Humans can certainly be self improving, both on an individual basis and in aggregate.

In humans, it seems that improvement in a new domain seems to follow a logarithmic scale.

Why wouldn’t this be the same for an AI?

Humans are, each individually and aggregates collectively, self-improving systems.

Much moreso than modern AI systems are.

Why are human doctors non-self improving?

If anything, using AI, they may improve more than before.

Please show me this self improving AI.

Currently that self-improving system isn’t so self-improving that it’s become better at any particular job than human beings, so I think the skepticism is warranted.