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What is the output value of the network for these inputs respectively, and why? (Linear activation function is fine.)

[2, 3][-1, 2][1, 0][3, 4]

My main question is how you take the 'backwards' directed paths into account.

enter image description here

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The neural Network in the image is a "Recurrent Neural Network"(RNN). Because of the connection leading backward from h10 to h01, h10 has to be a "memory node" (mn), meaning it can store its value from the previous input. The basic functionality of an RNN can be seen in this animation:


animation


Your example:

In the beginning, the storage of the mn is initialized with a value, probably 0.
Now the first input is fed into network:

  • i0 = 2
  • i1 = 3
  • h00 = (i0 * 0.4) = 0.8
  • h01 = (i1 * -0.9) + ("the stored value of h10" * 1.2) = -2.7
    ("the stored value of h10" in the first run is 0.)
  • h10 = (h00 * 0.85) + (h01 * -0.2) = 1.22
  • out = (h10 * 0.3) + (h01 * 0.1) = 0.096

Now you can feed the next input through the network and use -2.7 as "the stored value of h10" and so on. You can also add an activation function as you would for any other NN.

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  • $\begingroup$ Why is out calculated later than h10? Technically, out and h10 is on the same layer, just like h00 is to h01. What is the algorithm for the calculation order? $\endgroup$ – andras Mar 31 '18 at 13:23

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