Is it possible to specify what the asymptotic behaviour of a Neural Networks (NN) model should be? I am thinking on NN which try to learn a mapping $\vec y=f(\vec x)$ with $\vec x$ a vector of features of dimension d and $\vec y$ a vector of outputs of dimension p. Is it possible to specify that for instance the NN should have a fixed value when $x_1$ goes to infinite? I mean: $$ \lim_{x_1\to \infty} f(\vec x) = \vec c $$

If it is not possible with NN, do you know other machine learning models (for instance Gaussian Process Regression or Support Vector Regression) which have a known asymptotic behaviour?

Cheers and thanks in advance, Ken

  • $\begingroup$ to gaurantee you would have to do some analysis on your network znd define the conditions of your network explicitly, but if you are okay with an approximation, you can define an auxillary loss $h(f(x,x_1=\alpha) - f(x,x_1=g(\alpha)))$ to try to make it fall in some form of algorithmic patter that will follow your needs $\endgroup$ – mshlis Aug 21 '19 at 20:31

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