Can you show the world this can be made to work for, say, a toy benchmark like MNIST classification?

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To be 100% clear: My question about practical application today is orthogonal to the question about whether this research is worth pursuing!

(Multidirectional) biological neural networks are no longer superior in MNIST benchmark ... but e.g. consciousness, or being able to learn from single examples.

And no, recreating it is not a task a single person can complete.

Alright. I've added you preprint to my reading list, so I can take a closer look at this.

Just represent joint density for each neuron as a linear combination - then you can inexpensively propagate in both directions e.g. as E[X|Y,Z] or E[Y,Z|X] by substituting and normalizing ... the formulas turn out quite simple - could be hidden in dynamics of (bidirectional) biological NN ...

And for pairwise distribution becomes ~KAN, which turned out quit successful ... so we are talking about its extension: adding more possibilities, like triplewise dependencies and multidirectional propagation.