These scaling laws are even funnier than that, as are more recent ones.

I continue to be extremely amused by the fact that you can take a LLM 'reasoning' trace, replace all the 'reasoning' with dashes or spaces, re-run the attention mechanism, and have what comes out the other end improve by a significant fraction as much as if you let it exude text that has the appearance of having to do with the topic at hand. It's just more opportunity for the embedding vectors to dance against each other before you translate the abstract vectors back into natural language. Hence recent frontier models doing a thing where instead of doing a long reasoning trace, they build the attention matrix, allow the vectors to push each other around... then let those new vectors push each other around again, and again, and again, multiple rounds, before you start decoding.

More recently, I have seen some vague math into the scaling of the speed with which running many parallel systems with access to a common pool of text produce a legible result. If I recall, it comes to roughly:

N parallel systems

Finish in ~1/N^0.5 as much time

At ~N^0.5x the cost

So 16 parallel systems crosstalking finish complex tasks in 1/4 the time at 4x the cost (and 16x the instantaneous rate of operation per second)