>At infinite cycles, without new input, you'll end up with a locked state or oscillations.
I don't think that's true; there are computations that take infinite steps but never converge or repeat, like the mandelbrot set.
Looping for millions or billions of steps is absolutely normal in traditional algorithms. We know from complexity theory that some computations require a minimum number of steps. More depth is just more room for computation.
Sure, but I don't think that's related to what you're implying, which is that, correct me if I'm wrong, the same number of weight should be able to hold many orders of magnitude more information by being reused.
These are not deterministic functions or systems that have infinite precision. See the "should I drive or walk my car to the car wash", or any of the other logic riddle problems, for examples of a statistical attractors.
I don't think that's true; there are computations that take infinite steps but never converge or repeat, like the mandelbrot set.
Looping for millions or billions of steps is absolutely normal in traditional algorithms. We know from complexity theory that some computations require a minimum number of steps. More depth is just more room for computation.