Presumably, the number of 'possible' states of the universe is the exact same as the number 'possible' alternate universes. (Edit: unless you are using two different meanings of 'possible')

The question of convergence then simply boils down to: Are there any possible states of the universe that can arise from more than one prior state. Based on my limited quantum mechanics knowledge, it seems the only place this might be able to happen is in black holes: https://en.wikipedia.org/wiki/Black_hole_information_paradox

Think larger scale. Mass extinctions should do the trick.

I guess it would work if there is some kind of force that leads some timelines to go out of existence or converge back towards heavier nodes, something like a neural network structure.

I've always enjoyed the thought that there are multiple universes, and there are two opposing forces at play. Chaos causes the universes to drift over time. Another stabilizing force tends to bring them back together in the most efficient way possible. This stabilizing force is felt by us as experiences of fate, or a sense (or lack) of belonging. It's not that there's a preordained destiny, but a consensus among universes that you are either in or out of.

Have had very much the same thought myself.

If there were two opposing forces, always exponentially self improving towards maximum efficiency in two opposite sides: 1) ordered/creative/perfectionist/preservative/etc, 2) chaotic/destructive/disruptive/etc... suppose our universe sits roughly in the middle of these two, does that not seem to explain where we are?

Also, given the seemingly limitless propensity of the universe towards balance, and its apparently limitless capacity in both regards, it would seem natural to infer that both forces keep going in ways beyond that which we can directly observe.

Intuitively, certainly, it seems very right. Of course, it also gels very well with countless esoteric/mystical beliefs going back eons as well.

Temporal backpropagation?

The Hylean flow.

Sounds like something LeCun would say..."I actually invented time as a special case of a deep network back in 19xx...."