I absolutely do find infuriating when math is written down vaguely/confusingly/poorly, and ML papers are a great example of this happening way too often. BUT,

I absolutely do find infuriating when math is written down vaguely/confusingly/poorly, and ML papers are a great example of this happening way too often. BUT, for your specific examples (in case that is an actual question): The first one can be parsed using the fact that y_i in the second term wouldn't make sense if it was outside the summation, since the i index is only defined inside The second (and actually, the first one, too) uses the very well established convention that multiplication always has precedence over summation, in every kind of expression. So the 2 multiplies the second sigma, and then the product is summed to the first sigma. This rule should make a lot of cases much clearer.