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I want to say that I used Neural Networks for approximating functions. My doubt is in the following line : I was amazed by their ability to learn the underlying relationships across a wide array of mathematical functions.

Underlying relationship of function x is different form that of y. So I mean to say that it learnt the underlying relationship in x as well as in y as well as in z. I want to make a generalized statement that across a wide array of functions it was able to do so. So in my original statement should I use relationship or relationships?

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  • So, how many relationships are there?
    – Hot Licks
    Oct 18 '18 at 12:44
  • every function has its own single and unique underlying relationship. Oct 18 '18 at 12:46
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If we use the singular form, it could mean that all the functions share just one common relationship.

If we use the plural form, it could mean that each function has several relationships.

For the general case it is more accurate to use the plural form, but we should not expect a single general statement to convey a precise meaning. This should not be a problem here, as there should be ample opportunity to more closely define the meaning elsewhere in the text.

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It sounds to me like you have a machine learning program that takes as input a table of X and Y values, and from this infers the rules (or a class of rules) by which Y can be calculated from X, or vice versa.

If your purpose is to infer the “best” relationship for any given case, then the singular form is best. To me this seems consistent with the comment you added to your original post.

If there is ambiguity, such as a polynomial being just as likely as a transcendental function, then relationships is better.

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  • You got it right. for example I want to approximate the function f(x,y) = Sin(x) + log (y). Based on this function will generate input output data. Then I'll use this data to train a machine learning model. That model successful predicts the output i.e. the output from the above equation and the output by that model will be close. So in a way that model has learnt the underlying relationship between inputs and outputs. Now this model is able to do so across a wide array of functions. This is what I mean. Oct 19 '18 at 17:21

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