its unclear how exactly these three (h_t, y_(t-1) and c) variables can be included in softmax.

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1 Answer 1

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The paper's Appendix A has the exact formulas used. Specifically A.1 contains the exact formula for calculating $\mathbf{c}$, and A.1.1 contains details on where and how it is used.

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  • $\begingroup$ Ohkay I missed that. This is how it defines y. I might take some time to get the intuition behind that. But the immediate doubt is that I dont find g_j (smaller g) defined anywhere. Is it the jth component G (larger G) defined at the end? $\endgroup$
    – Mahesha999
    Apr 17, 2023 at 11:19
  • $\begingroup$ Oof, that's a pretty big omission... I've been out of the MT field for a few years now, my guess would be that g and s relate to the output language model that is integrated into the translation system. $\endgroup$
    – masaers
    Apr 18, 2023 at 3:24
  • $\begingroup$ I guess $g$ refers to single row of $G$, a standard practice: refer individual row / column with small letters and whole matrix with capital letters. $\endgroup$
    – Mahesha999
    Apr 18, 2023 at 8:44
  • $\begingroup$ Right, that would make $g_j$ the $K \times 1$ embedding vector for the $j$th output type, which makes sense in the context. $\endgroup$
    – masaers
    Apr 19, 2023 at 5:24

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