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I am attempting to train a neural network where I can say the following:

For most inputs, I know the sign of the relationship between that input and several specific outputs. I.e. whatever set of values the inputs are set to, I can point to individual input and say that so long as the other inputs are unchanged, the output should monotonically increase/decrease as I change this input's value.

This is not to say that the inputs don't interact with each other, they do, but the interaction never changes the sign (i.e. increasing vs decreasing) nature of the monotonic relationships between specific inputs and outputs.

I am wondering how I can use this information to help my network learn fast and/or perform well.

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    $\begingroup$ Can you provide some more information about what your network needs to predict? $\endgroup$
    – respectful
    Dec 17 '21 at 23:35
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    $\begingroup$ Also, more information about the problem in general would be helpful. Like how do you know which inputs/outputs have the monotonic relationships? $\endgroup$
    – respectful
    Dec 17 '21 at 23:44
  • $\begingroup$ @respectful: I have 21 inputs and 3 outputs. Out of that I know with confidence the sign of a monotonic relationship between 18 of the inputs and all of the outputs. But due to a confidentiality agreement I can not say exactly what the problem is. I have in the ballpark of 100k input/output pairs for training. $\endgroup$
    – Mick
    Dec 18 '21 at 7:07
  • $\begingroup$ If you are familiar with latex could you formalize the problem statement within the question. $\endgroup$
    – respectful
    Dec 21 '21 at 16:01

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