“Recursive” is a reasonable term because the generation N AIs will train the Generation N+1 AIs. The term “iterative” doesn’t reflect this nuance as well IMO.

Recursion reduces each step toward a base case: each step is defined in terms of previous/simpler steps, not more advanced ones. The "recursive" in "recursive self improvement" has things precisely backward. Iteration correctly describes a process where each step is the starting point of its successive step, so it should be "iterative self improvement" but I guess that didn't sound as cool.

I think you’re conflating the direction of definition with the direction of evaluation.

Compare the similarity of:

  AI(n) = improve(AI(n-1))
With:

  Fib(n) = Fib(n-1) + Fib(n-2)
The latter is a classic example of recursion. So why isn’t the former?

Edit: formatting

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It's not a nuance, it's a sequence.

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