Deeper independent, sure. Deeper shared though? Information and signal theory still apply here. At infinite cycles, without new input, you'll end up with a locked state or oscillations. Some point before that, any "attractors" in the latent space, with slightly higher statistics, will pull things towards a space that might eventually be only loosely related to the goal, because each loop would be lossy, right?

>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.