I don't think this is correct, "active parameters" is quite unambiguous in that it means a sum of all active experts plus shared parameters.

looks like they meant “effective dense size” which is the square root of total params×active params, so in this case sqrt(397 x 17) = ~82

But the claim that "one expert is 17B" is incorrect. Experts are picked with per-layer granularity (expert 1 for layer X may well be entirely unrelated to expert 1 for layer Y), and the individual layer-experts are tiny. The writeup for the original experiment is very clear on this.

Ok I am by no means an expert on this and I immediately stand corrected. But as I understand it, in order to understand the amount of active memory that’s required, it’s more accurate to go by the ~82B number, right?

The ~82B figure is an attempt to compare performance to an equivalent dense model. The amount of active parameters is given by the ~17B.