> But a machine learning researcher might want to double the precision of an experiment. In that case, the new result implies that they might have to quadruple

> But a machine learning researcher might want to double the precision of an experiment. In that case, the new result implies that they might have to quadruple the running time of their gradient descent algorithm. > But for other applications, like in numerical analysis, researchers might need to square their precision. To achieve such an improvement, they might have to square the running time of gradient descent I don't quite understand this. Say f(p) is the complexity of gradient descent for precision p. The first paragraph seems to imply that f(p) = c×p^2, so that f(2p) = c×4×p^2 = f(p). However, the second paragraph then just seems to imply that f(p) = c×p. Am I missing something? Incidentally, I love that Quanta brings attention to work mostly just on the basis of how important it is. 99% of the other stuff you hear about new research is really just driven by PR departments at the researcher's home institutions.