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I have a value $X$ that ranges between $[0, 100]$, and I would like to apply some "activation function" on it...

Let me explain.
Currently if i take just the value $X$, and use it as it is, I will get something like $f(x) = x$ obviously as "transformation function", but I would like to apply to $X$ some kind of function, that is "centered" on $50$ and that it limited on $[0, 100]$, something like: $$f(50) = 50$$ $$f(0) \approx 0$$ $$f(100) \approx 100$$

and that the "graph" of that function is similar to the logistic function graph: logistic function

However, I can't use the logistic function, since I need to perform this transformation in real-time, and $e^{-x}$ is very computational intensive, and so i was looking to a similar function, that uses more lightweight operators / functions

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  • $\begingroup$ $\arctan(x)$ works good too for logictic models $\endgroup$
    – L F
    Aug 31, 2020 at 18:17
  • $\begingroup$ @LuisFelipe yes I've already tried using it, but it's also very intensive as calculation $\endgroup$ Aug 31, 2020 at 18:18
  • $\begingroup$ what about logistic function using $e^x$ as a truncated form? i.e $\sum_{k=0}^{5} x^k / k!$ $\endgroup$
    – L F
    Aug 31, 2020 at 18:19
  • $\begingroup$ protiop: try to normalize your data before applying logictic function, also normalize data helps models to converge in neural netoworks. If you are using python, use a vectorized functionfor improve time execution $\endgroup$
    – L F
    Aug 31, 2020 at 18:28
  • $\begingroup$ @LuisFelipe i'll try the approximation, but what you mean with "normalize"? I came from a statistic course where normalization means the make it range between 0 and 1, like I suppose the vectors in algebra... but i can't see how this would help when applying the activation function, since it has $R$ as domain, and so normalizing it won't help, if not even make thing worse $\endgroup$ Sep 1, 2020 at 0:51

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