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Jules Tsukahara (Nov 08 2022 at 21:11):Very broad question but, does there exist a category theoretic approach to machine learning algorithms on multigraphs?
Andrew Dudzik (Nov 09 2022 at 10:37):I'm not aware of much existing work—simple graphs are more common—but the main results of Graph Neural Networks are Dynamic Programmers are valid for multigraphs. (they even apply to some hypergraphs, those where edges have one receiver but multiple senders)
Multigraphs are much more natural, categorically, speaking, than simple graphs. A multigraph is exactly a span from a set to itself, and spans are a fundamental concept.
Bruno Gavranović (Nov 09 2022 at 11:50):There's also the paper of mine Learning Functors using Gradient Descent that works on multigraphs.
This is from the categorical side. I'd expect there to be many papers in the machine learning community doing various things with multigrpahs.