Let's assume I have a net so the loss function is composed from 3 components: $C_1, C_2, C_3$, and each component is multiply by its weight $(w1, w2, w3)$. The weights should be a function of $\beta$, which is a function of the error/error rate/std etc, so the loss function can be written:

$$L=C_1 w_1(\beta) + C_2 w_2(\beta) + C_3 w_3(\beta)$$

In Mathematica, the loss would be:

  L = w1[beta]*C1 + w2[beta]*C2 + w3[beta]*C3

The net I have is shown in the diagram below.

The weights should be normalized I am guessing, and sum to one.

I would like the network to be able to learn the optimal weights. How can I do it and which layers I need to add to my network? How can I use the error and calculate the error rate or the standard deviation of the error signal, during the training process ?

Edit: The code that produced the above network is:

lossNet2 = NetGraph[
  <|"Net" -> UNET,
    "finalAddition" -> TotalLayer[],
   "C1" -> lossByWeights,
   "C2" -> lossByDev,
   "C3" -> lossByMinMax
   NetPort[ "Input"] -> "Net", "Net" -> NetPort["Output"],
   {"Net", NetPort[ "Target"]} -> "C1" -> "finalAddition",
   "Net" -> "C2" -> "finalAddition" -> NetPort["Loss"],
   {NetPort[ "Input"], NetPort["Target"]} -> "C3" -> "finalAddition"
  "Input" -> {1, 1, 512}]

Any help will be appreciate.



enter image description here

  • $\begingroup$ When editing your question, I thought your objective function was the sum of the terms. Is this correct? Or do you have a multi-objective function (which would be a more complex problem. Thanks $\endgroup$ – mjw Apr 3 at 13:19
  • 1
    $\begingroup$ I think it would be helpful to include the code you used to produce the network. $\endgroup$ – mjw Apr 3 at 13:22
  • $\begingroup$ I added the code, thanks $\endgroup$ – GM_jnj Apr 4 at 5:17
  • $\begingroup$ Getting this error message: "NetGraph::netinvnodes: UNET is not a net function." What is UNET? $\endgroup$ – mjw Apr 4 at 14:20
  • $\begingroup$ UNET is a customized net that I built. The specific net is not relevant, It can be any net. $\endgroup$ – GM_jnj Apr 7 at 4:33

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