Comment on The "Soft Maximum" functionComments−shalmanese16yIs there a accepted modification to the function to make it scale invariant? I'm kind of weirded out by something that would spit out a different result if did a unit change.−memetichazard16yHere's an idea. Take the scaled function: g(x, y; k) = log( exp(kx) + exp(ky) ) / kLet k be 1/max(x,y) so that you have:g(x,y) = log(exp(1)+exp(min(x,y)/max(x,y))*max(x,y)There are some issues if the maximum value can be negative or zero, though.
Comments
Is there a accepted modification to the function to make it scale invariant? I'm kind of weirded out by something that would spit out a different result if did a unit change.
Here's an idea. Take the scaled function: g(x, y; k) = log( exp(kx) + exp(ky) ) / k
Let k be 1/max(x,y) so that you have:
g(x,y) = log(exp(1)+exp(min(x,y)/max(x,y))*max(x,y)
There are some issues if the maximum value can be negative or zero, though.