Comment by sigmoid10
9 hours ago
The point is that the case T=0 doesn't just "exist" as a special code branch - it is still well defined mathematically without any change to the output function. What the above comment refers to with the extra "if" check is just a limitation of computers not liking to divide anything by zero, even if the actual function exists and is well behaved at zero. It is not some weird or special theoretical construction.
Floating point defines n/0 the same as math. It's infinity as long as n isn't zero.
In almost all forms of math, the value n/0 is undefined. It's definitely not infinity, for two reasons - depending on the value of n, it can be negative; and neither info nor -inf are numbers, so they can't be the result of an equation (unless you look at transfinite equations).
What you can do in math is talk about the limit of a series of fractions as the denominator approaches 0, and that's where you get some relation to infinity or -infinity. But the limit can also be any other number, if the numerator also gets closer to 0; or it can not exist, if the function oscillates.
I explicitly didn't say "infinity or negative infinity" because I didn't think that level of pedantry would be needed here on HN. I guess I was wrong.
3 replies →
> as long as n isn't zero
Which is the case with softmax function, as for T=0 you end up with a fraction that either becomes 0/0 or inf/inf [0]. So you do need branching as floating point arithmetic is not gonna get you there.
[0] except for weights that are exactly 0
edit: thinking more about it, one could always express the softmax formula in ways that this could work with floating point arithmetic but it would be very inefficient and sort of pointless