How to simplify the term $$1 - \frac{1}{1+\exp(1/x)}$$
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The only "simplifying" I see is to write "1" as a fraction with denominator 1+ exp(1/x) and do the subtraction.
You mean $$\frac{1+\exp(1/x) - 1}{1+\exp(1/x)}=\frac{\exp(1/x)}{1+\exp(1/x)}$$ doesn't it simplify to the sigmoid function?
Originally Posted by brianx You mean $$\frac{1+\exp(1/x) - 1}{1+\exp(1/x)}=\frac{\exp(1/x)}{1+\exp(1/x)}$$ doesn't it simplify to the sigmoid function? No. The sigmoid function deals with $\displaystyle e^{-x} = \frac{1}{e^x}$. This one deals with $\displaystyle e^{1/x}$ which is not the same thing. -Dan
Last edited by topsquark; Apr 17th 2018 at 05:35 AM.