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So im writing my own implementation of NEAT and i'm wondering how looped networks (like one shown in the image) can be useful. I'll probably implement them anyway because i want to fiddle around with as much features and improvements as i possibly can, but i just cant wrap my head around where they can be applied. What are the possible tasks that cant be solved (or are less likely to be solved) without looped networks?

NOTES just in case:

I'm not talking about networks that pass info from the previous timestep output like those that allow to solve e.g. double pole balancing without velocity info. (Or are they the same thing? Haven't really figured it out, but either way, question implies that networks like that are treated as a special case. Hopefully this remark makes any kind of sense)

Also i know how both looped and feed-forward networks are activated and i have algorithm in place to identify and separate both of them, im not asking about that.

Also, when i say "activating" the looped network, i mean algorithm like sharpNEAT has in place: https://github.com/colgreen/sharpneat/tree/master/src/SharpNeatLib/Phenomes/NeuralNets/CyclicNetwork

enter image description here

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