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OK I think I've figured out a way to put everything in one operation by basically having:
sigmoid(x)=max(1/2, 1/(1+e^(-x)) + min(1/2, e^x/(1+e^x)) - 1/2
The output is now
for the example in #1090
I've found it to be slightly slower than the original logistic function but not by much (600ms/800ms). @neubig if you can test in your environment maybe and let me know the result that would help.
TODO: