I seem to remember the following two forms:
x_1*exp(-k*x_1) + ... x_n*exp(-k*x_n)
softmin(x_1, x_2, ... x_n) = -------------------------------------
exp(-k*x_1) + ... exp(-k*x_n)
x_1*exp(k*x_1) + ... x_n*exp(k*x_n)
softmax(x_1, x_2, ... x_n) = -----------------------------------
exp(k*x_1) + ... exp(k*x_n)
The accuracy of the above two functions depends on the parameter k,
and the range and number of values x_i (in my case, the values x_i
lie in the interval [0,1]).
Are there any references where the behavior of these two (or other
softmin/max) functions is studied? Any pointers would be much appreciated.
Thanks.
Christian