Network 1 would work just fine (ignoring how you’d go about training such a thing). Each of the N^2 edges has a weight expressing the relationship of the vertices it connects. E.g. if nodes A and B are strongly anti-correlated the weight between them might be −1. You then fix the nodes you know and then either solve the system analytically or through numerical iteration until it settles down (hopefully!) and then you have expectations for all the unknown.
Typical networks for this sort of thing don’t have cycles so stability isn’t a question, but that doesn’t mean that networks with cycles can’t work and reach stable solutions. Some error correcting codes have graph representations that aren’t much better than this. :)
Network 1 would work just fine (ignoring how you’d go about training such a thing). Each of the N^2 edges has a weight expressing the relationship of the vertices it connects. E.g. if nodes A and B are strongly anti-correlated the weight between them might be −1. You then fix the nodes you know and then either solve the system analytically or through numerical iteration until it settles down (hopefully!) and then you have expectations for all the unknown.
Typical networks for this sort of thing don’t have cycles so stability isn’t a question, but that doesn’t mean that networks with cycles can’t work and reach stable solutions. Some error correcting codes have graph representations that aren’t much better than this. :)