The article was possibly aimed at engineers or mathematicians so the author thought the benefits didn't need explaining.<p>A soft maximum might be useful if you want a differentiable function that closely approximates the max() function. By differentiable I mean you can work out the rate of change of the function at any point. With the hard maximum, the rate of change at the hard edge is not defined. Nicer to have one function to represent the RoC and not have to worry about special cases.