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learning-to-communicate's Issues

Some question about the formula in this paper

Hi, may I ask you a question in this paper?
I am struggling for understanding formula (5) in this paper.
As I've tried as I know, I only get the point about that m(hat)(1-m(hat)) in the denominator comes from the derive of logistic function.
But I still don't get it why one of standard deviation terms beside square(2pi) is in the square() ? Secondly, why the other standard deviation term within the exponential is not twice times of itself?
It looks not like the form of Gaussian distribution.

Could you teach this to me?
If you do so, that will help my comprehension of this paper very much !

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