Technology tends to grow with a sigmoid curve. Extremely fast growth at the start, and then it slows down and eventually plateaus and new technology repeats the cycle. The only question is where on the curve are we for LLMs and AI in general?

I see this sigmoid growth prediction quite often. What is the basis for assuming it will follow this shape? What are some examples of this happening?

But interest and investment is also increasing exponentially. I've never really seen anything like this before in AI land, even when GANs and such were doing amazing things.

We have seen this level of rapid development and massive hype in AI before. Several times, in fact. Check it: https://en.wikipedia.org/wiki/AI_winter