Lightweight logistic function

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:

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

• $\arctan(x)$ works good too for logictic models
– L F
Aug 31, 2020 at 18:17
• @LuisFelipe yes I've already tried using it, but it's also very intensive as calculation Aug 31, 2020 at 18:18
• what about logistic function using $e^x$ as a truncated form? i.e $\sum_{k=0}^{5} x^k / k!$
– L F
Aug 31, 2020 at 18:19
• 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
– L F
Aug 31, 2020 at 18:28
• @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 Sep 1, 2020 at 0:51