The higher-order analogue of a graph is called a hypergraph, and instead of edges, it has “hyperedges.” Purvine and her colleagues analyzed a database of biological responses to viral infections, using hypergraphs to identify the most critical genes involved. They also showed how those interactions would have been missed by the usual pairwise analysis afforded by graph theory. However, generalizing from graphs to hypergraphs quickly gets complicated. There are lots of ways of generalizing this notion of a cut to a hypergraph. But there’s no one clear solution, because a hyperedge could be severed various ways, creating new groups of nodes.

2023-04-13: Another powerful concept only very vaguely related are Hypervectors (though this Github project seems to allow you to play with both)

Hyperdimensional computing promises a new world in which computing is efficient and robust, and machine-made decisions are entirely transparent.
Hyperdimensional computing tolerates errors better, because even if a hypervector suffers significant numbers of random bit flips, it is still close to the original vector. Another advantage of hyperdimensional computing is transparency: The algebra clearly tells you why the system chose the answer it did. The same is not true for traditional neural networks. It’s also compatible with “in-memory computing systems,” which perform the computing on the same hardware that stores data (unlike existing von Neumann computers that inefficiently shuttle data between memory and the central processing unit). Some of these new devices can be analog, operating at very low voltages, making them energy-efficient but also prone to random noise. For von Neumann computing, this randomness is “the wall that you can’t go beyond”. But with hyperdimensional computing, “you can just punch through it.”

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