I think the problematic assumption is that one doubling of CoT tokens amounts to one doubling in the time horizon
I’m not assuming that; I point out the contradiction this leads to in my comment above. The biggest problem with this is that there’s a finite time horizon with unlimited CoT.
My claim is that intuitively, I’d expect that doubling the looping or the number of layers is more similar to doubling the number of CoT tokens than to doubling the time horizon.
Perhaps confusingly, when I said “8 doublings in no-CoT serial reasoning ability,” I meant “whatever vague notion of serial reasoning ability we’re increasing with looping,” not time horizon.
I’m not assuming that; I point out the contradiction this leads to in my comment above. The biggest problem with this is that there’s a finite time horizon with unlimited CoT.
My claim is that intuitively, I’d expect that doubling the looping or the number of layers is more similar to doubling the number of CoT tokens than to doubling the time horizon.
Perhaps confusingly, when I said “8 doublings in no-CoT serial reasoning ability,” I meant “whatever vague notion of serial reasoning ability we’re increasing with looping,” not time horizon.