Although a neat thought, are the number of papers on ArXiv really something worth comparing to Moore's law? Like at that point, what can't you compare to Moore's law...
IMHO, the two are incomparable. The exponential growth rate of Moore's Law was driven largely by a linear rate of shrinkage in 2D, which drove up clock rates geometrically as microarchitecture component distances shrank two-fold (until CMOS' heat finally fought back). ML has no similar geometric driven basis that will continue to drive its rate of growth superlinear.
I suspect this plot is Dean's way of paying homage to Patterson, since he and Hennessy were famous for similar plots describing CPU performance in their two architecture textbooks.
I suspect that only a minority of ML PhD graduates stay in academia. So even though the growth is exponential, it's probably much closer to 1 than to the student:professor ratio.
Even more, an exponent increase in the number of papers on a subject might mean something but it could easily mean something other than the optimistic scenario.
